lst:=[[cos(d*x+c)^2*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,7,1/8*a*(4*A+3*C)*x+1/5*a*(5*A+4*C)*sin(d*x+c)/d+1/8*a*(4*A+3*C)*cos(d*x+c)*sin(d*x+c)/d+1/4*a*C*cos(d*x+c)^3*sin(d*x+c)/d+1/5*a*C*cos(d*x+c)^4*sin(d*x+c)/d-1/15*a*(5*A+4*C)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,3,1/8*a*(4*A+3*C)*x+1/3*a*(3*A+2*C)*sin(d*x+c)/d+1/8*a*(4*A+3*C)*cos(d*x+c)*sin(d*x+c)/d+1/3*a*C*cos(d*x+c)^2*sin(d*x+c)/d+1/4*a*C*cos(d*x+c)^3*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,2,1/2*a*(2*A+C)*x+1/3*a*(3*A+C)*sin(d*x+c)/d-1/6*a*C*cos(d*x+c)*sin(d*x+c)/d+1/3*C*(a+a*cos(d*x+c))^2*sin(d*x+c)/a/d,1],
[(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c),x,4,1/2*a*(2*A+C)*x+a*A*arctanh(sin(d*x+c))/d+a*C*sin(d*x+c)/d+1/2*a*C*cos(d*x+c)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,4,a*C*x+a*A*arctanh(sin(d*x+c))/d+a*C*sin(d*x+c)/d+a*A*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,4,a*C*x+1/2*a*(A+2*C)*arctanh(sin(d*x+c))/d+a*A*tan(d*x+c)/d+1/2*a*A*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,6,1/2*a*(A+2*C)*arctanh(sin(d*x+c))/d+1/3*a*(2*A+3*C)*tan(d*x+c)/d+1/2*a*A*sec(d*x+c)*tan(d*x+c)/d+1/3*a*A*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,7,1/8*a*(3*A+4*C)*arctanh(sin(d*x+c))/d+1/3*a*(2*A+3*C)*tan(d*x+c)/d+1/8*a*(3*A+4*C)*sec(d*x+c)*tan(d*x+c)/d+1/3*a*A*sec(d*x+c)^2*tan(d*x+c)/d+1/4*a*A*sec(d*x+c)^3*tan(d*x+c)/d,1],
[cos(d*x+c)^2*(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x,9,1/16*a^2*(14*A+11*C)*x+2/5*a^2*(5*A+4*C)*sin(d*x+c)/d+1/16*a^2*(14*A+11*C)*cos(d*x+c)*sin(d*x+c)/d+1/40*a^2*(10*A+9*C)*cos(d*x+c)^3*sin(d*x+c)/d+1/6*C*cos(d*x+c)^3*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+1/15*C*cos(d*x+c)^3*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d-2/15*a^2*(5*A+4*C)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x,5,1/4*a^2*(4*A+3*C)*x+1/3*a^2*(4*A+3*C)*sin(d*x+c)/d+1/12*a^2*(4*A+3*C)*cos(d*x+c)*sin(d*x+c)/d+1/30*(10*A+3*C)*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+1/5*C*cos(d*x+c)^2*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+1/10*C*(a+a*cos(d*x+c))^3*sin(d*x+c)/a/d,1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x,3,1/8*a^2*(12*A+7*C)*x+1/6*a^2*(12*A+7*C)*sin(d*x+c)/d+1/24*a^2*(12*A+7*C)*cos(d*x+c)*sin(d*x+c)/d-1/12*C*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+1/4*C*(a+a*cos(d*x+c))^3*sin(d*x+c)/a/d,1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c),x,6,a^2*(2*A+C)*x+a^2*A*arctanh(sin(d*x+c))/d+a^2*(A+C)*sin(d*x+c)/d+1/3*C*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+1/3*C*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,6,1/2*a^2*(2*A+3*C)*x+2*a^2*A*arctanh(sin(d*x+c))/d-1/2*a^2*(2*A-3*C)*sin(d*x+c)/d-1/2*(2*A-C)*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d+A*(a+a*cos(d*x+c))^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,6,2*a^2*C*x+1/2*a^2*(3*A+2*C)*arctanh(sin(d*x+c))/d-1/2*a^2*(3*A-2*C)*sin(d*x+c)/d+A*(a^2+a^2*cos(d*x+c))*tan(d*x+c)/d+1/2*A*(a+a*cos(d*x+c))^2*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,6,a^2*C*x+a^2*(A+2*C)*arctanh(sin(d*x+c))/d+a^2*(A+C)*tan(d*x+c)/d+1/3*A*(a^2+a^2*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(a+a*cos(d*x+c))^2*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,8,1/8*a^2*(7*A+12*C)*arctanh(sin(d*x+c))/d+2/3*a^2*(2*A+3*C)*tan(d*x+c)/d+1/24*a^2*(11*A+12*C)*sec(d*x+c)*tan(d*x+c)/d+1/6*A*(a^2+a^2*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a+a*cos(d*x+c))^2*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,9,1/4*a^2*(3*A+4*C)*arctanh(sin(d*x+c))/d+1/15*a^2*(18*A+25*C)*tan(d*x+c)/d+1/4*a^2*(3*A+4*C)*sec(d*x+c)*tan(d*x+c)/d+1/30*a^2*(9*A+10*C)*sec(d*x+c)^2*tan(d*x+c)/d+1/10*A*(a^2+a^2*cos(d*x+c))*sec(d*x+c)^3*tan(d*x+c)/d+1/5*A*(a+a*cos(d*x+c))^2*sec(d*x+c)^4*tan(d*x+c)/d,1],
[cos(d*x+c)^2*(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x,10,1/16*a^3*(26*A+21*C)*x+1/35*a^3*(133*A+108*C)*sin(d*x+c)/d+1/16*a^3*(26*A+21*C)*cos(d*x+c)*sin(d*x+c)/d+1/280*a^3*(154*A+129*C)*cos(d*x+c)^3*sin(d*x+c)/d+1/7*C*cos(d*x+c)^3*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+1/14*C*cos(d*x+c)^3*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d+1/5*(A+C)*cos(d*x+c)^3*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d-1/105*a^3*(133*A+108*C)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x,11,1/16*a^3*(30*A+23*C)*x+1/10*a^3*(30*A+23*C)*sin(d*x+c)/d+3/80*a^3*(30*A+23*C)*cos(d*x+c)*sin(d*x+c)/d+1/120*(30*A+7*C)*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+1/6*C*cos(d*x+c)^2*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+1/10*C*(a+a*cos(d*x+c))^4*sin(d*x+c)/a/d-1/120*a^3*(30*A+23*C)*sin(d*x+c)^3/d,1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x,9,1/8*a^3*(20*A+13*C)*x+1/5*a^3*(20*A+13*C)*sin(d*x+c)/d+3/40*a^3*(20*A+13*C)*cos(d*x+c)*sin(d*x+c)/d-1/20*C*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+1/5*C*(a+a*cos(d*x+c))^4*sin(d*x+c)/a/d-1/60*a^3*(20*A+13*C)*sin(d*x+c)^3/d,1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c),x,7,1/8*a^3*(28*A+15*C)*x+a^3*A*arctanh(sin(d*x+c))/d+5/8*a^3*(4*A+3*C)*sin(d*x+c)/d+1/4*C*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+1/4*C*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d+1/8*(4*A+5*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,7,1/2*a^3*(6*A+5*C)*x+3*a^3*A*arctanh(sin(d*x+c))/d+5/2*a^3*C*sin(d*x+c)/d-1/3*(3*A-C)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d-1/6*(6*A-5*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d+A*(a+a*cos(d*x+c))^3*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,7,1/2*a^3*(2*A+7*C)*x+1/2*a^3*(7*A+2*C)*arctanh(sin(d*x+c))/d-5/2*a^3*(A-C)*sin(d*x+c)/d-1/2*(4*A-C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d+3/2*A*(a^2+a^2*cos(d*x+c))^2*tan(d*x+c)/a/d+1/2*A*(a+a*cos(d*x+c))^3*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,7,3*a^3*C*x+1/2*a^3*(5*A+6*C)*arctanh(sin(d*x+c))/d-5/2*a^3*A*sin(d*x+c)/d+1/3*(5*A+3*C)*(a^3+a^3*cos(d*x+c))*tan(d*x+c)/d+1/2*A*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)*tan(d*x+c)/a/d+1/3*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,7,a^3*C*x+1/8*a^3*(15*A+28*C)*arctanh(sin(d*x+c))/d+5/8*a^3*(3*A+4*C)*tan(d*x+c)/d+1/8*(5*A+4*C)*(a^3+a^3*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/4*A*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^2*tan(d*x+c)/a/d+1/4*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,9,1/8*a^3*(13*A+20*C)*arctanh(sin(d*x+c))/d+1/15*a^3*(38*A+55*C)*tan(d*x+c)/d+1/120*a^3*(109*A+140*C)*sec(d*x+c)*tan(d*x+c)/d+1/30*(11*A+10*C)*(a^3+a^3*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d+3/20*A*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^3*tan(d*x+c)/a/d+1/5*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^4*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,x,10,1/16*a^3*(23*A+30*C)*arctanh(sin(d*x+c))/d+1/15*a^3*(34*A+45*C)*tan(d*x+c)/d+1/16*a^3*(23*A+30*C)*sec(d*x+c)*tan(d*x+c)/d+1/120*a^3*(73*A+90*C)*sec(d*x+c)^2*tan(d*x+c)/d+1/120*(31*A+30*C)*(a^3+a^3*cos(d*x+c))*sec(d*x+c)^3*tan(d*x+c)/d+1/10*A*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^4*tan(d*x+c)/a/d+1/6*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^5*tan(d*x+c)/d,1],
[cos(d*x+c)^2*(a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x,11,1/128*a^4*(392*A+323*C)*x+4/35*a^4*(63*A+52*C)*sin(d*x+c)/d+1/128*a^4*(392*A+323*C)*cos(d*x+c)*sin(d*x+c)/d+1/2240*a^4*(2408*A+2007*C)*cos(d*x+c)^3*sin(d*x+c)/d+1/14*a*C*cos(d*x+c)^3*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+1/8*C*cos(d*x+c)^3*(a+a*cos(d*x+c))^4*sin(d*x+c)/d+1/336*(56*A+61*C)*cos(d*x+c)^3*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/d+7/120*(8*A+7*C)*cos(d*x+c)^3*(a^4+a^4*cos(d*x+c))*sin(d*x+c)/d-4/105*a^4*(63*A+52*C)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x,14,1/4*a^4*(14*A+11*C)*x+16/35*a^4*(14*A+11*C)*sin(d*x+c)/d+27/140*a^4*(14*A+11*C)*cos(d*x+c)*sin(d*x+c)/d+1/70*a^4*(14*A+11*C)*cos(d*x+c)^3*sin(d*x+c)/d+1/105*(21*A+4*C)*(a+a*cos(d*x+c))^4*sin(d*x+c)/d+1/7*C*cos(d*x+c)^2*(a+a*cos(d*x+c))^4*sin(d*x+c)/d+2/21*C*(a+a*cos(d*x+c))^5*sin(d*x+c)/a/d-8/105*a^4*(14*A+11*C)*sin(d*x+c)^3/d,1],
[(a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x,12,7/16*a^4*(10*A+7*C)*x+4/5*a^4*(10*A+7*C)*sin(d*x+c)/d+27/80*a^4*(10*A+7*C)*cos(d*x+c)*sin(d*x+c)/d+1/40*a^4*(10*A+7*C)*cos(d*x+c)^3*sin(d*x+c)/d-1/30*C*(a+a*cos(d*x+c))^4*sin(d*x+c)/d+1/6*C*(a+a*cos(d*x+c))^5*sin(d*x+c)/a/d-2/15*a^4*(10*A+7*C)*sin(d*x+c)^3/d,1],
[(a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c),x,8,1/2*a^4*(12*A+7*C)*x+a^4*A*arctanh(sin(d*x+c))/d+1/2*a^4*(10*A+7*C)*sin(d*x+c)/d+1/5*a*C*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+1/5*C*(a+a*cos(d*x+c))^4*sin(d*x+c)/d+1/15*(5*A+7*C)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/d+1/6*(8*A+7*C)*(a^4+a^4*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,8,1/8*a^4*(52*A+35*C)*x+4*a^4*A*arctanh(sin(d*x+c))/d+5/8*a^4*(4*A+7*C)*sin(d*x+c)/d-1/4*a*(4*A-C)*(a+a*cos(d*x+c))^3*sin(d*x+c)/d-1/12*(12*A-7*C)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/d-1/24*(12*A-35*C)*(a^4+a^4*cos(d*x+c))*sin(d*x+c)/d+A*(a+a*cos(d*x+c))^4*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,8,2*a^4*(2*A+3*C)*x+1/2*a^4*(13*A+2*C)*arctanh(sin(d*x+c))/d-5/2*a^4*(A-2*C)*sin(d*x+c)/d-1/6*(15*A-2*C)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/d-1/3*(9*A-4*C)*(a^4+a^4*cos(d*x+c))*sin(d*x+c)/d+2*a*A*(a+a*cos(d*x+c))^3*tan(d*x+c)/d+1/2*A*(a+a*cos(d*x+c))^4*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,8,1/2*a^4*(2*A+13*C)*x+2*a^4*(3*A+2*C)*arctanh(sin(d*x+c))/d-5/2*a^4*(2*A-C)*sin(d*x+c)/d-1/6*(22*A+3*C)*(a^4+a^4*cos(d*x+c))*sin(d*x+c)/d+1/3*(8*A+3*C)*(a^2+a^2*cos(d*x+c))^2*tan(d*x+c)/d+2/3*a*A*(a+a*cos(d*x+c))^3*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(a+a*cos(d*x+c))^4*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,8,4*a^4*C*x+1/8*a^4*(35*A+52*C)*arctanh(sin(d*x+c))/d-5/8*a^4*(7*A+4*C)*sin(d*x+c)/d+1/12*(35*A+36*C)*(a^4+a^4*cos(d*x+c))*tan(d*x+c)/d+1/8*(7*A+4*C)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)*tan(d*x+c)/d+1/3*a*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a+a*cos(d*x+c))^4*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,8,a^4*C*x+1/2*a^4*(7*A+12*C)*arctanh(sin(d*x+c))/d+1/2*a^4*(7*A+10*C)*tan(d*x+c)/d+1/6*(7*A+8*C)*(a^4+a^4*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/15*(7*A+5*C)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^2*tan(d*x+c)/d+1/5*a*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^3*tan(d*x+c)/d+1/5*A*(a+a*cos(d*x+c))^4*sec(d*x+c)^4*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,x,10,7/16*a^4*(7*A+10*C)*arctanh(sin(d*x+c))/d+4/15*a^4*(18*A+25*C)*tan(d*x+c)/d+1/240*a^4*(417*A+550*C)*sec(d*x+c)*tan(d*x+c)/d+1/60*(43*A+50*C)*(a^4+a^4*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d+1/120*(37*A+30*C)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^3*tan(d*x+c)/d+2/15*a*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^4*tan(d*x+c)/d+1/6*A*(a+a*cos(d*x+c))^4*sec(d*x+c)^5*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^8,x,11,1/4*a^4*(11*A+14*C)*arctanh(sin(d*x+c))/d+1/105*a^4*(454*A+581*C)*tan(d*x+c)/d+1/4*a^4*(11*A+14*C)*sec(d*x+c)*tan(d*x+c)/d+1/210*a^4*(247*A+308*C)*sec(d*x+c)^2*tan(d*x+c)/d+1/210*(109*A+126*C)*(a^4+a^4*cos(d*x+c))*sec(d*x+c)^3*tan(d*x+c)/d+1/35*(8*A+7*C)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^4*tan(d*x+c)/d+2/21*a*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^5*tan(d*x+c)/d+1/7*A*(a+a*cos(d*x+c))^4*sec(d*x+c)^6*tan(d*x+c)/d,1],
[cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x,7,3/8*(4*A+5*C)*x/a-(3*A+4*C)*sin(d*x+c)/a/d+3/8*(4*A+5*C)*cos(d*x+c)*sin(d*x+c)/a/d+1/4*(4*A+5*C)*cos(d*x+c)^3*sin(d*x+c)/a/d-(A+C)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))+1/3*(3*A+4*C)*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x,6,-1/2*(2*A+3*C)*x/a+(3*A+4*C)*sin(d*x+c)/a/d-1/2*(2*A+3*C)*cos(d*x+c)*sin(d*x+c)/a/d-(A+C)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))-1/3*(3*A+4*C)*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x,2,1/2*(2*A+3*C)*x/a-(A+2*C)*sin(d*x+c)/a/d+1/2*(2*A+3*C)*cos(d*x+c)*sin(d*x+c)/a/d-(A+C)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x,3,-C*x/a+C*sin(d*x+c)/a/d+(A+C)*sin(d*x+c)/a/d/(1+cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c)),x,3,C*x/a+A*arctanh(sin(d*x+c))/a/d-(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c)),x,5,-A*arctanh(sin(d*x+c))/a/d+(2*A+C)*tan(d*x+c)/a/d-(A+C)*tan(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c)),x,6,1/2*(3*A+2*C)*arctanh(sin(d*x+c))/a/d-(2*A+C)*tan(d*x+c)/a/d+1/2*(3*A+2*C)*sec(d*x+c)*tan(d*x+c)/a/d-(A+C)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c)),x,6,-1/2*(3*A+2*C)*arctanh(sin(d*x+c))/a/d+(4*A+3*C)*tan(d*x+c)/a/d-1/2*(3*A+2*C)*sec(d*x+c)*tan(d*x+c)/a/d-(A+C)*sec(d*x+c)^2*tan(d*x+c)/d/(a+a*cos(d*x+c))+1/3*(4*A+3*C)*tan(d*x+c)^3/a/d,1],
[cos(d*x+c)^4*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,8,1/8*(28*A+55*C)*x/a^2-8*(A+2*C)*sin(d*x+c)/a^2/d+1/8*(28*A+55*C)*cos(d*x+c)*sin(d*x+c)/a^2/d+1/12*(28*A+55*C)*cos(d*x+c)^3*sin(d*x+c)/a^2/d-2*(A+2*C)*cos(d*x+c)^4*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A+C)*cos(d*x+c)^5*sin(d*x+c)/d/(a+a*cos(d*x+c))^2+8/3*(A+2*C)*sin(d*x+c)^3/a^2/d,1],
[cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,7,-(2*A+5*C)*x/a^2+(5*A+12*C)*sin(d*x+c)/a^2/d-(2*A+5*C)*cos(d*x+c)*sin(d*x+c)/a^2/d-2/3*(2*A+5*C)*cos(d*x+c)^3*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A+C)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))^2-1/3*(5*A+12*C)*sin(d*x+c)^3/a^2/d,1],
[cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,3,1/2*(2*A+7*C)*x/a^2-4/3*(A+4*C)*sin(d*x+c)/a^2/d+1/2*(2*A+7*C)*cos(d*x+c)*sin(d*x+c)/a^2/d-2/3*(A+4*C)*cos(d*x+c)^2*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A+C)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,6,-2*C*x/a^2+1/3*(A+4*C)*sin(d*x+c)/a^2/d+2*C*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A+C)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,3,C*x/a^2+1/3*(A-5*C)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))+1/3*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^2,x,4,A*arctanh(sin(d*x+c))/a^2/d-2/3*(2*A-C)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^2,x,6,-2*A*arctanh(sin(d*x+c))/a^2/d+1/3*(10*A+C)*tan(d*x+c)/a^2/d-2*A*tan(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A+C)*tan(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x,7,1/2*(7*A+2*C)*arctanh(sin(d*x+c))/a^2/d-4/3*(4*A+C)*tan(d*x+c)/a^2/d+1/2*(7*A+2*C)*sec(d*x+c)*tan(d*x+c)/a^2/d-2/3*(4*A+C)*sec(d*x+c)*tan(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A+C)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x,7,-(5*A+2*C)*arctanh(sin(d*x+c))/a^2/d+(12*A+5*C)*tan(d*x+c)/a^2/d-(5*A+2*C)*sec(d*x+c)*tan(d*x+c)/a^2/d-2/3*(5*A+2*C)*sec(d*x+c)^2*tan(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A+C)*sec(d*x+c)^2*tan(d*x+c)/d/(a+a*cos(d*x+c))^2+1/3*(12*A+5*C)*tan(d*x+c)^3/a^2/d,1],
[cos(d*x+c)^4*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,8,-1/2*(6*A+23*C)*x/a^3+4/5*(9*A+34*C)*sin(d*x+c)/a^3/d-1/2*(6*A+23*C)*cos(d*x+c)*sin(d*x+c)/a^3/d-1/5*(A+C)*cos(d*x+c)^5*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(3*A+13*C)*cos(d*x+c)^4*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/3*(6*A+23*C)*cos(d*x+c)^3*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c))-4/15*(9*A+34*C)*sin(d*x+c)^3/a^3/d,1],
[cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,4,1/2*(2*A+13*C)*x/a^3-2/15*(11*A+76*C)*sin(d*x+c)/a^3/d+1/2*(2*A+13*C)*cos(d*x+c)*sin(d*x+c)/a^3/d-1/5*(A+C)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(A+11*C)*cos(d*x+c)^3*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/15*(11*A+76*C)*cos(d*x+c)^2*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,7,-3*C*x/a^3+1/15*(2*A+27*C)*sin(d*x+c)/a^3/d-1/5*(A+C)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/15*(A-9*C)*cos(d*x+c)^2*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+3*C*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,5,C*x/a^3-1/5*(A+C)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(3*A-7*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+1/15*(6*A-29*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,3,1/5*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+2/15*(A-4*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+1/15*(2*A+7*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^3,x,5,A*arctanh(sin(d*x+c))/a^3/d-1/5*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(7*A-3*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/15*(22*A-3*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^3,x,7,-3*A*arctanh(sin(d*x+c))/a^3/d+2/15*(36*A+C)*tan(d*x+c)/a^3/d-1/5*(A+C)*tan(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(9*A-C)*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^2-3*A*tan(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^3,x,8,1/2*(13*A+2*C)*arctanh(sin(d*x+c))/a^3/d-2/15*(76*A+11*C)*tan(d*x+c)/a^3/d+1/2*(13*A+2*C)*sec(d*x+c)*tan(d*x+c)/a^3/d-1/5*(A+C)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(11*A+C)*sec(d*x+c)*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/15*(76*A+11*C)*sec(d*x+c)*tan(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^3,x,8,-1/2*(23*A+6*C)*arctanh(sin(d*x+c))/a^3/d+4/5*(34*A+9*C)*tan(d*x+c)/a^3/d-1/2*(23*A+6*C)*sec(d*x+c)*tan(d*x+c)/a^3/d-1/5*(A+C)*sec(d*x+c)^2*tan(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(13*A+3*C)*sec(d*x+c)^2*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/3*(23*A+6*C)*sec(d*x+c)^2*tan(d*x+c)/d/(a^3+a^3*cos(d*x+c))+4/15*(34*A+9*C)*tan(d*x+c)^3/a^3/d,1],
[cos(d*x+c)^4*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x,5,1/2*(2*A+21*C)*x/a^4-32/105*(5*A+54*C)*sin(d*x+c)/a^4/d+1/2*(2*A+21*C)*cos(d*x+c)*sin(d*x+c)/a^4/d-1/105*(10*A+129*C)*cos(d*x+c)^3*sin(d*x+c)/a^4/d/(1+cos(d*x+c))^2-16/105*(5*A+54*C)*cos(d*x+c)^2*sin(d*x+c)/a^4/d/(1+cos(d*x+c))-1/7*(A+C)*cos(d*x+c)^5*sin(d*x+c)/d/(a+a*cos(d*x+c))^4-2/5*C*cos(d*x+c)^4*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^3,1],
[cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x,8,-4*C*x/a^4+2/105*(3*A+122*C)*sin(d*x+c)/a^4/d+1/105*(3*A-88*C)*cos(d*x+c)^2*sin(d*x+c)/a^4/d/(1+cos(d*x+c))^2+4*C*sin(d*x+c)/a^4/d/(1+cos(d*x+c))-1/7*(A+C)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))^4+2/35*(A-6*C)*cos(d*x+c)^3*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^3,1],
[cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x,6,C*x/a^4-1/105*(8*A-55*C)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))^2+1/105*(16*A-215*C)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))-1/7*(A+C)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))^4+2/35*(2*A-5*C)*cos(d*x+c)^2*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^3,1],
[cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x,5,1/105*(23*A-54*C)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))^2+4/105*(2*A+9*C)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))-1/7*(A+C)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c))^4-2/35*(3*A-4*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^3,1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x,4,1/7*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^4+1/35*(3*A-11*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^3+1/105*(6*A+13*C)*sin(d*x+c)/d/(a^2+a^2*cos(d*x+c))^2+1/105*(6*A+13*C)*sin(d*x+c)/d/(a^4+a^4*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^4,x,6,A*arctanh(sin(d*x+c))/a^4/d-1/105*(55*A-8*C)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))^2-8/105*(20*A-C)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))-1/7*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^4-2/35*(5*A-2*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^3,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^4,x,8,-4*A*arctanh(sin(d*x+c))/a^4/d+2/105*(332*A+3*C)*tan(d*x+c)/a^4/d-1/105*(88*A-3*C)*tan(d*x+c)/a^4/d/(1+cos(d*x+c))^2-4*A*tan(d*x+c)/a^4/d/(1+cos(d*x+c))-1/7*(A+C)*tan(d*x+c)/d/(a+a*cos(d*x+c))^4-2/35*(6*A-C)*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^3,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^4,x,9,1/2*(21*A+2*C)*arctanh(sin(d*x+c))/a^4/d-32/105*(54*A+5*C)*tan(d*x+c)/a^4/d+1/2*(21*A+2*C)*sec(d*x+c)*tan(d*x+c)/a^4/d-1/105*(129*A+10*C)*sec(d*x+c)*tan(d*x+c)/a^4/d/(1+cos(d*x+c))^2-16/105*(54*A+5*C)*sec(d*x+c)*tan(d*x+c)/a^4/d/(1+cos(d*x+c))-1/7*(A+C)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c))^4-2/5*A*sec(d*x+c)*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^3,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^4,x,9,-2*(11*A+2*C)*arctanh(sin(d*x+c))/a^4/d+4/35*(454*A+83*C)*tan(d*x+c)/a^4/d-2*(11*A+2*C)*sec(d*x+c)*tan(d*x+c)/a^4/d-1/105*(178*A+31*C)*sec(d*x+c)^2*tan(d*x+c)/a^4/d/(1+cos(d*x+c))^2-4/3*(11*A+2*C)*sec(d*x+c)^2*tan(d*x+c)/a^4/d/(1+cos(d*x+c))-1/7*(A+C)*sec(d*x+c)^2*tan(d*x+c)/d/(a+a*cos(d*x+c))^4-2/35*(8*A+C)*sec(d*x+c)^2*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^3+4/105*(454*A+83*C)*tan(d*x+c)^3/a^4/d,1],
[cos(d*x+c)^3*sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,6,4/495*a*(99*A+80*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/693*a*(99*A+80*C)*cos(d*x+c)^3*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/99*a*C*cos(d*x+c)^4*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-8/3465*(99*A+80*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/11*C*cos(d*x+c)^4*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+4/1155*(99*A+80*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/a/d,1],
[cos(d*x+c)^2*sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,5,2/45*a*(21*A+16*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/63*a*C*cos(d*x+c)^3*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-4/315*(21*A+16*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/9*C*cos(d*x+c)^3*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/105*(21*A+16*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/a/d,1],
[cos(d*x+c)*sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,5,2/105*a*(35*A+27*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*(35*A+18*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/7*C*cos(d*x+c)^2*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/35*C*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/a/d,1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,3,2/15*a*(15*A+7*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-4/15*C*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/5*C*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/a/d,1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c),x,4,2*sqrt(a)*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+2/3*a*C*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/3*C*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,4,sqrt(a)*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-a*(A-2*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+A*sqrt(a+a*cos(d*x+c))*tan(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,4,1/4*sqrt(a)*(3*A+8*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/4*a*A*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/2*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,5,1/8*sqrt(a)*(5*A+8*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/8*a*(5*A+8*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/12*a*A*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/3*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,6,1/64*sqrt(a)*(35*A+48*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/64*a*(35*A+48*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/96*a*(35*A+48*C)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/24*a*A*sec(d*x+c)^2*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/4*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^3*tan(d*x+c)/d,1],
[cos(d*x+c)^2*(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x,6,2/165*a^2*(143*A+112*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/231*a^2*(33*A+28*C)*cos(d*x+c)^3*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-4/1155*a*(143*A+112*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/33*a*C*cos(d*x+c)^3*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/385*(143*A+112*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/11*C*cos(d*x+c)^3*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x,6,8/315*a^2*(63*A+47*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/315*a*(63*A+47*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/315*(63*A+22*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/9*C*cos(d*x+c)^2*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/21*C*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/a/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x,4,8/105*a^2*(35*A+19*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*a*(35*A+19*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d-4/35*C*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/7*C*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/a/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c),x,5,2*a^(3/2)*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+2/5*a^2*(5*A+4*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/5*a*C*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/5*C*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,5,3*a^(3/2)*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/3*a^2*(3*A-8*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/3*a*(3*A-2*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+A*(a+a*cos(d*x+c))^(3/2)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,5,1/4*a^(3/2)*(7*A+8*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/4*a^2*(5*A-8*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+3/4*a*A*sqrt(a+a*cos(d*x+c))*tan(d*x+c)/d+1/2*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,5,1/8*a^(3/2)*(11*A+24*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/24*a^2*(19*A+24*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/4*a*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,6,1/64*a^(3/2)*(75*A+112*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/64*a^2*(75*A+112*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/32*a^2*(13*A+16*C)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/8*a*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,7,1/128*a^(3/2)*(133*A+176*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/128*a^2*(133*A+176*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/192*a^2*(133*A+176*C)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/240*a^2*(67*A+80*C)*sec(d*x+c)^2*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+3/40*a*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^3*tan(d*x+c)/d+1/5*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^4*tan(d*x+c)/d,1],
[cos(d*x+c)^2*(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x,7,2/6435*a^3*(10439*A+8368*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/9009*a^3*(2717*A+2224*C)*cos(d*x+c)^3*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-4/45045*a^2*(10439*A+8368*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/1287*a^2*(143*A+136*C)*cos(d*x+c)^3*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/15015*a*(10439*A+8368*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+10/143*a*C*cos(d*x+c)^3*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/13*C*cos(d*x+c)^3*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x,7,64/693*a^3*(33*A+25*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+16/693*a^2*(33*A+25*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/231*a*(33*A+25*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/693*(99*A+26*C)*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d+2/11*C*cos(d*x+c)^2*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d+10/99*C*(a+a*cos(d*x+c))^(7/2)*sin(d*x+c)/a/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x,5,64/315*a^3*(21*A+13*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+16/315*a^2*(21*A+13*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/105*a*(21*A+13*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d-4/63*C*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d+2/9*C*(a+a*cos(d*x+c))^(7/2)*sin(d*x+c)/a/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c),x,6,2*a^(5/2)*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+2/21*a^3*(49*A+32*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/21*a^2*(7*A+8*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/7*a*C*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/7*C*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,6,5*a^(5/2)*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/15*a^3*(15*A+64*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/15*a^2*(15*A-16*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d-1/5*a*(5*A-2*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+A*(a+a*cos(d*x+c))^(5/2)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,6,1/4*a^(5/2)*(19*A+8*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/12*a^3*(27*A-56*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/12*a^2*(21*A-8*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+5/4*a*A*(a+a*cos(d*x+c))^(3/2)*tan(d*x+c)/d+1/2*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,6,5/8*a^(5/2)*(5*A+8*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/24*a^3*(49*A-24*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/24*a^2*(31*A+24*C)*sqrt(a+a*cos(d*x+c))*tan(d*x+c)/d+5/12*a*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,6,1/64*a^(5/2)*(163*A+304*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/192*a^3*(299*A+432*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/32*a^2*(17*A+16*C)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+5/24*a*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,7,1/128*a^(5/2)*(283*A+400*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/128*a^3*(283*A+400*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/960*a^3*(787*A+1040*C)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/240*a^2*(79*A+80*C)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d+1/8*a*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^3*tan(d*x+c)/d+1/5*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^4*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,x,8,1/512*a^(5/2)*(1015*A+1304*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/512*a^3*(1015*A+1304*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/768*a^3*(1015*A+1304*C)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/192*a^3*(109*A+136*C)*sec(d*x+c)^2*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/96*a^2*(23*A+24*C)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^3*tan(d*x+c)/d+1/12*a*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^4*tan(d*x+c)/d+1/6*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^5*tan(d*x+c)/d,1],
[cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/sqrt(a+a*cos(d*x+c)),x,8,-sqrt(2)*(A+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+4/315*(147*A+143*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*(21*A+19*C)*cos(d*x+c)^2*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-2/63*C*cos(d*x+c)^3*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/9*C*cos(d*x+c)^4*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-2/315*(21*A+29*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a/d,1],
[cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/sqrt(a+a*cos(d*x+c)),x,7,sqrt(2)*(A+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-4/105*(35*A+37*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-2/35*C*cos(d*x+c)^2*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/7*C*cos(d*x+c)^3*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*(35*A+31*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a/d,1],
[cos(d*x+c)*(A+C*cos(d*x+c)^2)/sqrt(a+a*cos(d*x+c)),x,6,-sqrt(2)*(A+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+2/15*(15*A+14*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/5*C*cos(d*x+c)^2*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-2/15*C*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a/d,1],
[(A+C*cos(d*x+c)^2)/sqrt(a+a*cos(d*x+c)),x,4,sqrt(2)*(A+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-4/3*C*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/3*C*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)/sqrt(a+a*cos(d*x+c)),x,6,2*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-sqrt(2)*(A+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+2*C*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^2/sqrt(a+a*cos(d*x+c)),x,6,-A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+sqrt(2)*(A+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+A*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^3/sqrt(a+a*cos(d*x+c)),x,7,1/4*(7*A+8*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-sqrt(2)*(A+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-1/4*A*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/2*A*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^4/sqrt(a+a*cos(d*x+c)),x,8,-1/8*(9*A+8*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+sqrt(2)*(A+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+1/8*(7*A+8*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/12*A*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/3*A*sec(d*x+c)^2*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^5/sqrt(a+a*cos(d*x+c)),x,9,1/64*(107*A+112*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-sqrt(2)*(A+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-1/64*(21*A+16*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/96*(43*A+48*C)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/24*A*sec(d*x+c)^2*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/4*A*sec(d*x+c)^3*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x,8,1/2*(11*A+19*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A+C)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)-1/105*(455*A+799*C)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/70*(35*A+67*C)*cos(d*x+c)^2*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))+1/14*(7*A+11*C)*cos(d*x+c)^3*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))+1/210*(245*A+397*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a^2/d,1],
[cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x,7,-1/2*(7*A+15*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A+C)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/5*(15*A+31*C)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))+1/10*(5*A+9*C)*cos(d*x+c)^2*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/10*(5*A+13*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a^2/d,1],
[cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x,6,1/2*(3*A+11*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A+C)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)-1/3*(3*A+13*C)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))+1/6*(3*A+7*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a^2/d,1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x,4,1/2*(A-7*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d+1/2*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+2*C*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(3/2),x,6,2*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(3/2)/d-1/2*(5*A-3*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(3/2),x,7,-3*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(3/2)/d+1/2*(9*A+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A+C)*tan(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/2*(3*A+C)*tan(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(3/2),x,8,1/4*(19*A+8*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(3/2)/d-1/2*(13*A+5*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/4*(7*A+2*C)*tan(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/2*(A+C)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/2*(2*A+C)*sec(d*x+c)*tan(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^(3/2),x,9,-1/8*(47*A+24*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(3/2)/d+1/2*(17*A+9*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d+3/8*(7*A+4*C)*tan(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/12*(13*A+6*C)*sec(d*x+c)*tan(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/2*(A+C)*sec(d*x+c)^2*tan(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/6*(5*A+3*C)*sec(d*x+c)^2*tan(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x,8,-1/16*(75*A+283*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A+C)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(5*A+21*C)*cos(d*x+c)^3*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+1/120*(465*A+1729*C)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))+1/80*(45*A+157*C)*cos(d*x+c)^2*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))-1/240*(195*A+787*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a^3/d,1],
[cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x,7,1/16*(19*A+163*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A+C)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(A+17*C)*cos(d*x+c)^2*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)-1/24*(21*A+197*C)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))+5/48*(3*A+19*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a^3/d,1],
[cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x,6,5/16*(A-15*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A+C)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(3*A-13*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+1/4*(A+9*C)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x,4,1/16*(3*A+19*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d+1/4*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)+1/16*(3*A-13*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(5/2),x,7,2*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(5/2)/d-1/16*(43*A-5*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(11*A-5*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(5/2),x,8,-5*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(5/2)/d+1/16*(115*A+3*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A+C)*tan(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(15*A-C)*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+1/16*(35*A+3*C)*tan(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(5/2),x,9,1/4*(39*A+8*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(5/2)/d-1/16*(219*A+43*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/16*(63*A+11*C)*tan(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))-1/4*(A+C)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(19*A+3*C)*sec(d*x+c)*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+1/16*(31*A+7*C)*sec(d*x+c)*tan(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,8,2/15*a*(9*A+7*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+10/231*a*(11*A+9*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+10/231*a*(11*A+9*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*a*(9*A+7*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/77*a*(11*A+9*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/9*a*C*cos(d*x+c)^(7/2)*sin(d*x+c)/d+2/11*a*C*cos(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,7,2/15*a*(9*A+7*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*a*(7*A+5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*a*(7*A+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*a*(9*A+7*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*a*C*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/9*a*C*cos(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,6,2/5*a*(5*A+3*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*a*(7*A+5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*a*(7*A+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*a*C*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*a*C*cos(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,5,2/5*a*(5*A+3*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*a*(3*A+C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*a*C*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*a*C*cos(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,5,-2*a*(A-C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*a*(3*A+C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2*a*A*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*a*C*sqrt(cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,5,-2*a*(A-C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*a*(A+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*a*A*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2*a*A*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,6,-2/5*a*(3*A+5*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*a*(A+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/5*a*A*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/3*a*A*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*a*(3*A+5*C)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,7,-2/5*a*(3*A+5*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*a*(5*A+7*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/7*a*A*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/5*a*A*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/21*a*(5*A+7*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*a*(3*A+5*C)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x,9,4/15*a^2*(9*A+7*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+8/231*a^2*(33*A+25*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+8/231*a^2*(33*A+25*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+4/45*a^2*(9*A+7*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/693*a^2*(99*A+89*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/11*C*cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+8/99*C*cos(d*x+c)^(5/2)*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x,8,16/15*a^2*(3*A+2*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^2*(7*A+5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/21*a^2*(7*A+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/105*a^2*(21*A+19*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/9*C*cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+8/63*C*cos(d*x+c)^(3/2)*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,7,4/5*a^2*(5*A+3*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+8/21*a^2*(7*A+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/105*a^2*(35*A+33*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/7*C*sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+8/35*C*sqrt(cos(d*x+c))*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,7,16/5*a^2*C*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/3*a^2*(3*A+C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-2/15*a^2*(15*A-7*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2*A*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(cos(d*x+c))-2/5*(5*A-C)*sqrt(cos(d*x+c))*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,7,-4*a^2*(A-C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+8/3*a^2*(A+C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-2/3*a^2*(5*A-C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/3*A*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(3/2)+8/3*A*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,7,-16/5*a^2*A*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/3*a^2*(A+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/15*a^2*(17*A+15*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/5*A*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(5/2)+8/15*A*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,8,-4/5*a^2*(3*A+5*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+8/21*a^2*(3*A+7*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/105*a^2*(33*A+35*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+4/5*a^2*(3*A+5*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/7*A*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(7/2)+8/35*A*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,9,-16/15*a^2*(2*A+3*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^2*(5*A+7*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/105*a^2*(19*A+21*C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)+4/21*a^2*(5*A+7*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+16/15*a^2*(2*A+3*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/9*A*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(9/2)+8/63*A*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x,10,4/195*a^3*(221*A+175*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/231*a^3*(121*A+95*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/231*a^3*(121*A+95*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+4/585*a^3*(221*A+175*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+40/9009*a^3*(143*A+118*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/13*C*cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+12/143*C*cos(d*x+c)^(5/2)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d+2/1287*(143*A+145*C)*cos(d*x+c)^(5/2)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x,9,4/5*a^3*(7*A+5*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/231*a^3*(143*A+105*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/231*a^3*(143*A+105*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+8/385*a^3*(44*A+35*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/11*C*cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+4/33*C*cos(d*x+c)^(3/2)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d+2/231*(33*A+35*C)*cos(d*x+c)^(3/2)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,8,4/15*a^3*(27*A+17*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^3*(21*A+11*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+8/105*a^3*(21*A+16*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/9*C*sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+4/21*C*sqrt(cos(d*x+c))*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d+2/315*(63*A+73*C)*sqrt(cos(d*x+c))*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,8,4/5*a^3*(5*A+7*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^3*(35*A+13*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-4/105*a^3*(35*A-41*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2*A*(a+a*cos(d*x+c))^3*sin(d*x+c)/d/sqrt(cos(d*x+c))-2/7*(7*A-C)*sqrt(cos(d*x+c))*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d-2/35*(35*A-11*C)*sqrt(cos(d*x+c))*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,8,-4/5*a^3*(5*A-9*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/3*a^3*(5*A+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-8/15*a^3*(10*A-3*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/3*A*(a+a*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(3/2)+4*A*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d/sqrt(cos(d*x+c))-2/15*(35*A-3*C)*sqrt(cos(d*x+c))*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,8,-4/5*a^3*(9*A-5*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/3*a^3*(3*A+5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-4/15*a^3*(21*A+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*A*(a+a*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(5/2)+4/5*A*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)+2/5*(11*A+5*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,8,-4/5*a^3*(7*A+5*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^3*(13*A+35*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+8/105*a^3*(53*A+70*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/7*A*(a+a*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(7/2)+12/35*A*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)+2/15*(7*A+5*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,9,-4/15*a^3*(17*A+27*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^3*(11*A+21*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+8/105*a^3*(16*A+21*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+4/15*a^3*(17*A+27*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/9*A*(a+a*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(9/2)+4/21*A*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d/cos(d*x+c)^(7/2)+2/315*(73*A+63*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x,10,-4/5*a^3*(5*A+7*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/231*a^3*(105*A+143*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+8/385*a^3*(35*A+44*C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)+4/231*a^3*(105*A+143*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+4/5*a^3*(5*A+7*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/11*A*(a+a*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(11/2)+4/33*A*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d/cos(d*x+c)^(9/2)+2/231*(35*A+33*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x,7,-3/5*(5*A+7*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d+5/21*(7*A+9*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d+5/21*(7*A+9*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d-1/5*(5*A+7*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/a/d+1/7*(7*A+9*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/a/d-(A+C)*cos(d*x+c)^(7/2)*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x,6,3/5*(5*A+7*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d-1/3*(3*A+5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d-1/3*(3*A+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d+1/5*(5*A+7*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/a/d-(A+C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x,5,-(A+3*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d+1/3*(3*A+5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d+1/3*(3*A+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d-(A+C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+a*cos(d*x+c)),x,4,(A+3*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d+(A-C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d-(A+C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x,5,-(3*A+C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d-(A-C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d+(3*A+C)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))-(A+C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x,6,(3*A+C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d+1/3*(5*A+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d+1/3*(5*A+3*C)*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)-(3*A+C)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))-(A+C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c)),x,7,-3/5*(7*A+5*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d-1/3*(5*A+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d+1/5*(7*A+5*C)*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)-1/3*(5*A+3*C)*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)+3/5*(7*A+5*C)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))-(A+C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c)),1],
[cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,7,4/5*(5*A+14*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d-5/3*(A+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d-5/3*(A+3*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d+4/15*(5*A+14*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/a^2/d-(A+3*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A+C)*cos(d*x+c)^(7/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,6,-(A+7*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d+2/3*(A+5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d+2/3*(A+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d-1/3*(A+7*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A+C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[sqrt(cos(d*x+c))*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,5,4*C*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d+1/3*(A-5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d+1/3*(A-5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A+C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^2,x,5,(A-C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d+2/3*(A+C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d-(A-C)*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A+C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x,6,-4*A*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d-1/3*(5*A-C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d+4*A*sin(d*x+c)/a^2/d/sqrt(cos(d*x+c))-1/3*(5*A-C)*sin(d*x+c)/a^2/d/sqrt(cos(d*x+c))/(1+cos(d*x+c))-1/3*(A+C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^2,1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x,7,(7*A+C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d+2/3*(5*A+C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d+2/3*(5*A+C)*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2)-(7*A+C)*sin(d*x+c)/a^2/d/sqrt(cos(d*x+c))-1/3*(7*A+C)*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2)/(1+cos(d*x+c))-1/3*(A+C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,1],
[cos(d*x+c)^(7/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,8,7/10*(7*A+33*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d-1/6*(13*A+63*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d-1/6*(13*A+63*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a^3/d+7/30*(7*A+33*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/a^3/d-1/5*(A+C)*cos(d*x+c)^(9/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-2/15*(A+6*C)*cos(d*x+c)^(7/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/10*(13*A+63*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,7,-1/10*(9*A+119*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d+1/2*(A+11*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d+1/2*(A+11*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a^3/d-1/5*(A+C)*cos(d*x+c)^(7/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-2/3*C*cos(d*x+c)^(5/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/30*(9*A+119*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,6,-1/10*(A-49*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d+1/6*(A-13*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d-1/5*(A+C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+2/15*(A-4*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+1/6*(A-13*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,6,1/10*(A-9*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d+1/6*(A+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d-1/5*(A+C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+2/15*(2*A-3*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/10*(A-9*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^3,x,6,1/10*(9*A-C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d+1/6*(3*A+C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d-1/5*(A+C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-2/15*(3*A-2*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/10*(9*A-C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x,7,-1/10*(49*A-C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d-1/6*(13*A-C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d+1/10*(49*A-C)*sin(d*x+c)/a^3/d/sqrt(cos(d*x+c))-1/5*(A+C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^3-2/15*(4*A-C)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^2-1/6*(13*A-C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/(a^3+a^3*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x,8,1/10*(119*A+9*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d+1/2*(11*A+C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d+1/2*(11*A+C)*sin(d*x+c)/a^3/d/cos(d*x+c)^(3/2)-1/10*(119*A+9*C)*sin(d*x+c)/a^3/d/sqrt(cos(d*x+c))-1/5*(A+C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3-2/3*A*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2-1/30*(119*A+9*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/(a^3+a^3*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,6,1/64*sqrt(a)*(48*A+35*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/64*a*(48*A+35*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/96*a*(48*A+35*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/24*a*C*cos(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/4*C*cos(d*x+c)^(5/2)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,5,1/8*sqrt(a)*(8*A+5*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/8*a*(8*A+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/12*a*C*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/3*C*cos(d*x+c)^(3/2)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,4,1/4*sqrt(a)*(8*A+3*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/4*a*C*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/2*C*sqrt(cos(d*x+c))*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,4,sqrt(a)*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-a*(2*A-C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2*A*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,4,2*sqrt(a)*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+2/3*a*A*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/3*A*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,3,2/15*a*A*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+2/15*a*(8*A+15*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/5*A*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,4,2/35*a*A*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+2/105*a*(24*A+35*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+4/105*a*(24*A+35*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/7*A*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,5,2/63*a*A*sin(d*x+c)/d/cos(d*x+c)^(7/2)/sqrt(a+a*cos(d*x+c))+2/105*a*(16*A+21*C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+8/315*a*(16*A+21*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+16/315*a*(16*A+21*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/9*A*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(9/2),1],
[cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x,7,1/128*a^(3/2)*(176*A+133*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/128*a^2*(176*A+133*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/192*a^2*(176*A+133*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/240*a^2*(80*A+67*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+3/40*a*C*cos(d*x+c)^(5/2)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+1/5*C*cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x,6,1/64*a^(3/2)*(112*A+75*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/64*a^2*(112*A+75*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/32*a^2*(16*A+13*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/8*a*C*cos(d*x+c)^(3/2)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+1/4*C*cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,5,1/8*a^(3/2)*(24*A+11*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/24*a^2*(24*A+19*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/4*a*C*sqrt(cos(d*x+c))*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+1/3*C*sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,5,1/4*a^(3/2)*(8*A+7*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/4*a^2*(8*A-5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/2*a*(4*A-C)*sqrt(cos(d*x+c))*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2*A*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,5,3*a^(3/2)*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/3*a^2*(8*A-3*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2*a*A*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*A*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,5,2*a^(3/2)*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+2/5*a^2*(4*A+5*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/5*a*A*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*A*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,4,2/15*a^2*(4*A+5*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+2/105*a^2*(104*A+175*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+6/35*a*A*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/7*A*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,5,2/315*a^2*(52*A+63*C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+2/315*a^2*(136*A+189*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+4/315*a^2*(136*A+189*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/21*a*A*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/9*A*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(9/2),1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x,6,2/231*a^2*(28*A+33*C)*sin(d*x+c)/d/cos(d*x+c)^(7/2)/sqrt(a+a*cos(d*x+c))+2/385*a^2*(112*A+143*C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+8/1155*a^2*(112*A+143*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+16/1155*a^2*(112*A+143*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/33*a*A*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(9/2)+2/11*A*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(11/2),1],
[cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x,8,1/512*a^(5/2)*(1304*A+1015*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/512*a^3*(1304*A+1015*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/768*a^3*(1304*A+1015*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/192*a^3*(136*A+109*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/96*a^2*(24*A+23*C)*cos(d*x+c)^(5/2)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+1/12*a*C*cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+1/6*C*cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x,7,1/128*a^(5/2)*(400*A+283*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/128*a^3*(400*A+283*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/960*a^3*(1040*A+787*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/240*a^2*(80*A+79*C)*cos(d*x+c)^(3/2)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+1/8*a*C*cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+1/5*C*cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,6,1/64*a^(5/2)*(304*A+163*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/192*a^3*(432*A+299*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/32*a^2*(16*A+17*C)*sqrt(cos(d*x+c))*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+5/24*a*C*sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+1/4*C*sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,6,5/8*a^(5/2)*(8*A+5*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/24*a^3*(24*A-49*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/4*a^2*(8*A-3*C)*sqrt(cos(d*x+c))*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d-1/3*a*(6*A-C)*sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2*A*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,6,1/4*a^(5/2)*(8*A+19*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/12*a^3*(56*A-27*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/2*a^2*(8*A-C)*sqrt(cos(d*x+c))*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+10/3*a*A*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*A*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,6,5*a^(5/2)*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/15*a^3*(64*A+15*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/5*a^2*(8*A+5*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*a*A*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*A*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,6,2*a^(5/2)*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+2/21*a^3*(32*A+49*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/21*a^2*(8*A+7*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/7*a*A*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/7*A*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,5,2/15*a^3*(8*A+11*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+2/315*a^3*(584*A+903*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/315*a^2*(64*A+63*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+10/63*a*A*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/9*A*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(9/2),1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x,6,2/693*a^3*(232*A+297*C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+2/693*a^3*(568*A+759*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+4/693*a^3*(568*A+759*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/231*a^2*(32*A+33*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2)+10/99*a*A*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(9/2)+2/11*A*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(11/2),1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(15/2),x,7,2/9009*a^3*(2224*A+2717*C)*sin(d*x+c)/d/cos(d*x+c)^(7/2)/sqrt(a+a*cos(d*x+c))+2/15015*a^3*(8368*A+10439*C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+8/45045*a^3*(8368*A+10439*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+16/45045*a^3*(8368*A+10439*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/1287*a^2*(136*A+143*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(9/2)+10/143*a*A*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(11/2)+2/13*A*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(13/2),1],
[cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/sqrt(a+a*cos(d*x+c)),x,8,-1/8*(8*A+9*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+sqrt(2)*(A+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+1/8*(8*A+7*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/12*C*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/3*C*cos(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(A+C*cos(d*x+c)^2)/sqrt(a+a*cos(d*x+c)),x,7,1/4*(8*A+7*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-sqrt(2)*(A+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-1/4*C*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/2*C*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),x,6,-C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+sqrt(2)*(A+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+C*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c)),x,6,2*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-sqrt(2)*(A+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+2*A*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c)),x,5,sqrt(2)*(A+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+2/3*A*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))-2/3*A*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/sqrt(a+a*cos(d*x+c)),x,6,-sqrt(2)*(A+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+2/5*A*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))-2/15*A*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+2/15*(13*A+15*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/sqrt(a+a*cos(d*x+c)),x,7,sqrt(2)*(A+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+2/7*A*sin(d*x+c)/d/cos(d*x+c)^(7/2)/sqrt(a+a*cos(d*x+c))-2/35*A*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+2/105*(31*A+35*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))-2/105*(43*A+35*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x,8,1/4*(8*A+19*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(3/2)/d-1/2*(5*A+13*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A+C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)-1/4*(2*A+7*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))+1/2*(A+2*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x,7,-3*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(3/2)/d+1/2*(A+9*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A+C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/2*(A+3*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x,6,2*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(3/2)/d+1/2*(3*A-5*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A+C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x,5,-1/2*(7*A-C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A+C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^(3/2)+1/2*(5*A+C)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x,6,1/2*(11*A+3*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A+C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2)+1/6*(7*A+3*C)*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))-1/6*(19*A+3*C)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x,7,-1/2*(15*A+7*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A+C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2)+1/10*(9*A+5*C)*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))-1/10*(13*A+5*C)*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+1/10*(49*A+25*C)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x,8,-5*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(5/2)/d+1/16*(3*A+115*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A+C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)+1/16*(A-15*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+1/16*(3*A+35*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x,7,2*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(5/2)/d+1/16*(5*A-43*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A+C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)+1/16*(5*A-11*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x,5,1/16*(19*A+3*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A+C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(9*A-7*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x,6,-5/16*(15*A-C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A+C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^(5/2)-1/16*(13*A-3*C)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^(3/2)+1/16*(49*A+C)*sin(d*x+c)/a^2/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x,7,1/16*(163*A+19*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A+C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2)-1/16*(17*A+C)*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2)+5/48*(19*A+3*C)*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))-1/48*(299*A+27*C)*sin(d*x+c)/a^2/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)^3*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,7,3/8*B*x+C*sin(d*x+c)/d+3/8*B*cos(d*x+c)*sin(d*x+c)/d+1/4*B*cos(d*x+c)^3*sin(d*x+c)/d-2/3*C*sin(d*x+c)^3/d+1/5*C*sin(d*x+c)^5/d,1],
[cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,7,3/8*C*x+B*sin(d*x+c)/d+3/8*C*cos(d*x+c)*sin(d*x+c)/d+1/4*C*cos(d*x+c)^3*sin(d*x+c)/d-1/3*B*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,6,1/2*B*x+C*sin(d*x+c)/d+1/2*B*cos(d*x+c)*sin(d*x+c)/d-1/3*C*sin(d*x+c)^3/d,1],
[B*cos(d*x+c)+C*cos(d*x+c)^2,x,4,1/2*C*x+B*sin(d*x+c)/d+1/2*C*cos(d*x+c)*sin(d*x+c)/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,3,B*x+C*sin(d*x+c)/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,3,C*x+B*arctanh(sin(d*x+c))/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,5,C*arctanh(sin(d*x+c))/d+B*tan(d*x+c)/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,6,1/2*B*arctanh(sin(d*x+c))/d+C*tan(d*x+c)/d+1/2*B*sec(d*x+c)*tan(d*x+c)/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,6,1/2*C*arctanh(sin(d*x+c))/d+B*tan(d*x+c)/d+1/2*C*sec(d*x+c)*tan(d*x+c)/d+1/3*B*tan(d*x+c)^3/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,7,3/8*B*arctanh(sin(d*x+c))/d+C*tan(d*x+c)/d+3/8*B*sec(d*x+c)*tan(d*x+c)/d+1/4*B*sec(d*x+c)^3*tan(d*x+c)/d+1/3*C*tan(d*x+c)^3/d,1],
[cos(d*x+c)^2*(a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,9,3/8*a*(B+C)*x+1/5*a*(5*B+4*C)*sin(d*x+c)/d+3/8*a*(B+C)*cos(d*x+c)*sin(d*x+c)/d+1/4*a*(B+C)*cos(d*x+c)^3*sin(d*x+c)/d+1/5*a*C*cos(d*x+c)^4*sin(d*x+c)/d-1/15*a*(5*B+4*C)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,8,1/8*a*(4*B+3*C)*x+a*(B+C)*sin(d*x+c)/d+1/8*a*(4*B+3*C)*cos(d*x+c)*sin(d*x+c)/d+1/4*a*C*cos(d*x+c)^3*sin(d*x+c)/d-1/3*a*(B+C)*sin(d*x+c)^3/d,1],
[(a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,2,1/2*a*(B+C)*x+1/3*a*(3*B+C)*sin(d*x+c)/d+1/6*a*(3*B-C)*cos(d*x+c)*sin(d*x+c)/d+1/3*C*(a+a*cos(d*x+c))^2*sin(d*x+c)/a/d,1],
[(a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,2,1/2*a*(2*B+C)*x+a*(B+C)*sin(d*x+c)/d+1/2*a*C*cos(d*x+c)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,5,a*(B+C)*x+a*B*arctanh(sin(d*x+c))/d+a*C*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,5,a*C*x+a*(B+C)*arctanh(sin(d*x+c))/d+a*B*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,7,1/2*a*(B+2*C)*arctanh(sin(d*x+c))/d+a*(B+C)*tan(d*x+c)/d+1/2*a*B*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,8,1/2*a*(B+C)*arctanh(sin(d*x+c))/d+1/3*a*(2*B+3*C)*tan(d*x+c)/d+1/2*a*(B+C)*sec(d*x+c)*tan(d*x+c)/d+1/3*a*B*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,8,1/8*a*(3*B+4*C)*arctanh(sin(d*x+c))/d+a*(B+C)*tan(d*x+c)/d+1/8*a*(3*B+4*C)*sec(d*x+c)*tan(d*x+c)/d+1/4*a*B*sec(d*x+c)^3*tan(d*x+c)/d+1/3*a*(B+C)*tan(d*x+c)^3/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,9,1/8*a^2*(7*B+6*C)*x+1/5*a^2*(10*B+9*C)*sin(d*x+c)/d+1/8*a^2*(7*B+6*C)*cos(d*x+c)*sin(d*x+c)/d+1/20*a^2*(5*B+6*C)*cos(d*x+c)^3*sin(d*x+c)/d+1/5*C*cos(d*x+c)^3*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d-1/15*a^2*(10*B+9*C)*sin(d*x+c)^3/d,1],
[(a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,3,1/8*a^2*(8*B+7*C)*x+1/6*a^2*(8*B+7*C)*sin(d*x+c)/d+1/24*a^2*(8*B+7*C)*cos(d*x+c)*sin(d*x+c)/d+1/12*(4*B-C)*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+1/4*C*(a+a*cos(d*x+c))^3*sin(d*x+c)/a/d,1],
[(a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,3,1/2*a^2*(3*B+2*C)*x+2/3*a^2*(3*B+2*C)*sin(d*x+c)/d+1/6*a^2*(3*B+2*C)*cos(d*x+c)*sin(d*x+c)/d+1/3*C*(a+a*cos(d*x+c))^2*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,6,1/2*a^2*(4*B+3*C)*x+a^2*B*arctanh(sin(d*x+c))/d+1/2*a^2*(2*B+3*C)*sin(d*x+c)/d+1/2*C*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,6,a^2*(B+2*C)*x+a^2*(2*B+C)*arctanh(sin(d*x+c))/d-a^2*(B-C)*sin(d*x+c)/d+B*(a^2+a^2*cos(d*x+c))*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,6,a^2*C*x+1/2*a^2*(3*B+4*C)*arctanh(sin(d*x+c))/d+1/2*a^2*(3*B+2*C)*tan(d*x+c)/d+1/2*B*(a^2+a^2*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,8,1/2*a^2*(2*B+3*C)*arctanh(sin(d*x+c))/d+1/3*a^2*(5*B+6*C)*tan(d*x+c)/d+1/6*a^2*(4*B+3*C)*sec(d*x+c)*tan(d*x+c)/d+1/3*B*(a^2+a^2*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,9,1/8*a^2*(7*B+8*C)*arctanh(sin(d*x+c))/d+1/3*a^2*(4*B+5*C)*tan(d*x+c)/d+1/8*a^2*(7*B+8*C)*sec(d*x+c)*tan(d*x+c)/d+1/12*a^2*(5*B+4*C)*sec(d*x+c)^2*tan(d*x+c)/d+1/4*B*(a^2+a^2*cos(d*x+c))*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x,9,1/8*a^2*(6*B+7*C)*arctanh(sin(d*x+c))/d+1/5*a^2*(9*B+10*C)*tan(d*x+c)/d+1/8*a^2*(6*B+7*C)*sec(d*x+c)*tan(d*x+c)/d+1/20*a^2*(6*B+5*C)*sec(d*x+c)^3*tan(d*x+c)/d+1/5*B*(a^2+a^2*cos(d*x+c))*sec(d*x+c)^4*tan(d*x+c)/d+1/15*a^2*(9*B+10*C)*tan(d*x+c)^3/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,10,1/16*a^3*(26*B+23*C)*x+1/5*a^3*(19*B+17*C)*sin(d*x+c)/d+1/16*a^3*(26*B+23*C)*cos(d*x+c)*sin(d*x+c)/d+1/40*a^3*(22*B+21*C)*cos(d*x+c)^3*sin(d*x+c)/d+1/6*a*C*cos(d*x+c)^3*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+1/15*(3*B+4*C)*cos(d*x+c)^3*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d-1/15*a^3*(19*B+17*C)*sin(d*x+c)^3/d,1],
[(a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,9,1/8*a^3*(15*B+13*C)*x+1/5*a^3*(15*B+13*C)*sin(d*x+c)/d+3/40*a^3*(15*B+13*C)*cos(d*x+c)*sin(d*x+c)/d+1/20*(5*B-C)*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+1/5*C*(a+a*cos(d*x+c))^4*sin(d*x+c)/a/d-1/60*a^3*(15*B+13*C)*sin(d*x+c)^3/d,1],
[(a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,9,5/8*a^3*(4*B+3*C)*x+a^3*(4*B+3*C)*sin(d*x+c)/d+3/8*a^3*(4*B+3*C)*cos(d*x+c)*sin(d*x+c)/d+1/4*C*(a+a*cos(d*x+c))^3*sin(d*x+c)/d-1/12*a^3*(4*B+3*C)*sin(d*x+c)^3/d,1],
[(a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,7,1/2*a^3*(7*B+5*C)*x+a^3*B*arctanh(sin(d*x+c))/d+5/2*a^3*(B+C)*sin(d*x+c)/d+1/3*a*C*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+1/6*(3*B+5*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,7,1/2*a^3*(6*B+7*C)*x+a^3*(3*B+C)*arctanh(sin(d*x+c))/d+5/2*a^3*C*sin(d*x+c)/d-1/2*(2*B-C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d+a*B*(a+a*cos(d*x+c))^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,7,a^3*(B+3*C)*x+1/2*a^3*(7*B+6*C)*arctanh(sin(d*x+c))/d-5/2*a^3*B*sin(d*x+c)/d+(2*B+C)*(a^3+a^3*cos(d*x+c))*tan(d*x+c)/d+1/2*a*B*(a+a*cos(d*x+c))^2*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,7,a^3*C*x+1/2*a^3*(5*B+7*C)*arctanh(sin(d*x+c))/d+5/2*a^3*(B+C)*tan(d*x+c)/d+1/6*(5*B+3*C)*(a^3+a^3*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/3*a*B*(a+a*cos(d*x+c))^2*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,9,5/8*a^3*(3*B+4*C)*arctanh(sin(d*x+c))/d+1/3*a^3*(9*B+11*C)*tan(d*x+c)/d+1/24*a^3*(27*B+28*C)*sec(d*x+c)*tan(d*x+c)/d+1/6*(3*B+2*C)*(a^3+a^3*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d+1/4*a*B*(a+a*cos(d*x+c))^2*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x,10,1/8*a^3*(13*B+15*C)*arctanh(sin(d*x+c))/d+1/15*a^3*(38*B+45*C)*tan(d*x+c)/d+1/8*a^3*(13*B+15*C)*sec(d*x+c)*tan(d*x+c)/d+1/60*a^3*(43*B+45*C)*sec(d*x+c)^2*tan(d*x+c)/d+1/20*(7*B+5*C)*(a^3+a^3*cos(d*x+c))*sec(d*x+c)^3*tan(d*x+c)/d+1/5*a*B*(a+a*cos(d*x+c))^2*sec(d*x+c)^4*tan(d*x+c)/d,1],
[cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x,7,3/2*(B-C)*x/a-(3*B-4*C)*sin(d*x+c)/a/d+3/2*(B-C)*cos(d*x+c)*sin(d*x+c)/a/d+(B-C)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))+1/3*(3*B-4*C)*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x,3,-1/2*(2*B-3*C)*x/a+2*(B-C)*sin(d*x+c)/a/d-1/2*(2*B-3*C)*cos(d*x+c)*sin(d*x+c)/a/d+(B-C)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x,4,(B-C)*x/a+C*sin(d*x+c)/a/d-(B-C)*sin(d*x+c)/a/d/(1+cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c)),x,3,C*x/a+(B-C)*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c)),x,4,B*arctanh(sin(d*x+c))/a/d-(B-C)*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c)),x,6,-(B-C)*arctanh(sin(d*x+c))/a/d+(2*B-C)*tan(d*x+c)/a/d-(B-C)*tan(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c)),x,7,1/2*(3*B-2*C)*arctanh(sin(d*x+c))/a/d-2*(B-C)*tan(d*x+c)/a/d+1/2*(3*B-2*C)*sec(d*x+c)*tan(d*x+c)/a/d-(B-C)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5/(a+a*cos(d*x+c)),x,7,-3/2*(B-C)*arctanh(sin(d*x+c))/a/d+(4*B-3*C)*tan(d*x+c)/a/d-3/2*(B-C)*sec(d*x+c)*tan(d*x+c)/a/d-(B-C)*sec(d*x+c)^2*tan(d*x+c)/d/(a+a*cos(d*x+c))+1/3*(4*B-3*C)*tan(d*x+c)^3/a/d,1],
[cos(d*x+c)^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,8,1/2*(7*B-10*C)*x/a^2-4*(2*B-3*C)*sin(d*x+c)/a^2/d+1/2*(7*B-10*C)*cos(d*x+c)*sin(d*x+c)/a^2/d+1/3*(7*B-10*C)*cos(d*x+c)^3*sin(d*x+c)/a^2/d/(1+cos(d*x+c))+1/3*(B-C)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))^2+4/3*(2*B-3*C)*sin(d*x+c)^3/a^2/d,1],
[cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,4,-1/2*(4*B-7*C)*x/a^2+2/3*(5*B-8*C)*sin(d*x+c)/a^2/d-1/2*(4*B-7*C)*cos(d*x+c)*sin(d*x+c)/a^2/d+1/3*(5*B-8*C)*cos(d*x+c)^2*sin(d*x+c)/a^2/d/(1+cos(d*x+c))+1/3*(B-C)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,7,(B-2*C)*x/a^2-1/3*(B-4*C)*sin(d*x+c)/a^2/d-(B-2*C)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))+1/3*(B-C)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,3,C*x/a^2+1/3*(2*B-5*C)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(B-C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^2,x,3,1/3*(B-C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2+1/3*(B+2*C)*sin(d*x+c)/d/(a^2+a^2*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^2,x,5,B*arctanh(sin(d*x+c))/a^2/d-1/3*(4*B-C)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(B-C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x,7,-(2*B-C)*arctanh(sin(d*x+c))/a^2/d+2/3*(5*B-2*C)*tan(d*x+c)/a^2/d-(2*B-C)*tan(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(B-C)*tan(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x,8,1/2*(7*B-4*C)*arctanh(sin(d*x+c))/a^2/d-2/3*(8*B-5*C)*tan(d*x+c)/a^2/d+1/2*(7*B-4*C)*sec(d*x+c)*tan(d*x+c)/a^2/d-1/3*(8*B-5*C)*sec(d*x+c)*tan(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(B-C)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[cos(d*x+c)^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,5,-1/2*(6*B-13*C)*x/a^3+8/15*(9*B-19*C)*sin(d*x+c)/a^3/d-1/2*(6*B-13*C)*cos(d*x+c)*sin(d*x+c)/a^3/d+1/5*(B-C)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/15*(6*B-11*C)*cos(d*x+c)^3*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+4/15*(9*B-19*C)*cos(d*x+c)^2*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,8,(B-3*C)*x/a^3-1/15*(7*B-27*C)*sin(d*x+c)/a^3/d+1/5*(B-C)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/15*(4*B-9*C)*cos(d*x+c)^2*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-(B-3*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,6,C*x/a^3+1/5*(B-C)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(2*B-7*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+1/15*(4*B-29*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,3,-1/5*(B-C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/15*(3*B-8*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+1/15*(3*B+7*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^3,x,4,1/5*(B-C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/15*(2*B+3*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+1/15*(2*B+3*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^3,x,6,B*arctanh(sin(d*x+c))/a^3/d-1/5*(B-C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(7*B-2*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-2/15*(11*B-C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^3,x,8,-(3*B-C)*arctanh(sin(d*x+c))/a^3/d+2/15*(36*B-11*C)*tan(d*x+c)/a^3/d-1/5*(B-C)*tan(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(9*B-4*C)*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^2-(3*B-C)*tan(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^3,x,9,1/2*(13*B-6*C)*arctanh(sin(d*x+c))/a^3/d-8/15*(19*B-9*C)*tan(d*x+c)/a^3/d+1/2*(13*B-6*C)*sec(d*x+c)*tan(d*x+c)/a^3/d-1/5*(B-C)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(11*B-6*C)*sec(d*x+c)*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^2-4/15*(19*B-9*C)*sec(d*x+c)*tan(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,3,2/15*a*(5*B+7*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*(5*B-2*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/5*C*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/a/d,1],
[(a+a*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,4,8/105*a^2*(21*B+19*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*a*(21*B+19*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/35*(7*B-2*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/7*C*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/a/d,1],
[(a+a*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,5,64/315*a^3*(15*B+13*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+16/315*a^2*(15*B+13*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/105*a*(15*B+13*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/63*(9*B-2*C)*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d+2/9*C*(a+a*cos(d*x+c))^(7/2)*sin(d*x+c)/a/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+a*cos(d*x+c)),x,4,-sqrt(2)*(B-C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+2/3*(3*B-2*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/3*C*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x,4,1/2*(3*B-7*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(B-C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+2*C*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x,4,1/16*(5*B+19*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(B-C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)+1/16*(5*B-13*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2),1],
[cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,7,6/5*B*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+10/21*C*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+10/21*C*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*B*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*C*cos(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,6,6/5*C*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*B*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*B*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*C*cos(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,5,2*B*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*C*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*C*sqrt(cos(d*x+c))*sin(d*x+c)/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,4,2*C*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2*B*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,5,-2*B*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2*C*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2*B*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,6,-2*C*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*B*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*B*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2*C*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,7,-6/5*B*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*C*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/5*B*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/3*C*sin(d*x+c)/d/cos(d*x+c)^(3/2)+6/5*B*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[cos(d*x+c)^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,7,1/16*(6*A+5*C)*x+B*sin(d*x+c)/d+1/16*(6*A+5*C)*cos(d*x+c)*sin(d*x+c)/d+1/24*(6*A+5*C)*cos(d*x+c)^3*sin(d*x+c)/d+1/6*C*cos(d*x+c)^5*sin(d*x+c)/d-2/3*B*sin(d*x+c)^3/d+1/5*B*sin(d*x+c)^5/d,1],
[cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,7,3/8*B*x+1/5*(5*A+4*C)*sin(d*x+c)/d+3/8*B*cos(d*x+c)*sin(d*x+c)/d+1/4*B*cos(d*x+c)^3*sin(d*x+c)/d+1/5*C*cos(d*x+c)^4*sin(d*x+c)/d-1/15*(5*A+4*C)*sin(d*x+c)^3/d,1],
[cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,6,1/8*(4*A+3*C)*x+B*sin(d*x+c)/d+1/8*(4*A+3*C)*cos(d*x+c)*sin(d*x+c)/d+1/4*C*cos(d*x+c)^3*sin(d*x+c)/d-1/3*B*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,2,1/2*B*x+1/3*(3*A+2*C)*sin(d*x+c)/d+1/2*B*cos(d*x+c)*sin(d*x+c)/d+1/3*C*cos(d*x+c)^2*sin(d*x+c)/d,1],
[A+B*cos(d*x+c)+C*cos(d*x+c)^2,x,4,A*x+1/2*C*x+B*sin(d*x+c)/d+1/2*C*cos(d*x+c)*sin(d*x+c)/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,3,B*x+A*arctanh(sin(d*x+c))/d+C*sin(d*x+c)/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,3,C*x+B*arctanh(sin(d*x+c))/d+A*tan(d*x+c)/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,5,1/2*(A+2*C)*arctanh(sin(d*x+c))/d+B*tan(d*x+c)/d+1/2*A*sec(d*x+c)*tan(d*x+c)/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,6,1/2*B*arctanh(sin(d*x+c))/d+1/3*(2*A+3*C)*tan(d*x+c)/d+1/2*B*sec(d*x+c)*tan(d*x+c)/d+1/3*A*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,6,1/8*(3*A+4*C)*arctanh(sin(d*x+c))/d+B*tan(d*x+c)/d+1/8*(3*A+4*C)*sec(d*x+c)*tan(d*x+c)/d+1/4*A*sec(d*x+c)^3*tan(d*x+c)/d+1/3*B*tan(d*x+c)^3/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,7,3/8*B*arctanh(sin(d*x+c))/d+1/5*(4*A+5*C)*tan(d*x+c)/d+3/8*B*sec(d*x+c)*tan(d*x+c)/d+1/4*B*sec(d*x+c)^3*tan(d*x+c)/d+1/5*A*sec(d*x+c)^4*tan(d*x+c)/d+1/15*(4*A+5*C)*tan(d*x+c)^3/d,1],
[cos(d*x+c)^2*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,7,1/8*a*(4*A+3*B+3*C)*x+1/5*a*(5*A+5*B+4*C)*sin(d*x+c)/d+1/8*a*(4*A+3*B+3*C)*cos(d*x+c)*sin(d*x+c)/d+1/4*a*(B+C)*cos(d*x+c)^3*sin(d*x+c)/d+1/5*a*C*cos(d*x+c)^4*sin(d*x+c)/d-1/15*a*(5*A+5*B+4*C)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,3,1/8*a*(4*A+4*B+3*C)*x+1/3*a*(3*A+2*B+2*C)*sin(d*x+c)/d+1/8*a*(4*A+4*B+3*C)*cos(d*x+c)*sin(d*x+c)/d+1/3*a*(B+C)*cos(d*x+c)^2*sin(d*x+c)/d+1/4*a*C*cos(d*x+c)^3*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,2,1/2*a*(2*A+B+C)*x+1/3*a*(3*A+3*B+C)*sin(d*x+c)/d+1/6*a*(3*B-C)*cos(d*x+c)*sin(d*x+c)/d+1/3*C*(a+a*cos(d*x+c))^2*sin(d*x+c)/a/d,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,4,1/2*a*(2*A+2*B+C)*x+a*A*arctanh(sin(d*x+c))/d+a*(B+C)*sin(d*x+c)/d+1/2*a*C*cos(d*x+c)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,4,a*(B+C)*x+a*(A+B)*arctanh(sin(d*x+c))/d+a*C*sin(d*x+c)/d+a*A*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,4,a*C*x+1/2*a*(A+2*B+2*C)*arctanh(sin(d*x+c))/d+a*(A+B)*tan(d*x+c)/d+1/2*a*A*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,6,1/2*a*(A+B+2*C)*arctanh(sin(d*x+c))/d+1/3*a*(2*A+3*B+3*C)*tan(d*x+c)/d+1/2*a*(A+B)*sec(d*x+c)*tan(d*x+c)/d+1/3*a*A*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,7,1/8*a*(3*A+4*B+4*C)*arctanh(sin(d*x+c))/d-1/3*a*(-2*A-2*B-3*C)*tan(d*x+c)/d+1/8*a*(3*A+4*B+4*C)*sec(d*x+c)*tan(d*x+c)/d+1/3*a*(A+B)*sec(d*x+c)^2*tan(d*x+c)/d+1/4*a*A*sec(d*x+c)^3*tan(d*x+c)/d,1],
[cos(d*x+c)^2*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,9,1/16*a^2*(14*A+12*B+11*C)*x+1/5*a^2*(10*A+9*B+8*C)*sin(d*x+c)/d+1/16*a^2*(14*A+12*B+11*C)*cos(d*x+c)*sin(d*x+c)/d+1/40*a^2*(10*A+12*B+9*C)*cos(d*x+c)^3*sin(d*x+c)/d+1/6*C*cos(d*x+c)^3*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+1/15*(3*B+C)*cos(d*x+c)^3*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d-1/15*a^2*(10*A+9*B+8*C)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,5,1/8*a^2*(8*A+7*B+6*C)*x+1/6*a^2*(8*A+7*B+6*C)*sin(d*x+c)/d+1/24*a^2*(8*A+7*B+6*C)*cos(d*x+c)*sin(d*x+c)/d+1/60*(20*A-5*B+6*C)*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+1/5*C*cos(d*x+c)^2*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+1/20*(5*B+2*C)*(a+a*cos(d*x+c))^3*sin(d*x+c)/a/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,3,1/8*a^2*(12*A+8*B+7*C)*x+1/6*a^2*(12*A+8*B+7*C)*sin(d*x+c)/d+1/24*a^2*(12*A+8*B+7*C)*cos(d*x+c)*sin(d*x+c)/d+1/12*(4*B-C)*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+1/4*C*(a+a*cos(d*x+c))^3*sin(d*x+c)/a/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,6,1/2*a^2*(4*A+3*B+2*C)*x+a^2*A*arctanh(sin(d*x+c))/d+1/2*a^2*(2*A+3*B+2*C)*sin(d*x+c)/d+1/3*C*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+1/6*(3*B+2*C)*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,6,1/2*a^2*(2*A+4*B+3*C)*x+a^2*(2*A+B)*arctanh(sin(d*x+c))/d-1/2*a^2*(2*A-2*B-3*C)*sin(d*x+c)/d-1/2*(2*A-C)*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d+A*(a+a*cos(d*x+c))^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,6,a^2*(B+2*C)*x+1/2*a^2*(3*A+4*B+2*C)*arctanh(sin(d*x+c))/d-1/2*a^2*(3*A+2*B-2*C)*sin(d*x+c)/d+(A+B)*(a^2+a^2*cos(d*x+c))*tan(d*x+c)/d+1/2*A*(a+a*cos(d*x+c))^2*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,6,a^2*C*x+1/2*a^2*(2*A+3*B+4*C)*arctanh(sin(d*x+c))/d+1/2*a^2*(2*A+3*B+2*C)*tan(d*x+c)/d+1/6*(2*A+3*B)*(a^2+a^2*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(a+a*cos(d*x+c))^2*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,8,1/8*a^2*(7*A+8*B+12*C)*arctanh(sin(d*x+c))/d+1/3*a^2*(4*A+5*B+6*C)*tan(d*x+c)/d+1/24*a^2*(11*A+16*B+12*C)*sec(d*x+c)*tan(d*x+c)/d+1/6*(A+2*B)*(a^2+a^2*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a+a*cos(d*x+c))^2*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,9,1/8*a^2*(6*A+7*B+8*C)*arctanh(sin(d*x+c))/d+1/15*a^2*(18*A+20*B+25*C)*tan(d*x+c)/d+1/8*a^2*(6*A+7*B+8*C)*sec(d*x+c)*tan(d*x+c)/d+1/60*a^2*(18*A+25*B+20*C)*sec(d*x+c)^2*tan(d*x+c)/d+1/20*(2*A+5*B)*(a^2+a^2*cos(d*x+c))*sec(d*x+c)^3*tan(d*x+c)/d+1/5*A*(a+a*cos(d*x+c))^2*sec(d*x+c)^4*tan(d*x+c)/d,1],
[cos(d*x+c)^2*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,10,1/16*a^3*(26*A+23*B+21*C)*x+1/35*a^3*(133*A+119*B+108*C)*sin(d*x+c)/d+1/16*a^3*(26*A+23*B+21*C)*cos(d*x+c)*sin(d*x+c)/d+1/280*a^3*(154*A+147*B+129*C)*cos(d*x+c)^3*sin(d*x+c)/d+1/7*C*cos(d*x+c)^3*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+1/42*(7*B+3*C)*cos(d*x+c)^3*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d+1/15*(3*A+4*B+3*C)*cos(d*x+c)^3*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d-1/105*a^3*(133*A+119*B+108*C)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,11,1/16*a^3*(30*A+26*B+23*C)*x+1/10*a^3*(30*A+26*B+23*C)*sin(d*x+c)/d+3/80*a^3*(30*A+26*B+23*C)*cos(d*x+c)*sin(d*x+c)/d+1/120*(30*A-6*B+7*C)*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+1/6*C*cos(d*x+c)^2*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+1/10*(2*B+C)*(a+a*cos(d*x+c))^4*sin(d*x+c)/a/d-1/120*a^3*(30*A+26*B+23*C)*sin(d*x+c)^3/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,9,1/8*a^3*(20*A+15*B+13*C)*x+1/5*a^3*(20*A+15*B+13*C)*sin(d*x+c)/d+3/40*a^3*(20*A+15*B+13*C)*cos(d*x+c)*sin(d*x+c)/d+1/20*(5*B-C)*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+1/5*C*(a+a*cos(d*x+c))^4*sin(d*x+c)/a/d-1/60*a^3*(20*A+15*B+13*C)*sin(d*x+c)^3/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,7,1/8*a^3*(28*A+20*B+15*C)*x+a^3*A*arctanh(sin(d*x+c))/d+5/8*a^3*(4*A+4*B+3*C)*sin(d*x+c)/d+1/4*C*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+1/12*(4*B+3*C)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d+1/24*(12*A+20*B+15*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,7,1/2*a^3*(6*A+7*B+5*C)*x+a^3*(3*A+B)*arctanh(sin(d*x+c))/d+5/2*a^3*(B+C)*sin(d*x+c)/d-1/3*(3*A-C)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d-1/6*(6*A-3*B-5*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d+A*(a+a*cos(d*x+c))^3*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,7,1/2*a^3*(2*A+6*B+7*C)*x+1/2*a^3*(7*A+6*B+2*C)*arctanh(sin(d*x+c))/d-5/2*a^3*(A-C)*sin(d*x+c)/d-1/2*(4*A+2*B-C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d+1/2*(3*A+2*B)*(a^2+a^2*cos(d*x+c))^2*tan(d*x+c)/a/d+1/2*A*(a+a*cos(d*x+c))^3*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,7,a^3*(B+3*C)*x+1/2*a^3*(5*A+7*B+6*C)*arctanh(sin(d*x+c))/d-5/2*a^3*(A+B)*sin(d*x+c)/d+1/3*(5*A+6*B+3*C)*(a^3+a^3*cos(d*x+c))*tan(d*x+c)/d+1/2*(A+B)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)*tan(d*x+c)/a/d+1/3*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,7,a^3*C*x+1/8*a^3*(15*A+20*B+28*C)*arctanh(sin(d*x+c))/d+5/8*a^3*(3*A+4*B+4*C)*tan(d*x+c)/d+1/24*(15*A+20*B+12*C)*(a^3+a^3*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/12*(3*A+4*B)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^2*tan(d*x+c)/a/d+1/4*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,9,1/8*a^3*(13*A+15*B+20*C)*arctanh(sin(d*x+c))/d+1/15*a^3*(38*A+45*B+55*C)*tan(d*x+c)/d+1/120*a^3*(109*A+135*B+140*C)*sec(d*x+c)*tan(d*x+c)/d+1/30*(11*A+15*B+10*C)*(a^3+a^3*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d+1/20*(3*A+5*B)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^3*tan(d*x+c)/a/d+1/5*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^4*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x,10,1/16*a^3*(23*A+26*B+30*C)*arctanh(sin(d*x+c))/d+1/15*a^3*(34*A+38*B+45*C)*tan(d*x+c)/d+1/16*a^3*(23*A+26*B+30*C)*sec(d*x+c)*tan(d*x+c)/d+1/120*a^3*(73*A+86*B+90*C)*sec(d*x+c)^2*tan(d*x+c)/d+1/120*(31*A+42*B+30*C)*(a^3+a^3*cos(d*x+c))*sec(d*x+c)^3*tan(d*x+c)/d+1/10*(A+2*B)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^4*tan(d*x+c)/a/d+1/6*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^5*tan(d*x+c)/d,1],
[cos(d*x+c)^2*(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,11,1/128*a^4*(392*A+352*B+323*C)*x+1/35*a^4*(252*A+227*B+208*C)*sin(d*x+c)/d+1/128*a^4*(392*A+352*B+323*C)*cos(d*x+c)*sin(d*x+c)/d+1/2240*a^4*(2408*A+2208*B+2007*C)*cos(d*x+c)^3*sin(d*x+c)/d+1/14*a*(2*B+C)*cos(d*x+c)^3*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+1/8*C*cos(d*x+c)^3*(a+a*cos(d*x+c))^4*sin(d*x+c)/d+1/336*(56*A+80*B+61*C)*cos(d*x+c)^3*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/d+7/120*(8*A+8*B+7*C)*cos(d*x+c)^3*(a^4+a^4*cos(d*x+c))*sin(d*x+c)/d-1/105*a^4*(252*A+227*B+208*C)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,14,1/16*a^4*(56*A+49*B+44*C)*x+4/35*a^4*(56*A+49*B+44*C)*sin(d*x+c)/d+27/560*a^4*(56*A+49*B+44*C)*cos(d*x+c)*sin(d*x+c)/d+1/280*a^4*(56*A+49*B+44*C)*cos(d*x+c)^3*sin(d*x+c)/d+1/210*(42*A-7*B+8*C)*(a+a*cos(d*x+c))^4*sin(d*x+c)/d+1/7*C*cos(d*x+c)^2*(a+a*cos(d*x+c))^4*sin(d*x+c)/d+1/42*(7*B+4*C)*(a+a*cos(d*x+c))^5*sin(d*x+c)/a/d-2/105*a^4*(56*A+49*B+44*C)*sin(d*x+c)^3/d,1],
[(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,12,7/16*a^4*(10*A+8*B+7*C)*x+4/5*a^4*(10*A+8*B+7*C)*sin(d*x+c)/d+27/80*a^4*(10*A+8*B+7*C)*cos(d*x+c)*sin(d*x+c)/d+1/40*a^4*(10*A+8*B+7*C)*cos(d*x+c)^3*sin(d*x+c)/d+1/30*(6*B-C)*(a+a*cos(d*x+c))^4*sin(d*x+c)/d+1/6*C*(a+a*cos(d*x+c))^5*sin(d*x+c)/a/d-2/15*a^4*(10*A+8*B+7*C)*sin(d*x+c)^3/d,1],
[(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,8,1/8*a^4*(48*A+35*B+28*C)*x+a^4*A*arctanh(sin(d*x+c))/d+1/8*a^4*(40*A+35*B+28*C)*sin(d*x+c)/d+1/20*a*(5*B+4*C)*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+1/5*C*(a+a*cos(d*x+c))^4*sin(d*x+c)/d+1/60*(20*A+35*B+28*C)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/d+1/24*(32*A+35*B+28*C)*(a^4+a^4*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,8,1/8*a^4*(52*A+48*B+35*C)*x+a^4*(4*A+B)*arctanh(sin(d*x+c))/d+5/8*a^4*(4*A+8*B+7*C)*sin(d*x+c)/d-1/4*a*(4*A-C)*(a+a*cos(d*x+c))^3*sin(d*x+c)/d-1/12*(12*A-4*B-7*C)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/d-1/24*(12*A-32*B-35*C)*(a^4+a^4*cos(d*x+c))*sin(d*x+c)/d+A*(a+a*cos(d*x+c))^4*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,8,1/2*a^4*(8*A+13*B+12*C)*x+1/2*a^4*(13*A+8*B+2*C)*arctanh(sin(d*x+c))/d-5/2*a^4*(A-B-2*C)*sin(d*x+c)/d-1/6*(15*A+6*B-2*C)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/d-1/6*(18*A+3*B-8*C)*(a^4+a^4*cos(d*x+c))*sin(d*x+c)/d+a*(2*A+B)*(a+a*cos(d*x+c))^3*tan(d*x+c)/d+1/2*A*(a+a*cos(d*x+c))^4*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,8,1/2*a^4*(2*A+8*B+13*C)*x+1/2*a^4*(12*A+13*B+8*C)*arctanh(sin(d*x+c))/d-5/2*a^4*(2*A+B-C)*sin(d*x+c)/d-1/6*(22*A+18*B+3*C)*(a^4+a^4*cos(d*x+c))*sin(d*x+c)/d+1/6*(16*A+15*B+6*C)*(a^2+a^2*cos(d*x+c))^2*tan(d*x+c)/d+1/6*a*(4*A+3*B)*(a+a*cos(d*x+c))^3*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(a+a*cos(d*x+c))^4*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,8,a^4*(B+4*C)*x+1/8*a^4*(35*A+48*B+52*C)*arctanh(sin(d*x+c))/d-5/8*a^4*(7*A+8*B+4*C)*sin(d*x+c)/d+1/12*(35*A+44*B+36*C)*(a^4+a^4*cos(d*x+c))*tan(d*x+c)/d+1/8*(7*A+8*B+4*C)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)*tan(d*x+c)/d+1/3*a*(A+B)*(a+a*cos(d*x+c))^3*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a+a*cos(d*x+c))^4*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,8,a^4*C*x+1/8*a^4*(28*A+35*B+48*C)*arctanh(sin(d*x+c))/d+1/8*a^4*(28*A+35*B+40*C)*tan(d*x+c)/d+1/24*(28*A+35*B+32*C)*(a^4+a^4*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/60*(28*A+35*B+20*C)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^2*tan(d*x+c)/d+1/20*a*(4*A+5*B)*(a+a*cos(d*x+c))^3*sec(d*x+c)^3*tan(d*x+c)/d+1/5*A*(a+a*cos(d*x+c))^4*sec(d*x+c)^4*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x,10,7/16*a^4*(7*A+8*B+10*C)*arctanh(sin(d*x+c))/d+1/15*a^4*(72*A+83*B+100*C)*tan(d*x+c)/d+1/240*a^4*(417*A+488*B+550*C)*sec(d*x+c)*tan(d*x+c)/d+1/60*(43*A+52*B+50*C)*(a^4+a^4*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d+1/120*(37*A+48*B+30*C)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^3*tan(d*x+c)/d+1/15*a*(2*A+3*B)*(a+a*cos(d*x+c))^3*sec(d*x+c)^4*tan(d*x+c)/d+1/6*A*(a+a*cos(d*x+c))^4*sec(d*x+c)^5*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^8,x,11,1/16*a^4*(44*A+49*B+56*C)*arctanh(sin(d*x+c))/d+1/105*a^4*(454*A+504*B+581*C)*tan(d*x+c)/d+1/16*a^4*(44*A+49*B+56*C)*sec(d*x+c)*tan(d*x+c)/d+1/840*a^4*(988*A+1113*B+1232*C)*sec(d*x+c)^2*tan(d*x+c)/d+1/840*(436*A+511*B+504*C)*(a^4+a^4*cos(d*x+c))*sec(d*x+c)^3*tan(d*x+c)/d+1/70*(16*A+21*B+14*C)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^4*tan(d*x+c)/d+1/42*a*(4*A+7*B)*(a+a*cos(d*x+c))^3*sec(d*x+c)^5*tan(d*x+c)/d+1/7*A*(a+a*cos(d*x+c))^4*sec(d*x+c)^6*tan(d*x+c)/d,1],
[cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x,7,3/8*(4*A-4*B+5*C)*x/a-(3*A-4*B+4*C)*sin(d*x+c)/a/d+3/8*(4*A-4*B+5*C)*cos(d*x+c)*sin(d*x+c)/a/d+1/4*(4*A-4*B+5*C)*cos(d*x+c)^3*sin(d*x+c)/a/d-(A-B+C)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))+1/3*(3*A-4*B+4*C)*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x,6,-1/2*(2*A-3*B+3*C)*x/a+(3*A-3*B+4*C)*sin(d*x+c)/a/d-1/2*(2*A-3*B+3*C)*cos(d*x+c)*sin(d*x+c)/a/d-(A-B+C)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))-1/3*(3*A-3*B+4*C)*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x,2,1/2*(2*A-2*B+3*C)*x/a-(A-2*B+2*C)*sin(d*x+c)/a/d+1/2*(2*A-2*B+3*C)*cos(d*x+c)*sin(d*x+c)/a/d-(A-B+C)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x,3,(B-C)*x/a+C*sin(d*x+c)/a/d+(A-B+C)*sin(d*x+c)/a/d/(1+cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c)),x,3,C*x/a+A*arctanh(sin(d*x+c))/a/d-(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c)),x,5,-(A-B)*arctanh(sin(d*x+c))/a/d+(2*A-B+C)*tan(d*x+c)/a/d-(A-B+C)*tan(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c)),x,6,1/2*(3*A-2*B+2*C)*arctanh(sin(d*x+c))/a/d-(2*A-2*B+C)*tan(d*x+c)/a/d+1/2*(3*A-2*B+2*C)*sec(d*x+c)*tan(d*x+c)/a/d-(A-B+C)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c)),x,6,-1/2*(3*A-3*B+2*C)*arctanh(sin(d*x+c))/a/d+(4*A-3*B+3*C)*tan(d*x+c)/a/d-1/2*(3*A-3*B+2*C)*sec(d*x+c)*tan(d*x+c)/a/d-(A-B+C)*sec(d*x+c)^2*tan(d*x+c)/d/(a+a*cos(d*x+c))+1/3*(4*A-3*B+3*C)*tan(d*x+c)^3/a/d,1],
[cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,7,-1/2*(4*A-7*B+10*C)*x/a^2+(5*A-8*B+12*C)*sin(d*x+c)/a^2/d-1/2*(4*A-7*B+10*C)*cos(d*x+c)*sin(d*x+c)/a^2/d-1/3*(4*A-7*B+10*C)*cos(d*x+c)^3*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A-B+C)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))^2-1/3*(5*A-8*B+12*C)*sin(d*x+c)^3/a^2/d,1],
[cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,3,1/2*(2*A-4*B+7*C)*x/a^2-2/3*(2*A-5*B+8*C)*sin(d*x+c)/a^2/d+1/2*(2*A-4*B+7*C)*cos(d*x+c)*sin(d*x+c)/a^2/d-1/3*(2*A-5*B+8*C)*cos(d*x+c)^2*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A-B+C)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,6,(B-2*C)*x/a^2+1/3*(A-B+4*C)*sin(d*x+c)/a^2/d-(B-2*C)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A-B+C)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,3,C*x/a^2+1/3*(A+2*B-5*C)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))+1/3*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^2,x,4,A*arctanh(sin(d*x+c))/a^2/d-1/3*(4*A-B-2*C)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^2,x,6,-(2*A-B)*arctanh(sin(d*x+c))/a^2/d+1/3*(10*A-4*B+C)*tan(d*x+c)/a^2/d-(2*A-B)*tan(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A-B+C)*tan(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x,7,1/2*(7*A-4*B+2*C)*arctanh(sin(d*x+c))/a^2/d-2/3*(8*A-5*B+2*C)*tan(d*x+c)/a^2/d+1/2*(7*A-4*B+2*C)*sec(d*x+c)*tan(d*x+c)/a^2/d-1/3*(8*A-5*B+2*C)*sec(d*x+c)*tan(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A-B+C)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x,7,-1/2*(10*A-7*B+4*C)*arctanh(sin(d*x+c))/a^2/d+(12*A-8*B+5*C)*tan(d*x+c)/a^2/d-1/2*(10*A-7*B+4*C)*sec(d*x+c)*tan(d*x+c)/a^2/d-1/3*(10*A-7*B+4*C)*sec(d*x+c)^2*tan(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A-B+C)*sec(d*x+c)^2*tan(d*x+c)/d/(a+a*cos(d*x+c))^2+1/3*(12*A-8*B+5*C)*tan(d*x+c)^3/a^2/d,1],
[cos(d*x+c)^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,8,-1/2*(6*A-13*B+23*C)*x/a^3+4/5*(9*A-19*B+34*C)*sin(d*x+c)/a^3/d-1/2*(6*A-13*B+23*C)*cos(d*x+c)*sin(d*x+c)/a^3/d-1/5*(A-B+C)*cos(d*x+c)^5*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(3*A-8*B+13*C)*cos(d*x+c)^4*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/3*(6*A-13*B+23*C)*cos(d*x+c)^3*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c))-4/15*(9*A-19*B+34*C)*sin(d*x+c)^3/a^3/d,1],
[cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,4,1/2*(2*A-6*B+13*C)*x/a^3-2/15*(11*A-36*B+76*C)*sin(d*x+c)/a^3/d+1/2*(2*A-6*B+13*C)*cos(d*x+c)*sin(d*x+c)/a^3/d-1/5*(A-B+C)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(A-6*B+11*C)*cos(d*x+c)^3*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/15*(11*A-36*B+76*C)*cos(d*x+c)^2*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,7,(B-3*C)*x/a^3+1/15*(2*A-7*B+27*C)*sin(d*x+c)/a^3/d-1/5*(A-B+C)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/15*(A+4*B-9*C)*cos(d*x+c)^2*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-(B-3*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,5,C*x/a^3-1/5*(A-B+C)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(3*A+2*B-7*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+1/15*(6*A+4*B-29*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,3,1/5*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/15*(2*A+3*B-8*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+1/15*(2*A+3*B+7*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^3,x,5,A*arctanh(sin(d*x+c))/a^3/d-1/5*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(7*A-2*B-3*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/15*(22*A-2*B-3*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^3,x,7,-(3*A-B)*arctanh(sin(d*x+c))/a^3/d+2/15*(36*A-11*B+C)*tan(d*x+c)/a^3/d-1/5*(A-B+C)*tan(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(9*A-4*B-C)*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^2-(3*A-B)*tan(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^3,x,8,1/2*(13*A-6*B+2*C)*arctanh(sin(d*x+c))/a^3/d-2/15*(76*A-36*B+11*C)*tan(d*x+c)/a^3/d+1/2*(13*A-6*B+2*C)*sec(d*x+c)*tan(d*x+c)/a^3/d-1/5*(A-B+C)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(11*A-6*B+C)*sec(d*x+c)*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/15*(76*A-36*B+11*C)*sec(d*x+c)*tan(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^3,x,8,-1/2*(23*A-13*B+6*C)*arctanh(sin(d*x+c))/a^3/d+4/5*(34*A-19*B+9*C)*tan(d*x+c)/a^3/d-1/2*(23*A-13*B+6*C)*sec(d*x+c)*tan(d*x+c)/a^3/d-1/5*(A-B+C)*sec(d*x+c)^2*tan(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(13*A-8*B+3*C)*sec(d*x+c)^2*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/3*(23*A-13*B+6*C)*sec(d*x+c)^2*tan(d*x+c)/d/(a^3+a^3*cos(d*x+c))+4/15*(34*A-19*B+9*C)*tan(d*x+c)^3/a^3/d,1],
[cos(d*x+c)^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x,5,1/2*(2*A-8*B+21*C)*x/a^4-8/105*(20*A-83*B+216*C)*sin(d*x+c)/a^4/d+1/2*(2*A-8*B+21*C)*cos(d*x+c)*sin(d*x+c)/a^4/d-1/105*(10*A-52*B+129*C)*cos(d*x+c)^3*sin(d*x+c)/a^4/d/(1+cos(d*x+c))^2-4/105*(20*A-83*B+216*C)*cos(d*x+c)^2*sin(d*x+c)/a^4/d/(1+cos(d*x+c))-1/7*(A-B+C)*cos(d*x+c)^5*sin(d*x+c)/d/(a+a*cos(d*x+c))^4+1/5*(B-2*C)*cos(d*x+c)^4*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^3,1],
[cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x,8,(B-4*C)*x/a^4+1/105*(6*A-55*B+244*C)*sin(d*x+c)/a^4/d+1/105*(3*A+25*B-88*C)*cos(d*x+c)^2*sin(d*x+c)/a^4/d/(1+cos(d*x+c))^2-(B-4*C)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))-1/7*(A-B+C)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))^4+1/35*(2*A+5*B-12*C)*cos(d*x+c)^3*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^3,1],
[cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x,6,C*x/a^4-1/105*(8*A+6*B-55*C)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))^2+1/105*(16*A+12*B-215*C)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))-1/7*(A-B+C)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))^4+1/35*(4*A+3*B-10*C)*cos(d*x+c)^2*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^3,1],
[cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x,5,1/105*(23*A-2*B-54*C)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))^2+1/105*(8*A+13*B+36*C)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))-1/7*(A-B+C)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c))^4-1/35*(6*A+B-8*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^3,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^4,x,4,1/7*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^4+1/35*(3*A+4*B-11*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^3+1/105*(6*A+8*B+13*C)*sin(d*x+c)/d/(a^2+a^2*cos(d*x+c))^2+1/105*(6*A+8*B+13*C)*sin(d*x+c)/d/(a^4+a^4*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^4,x,6,A*arctanh(sin(d*x+c))/a^4/d-1/105*(55*A-6*B-8*C)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))^2-2/105*(80*A-3*B-4*C)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))-1/7*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^4-1/35*(10*A-3*B-4*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^3,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^4,x,8,-(4*A-B)*arctanh(sin(d*x+c))/a^4/d+2/105*(332*A-80*B+3*C)*tan(d*x+c)/a^4/d-1/105*(88*A-25*B-3*C)*tan(d*x+c)/a^4/d/(1+cos(d*x+c))^2-(4*A-B)*tan(d*x+c)/a^4/d/(1+cos(d*x+c))-1/7*(A-B+C)*tan(d*x+c)/d/(a+a*cos(d*x+c))^4-1/35*(12*A-5*B-2*C)*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^3,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^4,x,9,1/2*(21*A-8*B+2*C)*arctanh(sin(d*x+c))/a^4/d-8/105*(216*A-83*B+20*C)*tan(d*x+c)/a^4/d+1/2*(21*A-8*B+2*C)*sec(d*x+c)*tan(d*x+c)/a^4/d-1/105*(129*A-52*B+10*C)*sec(d*x+c)*tan(d*x+c)/a^4/d/(1+cos(d*x+c))^2-4/105*(216*A-83*B+20*C)*sec(d*x+c)*tan(d*x+c)/a^4/d/(1+cos(d*x+c))-1/7*(A-B+C)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c))^4-1/5*(2*A-B)*sec(d*x+c)*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^3,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^4,x,9,-1/2*(44*A-21*B+8*C)*arctanh(sin(d*x+c))/a^4/d+4/35*(454*A-216*B+83*C)*tan(d*x+c)/a^4/d-1/2*(44*A-21*B+8*C)*sec(d*x+c)*tan(d*x+c)/a^4/d-1/105*(178*A-87*B+31*C)*sec(d*x+c)^2*tan(d*x+c)/a^4/d/(1+cos(d*x+c))^2-1/3*(44*A-21*B+8*C)*sec(d*x+c)^2*tan(d*x+c)/a^4/d/(1+cos(d*x+c))-1/7*(A-B+C)*sec(d*x+c)^2*tan(d*x+c)/d/(a+a*cos(d*x+c))^4-1/35*(16*A-9*B+2*C)*sec(d*x+c)^2*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^3+4/105*(454*A-216*B+83*C)*tan(d*x+c)^3/a^4/d,1],
[cos(d*x+c)^3*sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,6,4/495*a*(99*A+88*B+80*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/693*a*(99*A+88*B+80*C)*cos(d*x+c)^3*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/99*a*(11*B+C)*cos(d*x+c)^4*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-8/3465*(99*A+88*B+80*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/11*C*cos(d*x+c)^4*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+4/1155*(99*A+88*B+80*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/a/d,1],
[cos(d*x+c)^2*sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,5,2/45*a*(21*A+18*B+16*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/63*a*(9*B+C)*cos(d*x+c)^3*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-4/315*(21*A+18*B+16*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/9*C*cos(d*x+c)^3*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/105*(21*A+18*B+16*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/a/d,1],
[cos(d*x+c)*sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,5,2/105*a*(35*A+49*B+27*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*(35*A-14*B+18*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/7*C*cos(d*x+c)^2*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/35*(7*B+C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/a/d,1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,3,2/15*a*(15*A+5*B+7*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*(5*B-2*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/5*C*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/a/d,1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,4,2*sqrt(a)*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+2/3*a*(3*B+C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/3*C*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,4,sqrt(a)*(A+2*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-a*(A-2*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+A*sqrt(a+a*cos(d*x+c))*tan(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,4,1/4*sqrt(a)*(3*A+4*B+8*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/4*a*(A+4*B)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/2*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,5,1/8*sqrt(a)*(5*A+6*B+8*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/8*a*(5*A+6*B+8*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/12*a*(A+6*B)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/3*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,6,1/64*sqrt(a)*(35*A+40*B+48*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/64*a*(35*A+40*B+48*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/96*a*(35*A+40*B+48*C)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/24*a*(A+8*B)*sec(d*x+c)^2*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/4*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^3*tan(d*x+c)/d,1],
[cos(d*x+c)^2*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,6,2/495*a^2*(429*A+374*B+336*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/693*a^2*(99*A+110*B+84*C)*cos(d*x+c)^3*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-4/3465*a*(429*A+374*B+336*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/99*a*(11*B+3*C)*cos(d*x+c)^3*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/1155*(429*A+374*B+336*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/11*C*cos(d*x+c)^3*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,6,8/315*a^2*(63*A+57*B+47*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/315*a*(63*A+57*B+47*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/315*(63*A-18*B+22*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/9*C*cos(d*x+c)^2*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/21*(3*B+C)*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/a/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,4,8/105*a^2*(35*A+21*B+19*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*a*(35*A+21*B+19*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/35*(7*B-2*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/7*C*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/a/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,5,2*a^(3/2)*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+2/15*a^2*(15*A+20*B+12*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*a*(5*B+3*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/5*C*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,5,a^(3/2)*(3*A+2*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/3*a^2*(3*A-6*B-8*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/3*a*(3*A-2*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+A*(a+a*cos(d*x+c))^(3/2)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,5,1/4*a^(3/2)*(7*A+12*B+8*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/4*a^2*(5*A+4*B-8*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/4*a*(3*A+4*B)*sqrt(a+a*cos(d*x+c))*tan(d*x+c)/d+1/2*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,5,1/8*a^(3/2)*(11*A+14*B+24*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/24*a^2*(19*A+30*B+24*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/4*a*(A+2*B)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,6,1/64*a^(3/2)*(75*A+88*B+112*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/64*a^2*(75*A+88*B+112*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/96*a^2*(39*A+56*B+48*C)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/24*a*(3*A+8*B)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,7,1/128*a^(3/2)*(133*A+150*B+176*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/128*a^2*(133*A+150*B+176*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/192*a^2*(133*A+150*B+176*C)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/240*a^2*(67*A+90*B+80*C)*sec(d*x+c)^2*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/40*a*(3*A+10*B)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^3*tan(d*x+c)/d+1/5*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^4*tan(d*x+c)/d,1],
[cos(d*x+c)^2*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,7,2/6435*a^3*(10439*A+9230*B+8368*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/9009*a^3*(2717*A+2522*B+2224*C)*cos(d*x+c)^3*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-4/45045*a^2*(10439*A+9230*B+8368*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/1287*a^2*(143*A+182*B+136*C)*cos(d*x+c)^3*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/15015*a*(10439*A+9230*B+8368*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/143*a*(13*B+5*C)*cos(d*x+c)^3*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/13*C*cos(d*x+c)^3*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,7,64/3465*a^3*(165*A+143*B+125*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+16/3465*a^2*(165*A+143*B+125*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/1155*a*(165*A+143*B+125*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/693*(99*A-22*B+26*C)*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d+2/11*C*cos(d*x+c)^2*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d+2/99*(11*B+5*C)*(a+a*cos(d*x+c))^(7/2)*sin(d*x+c)/a/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,5,64/315*a^3*(21*A+15*B+13*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+16/315*a^2*(21*A+15*B+13*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/105*a*(21*A+15*B+13*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/63*(9*B-2*C)*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d+2/9*C*(a+a*cos(d*x+c))^(7/2)*sin(d*x+c)/a/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,6,2*a^(5/2)*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+2/105*a^3*(245*A+224*B+160*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*a^2*(35*A+56*B+40*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/35*a*(7*B+5*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/7*C*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,6,a^(5/2)*(5*A+2*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/15*a^3*(15*A+70*B+64*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/15*a^2*(15*A-10*B-16*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d-1/5*a*(5*A-2*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+A*(a+a*cos(d*x+c))^(5/2)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,6,1/4*a^(5/2)*(19*A+20*B+8*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/12*a^3*(27*A-12*B-56*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/12*a^2*(21*A+12*B-8*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+1/4*a*(5*A+4*B)*(a+a*cos(d*x+c))^(3/2)*tan(d*x+c)/d+1/2*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,6,1/8*a^(5/2)*(25*A+38*B+40*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/24*a^3*(49*A+54*B-24*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/24*a^2*(31*A+42*B+24*C)*sqrt(a+a*cos(d*x+c))*tan(d*x+c)/d+1/12*a*(5*A+6*B)*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,6,1/64*a^(5/2)*(163*A+200*B+304*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/192*a^3*(299*A+392*B+432*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/32*a^2*(17*A+24*B+16*C)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/24*a*(5*A+8*B)*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,7,1/128*a^(5/2)*(283*A+326*B+400*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/128*a^3*(283*A+326*B+400*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/960*a^3*(787*A+950*B+1040*C)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/240*a^2*(79*A+110*B+80*C)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d+1/8*a*(A+2*B)*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^3*tan(d*x+c)/d+1/5*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^4*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x,8,1/512*a^(5/2)*(1015*A+1132*B+1304*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/512*a^3*(1015*A+1132*B+1304*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/768*a^3*(1015*A+1132*B+1304*C)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/960*a^3*(545*A+628*B+680*C)*sec(d*x+c)^2*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/480*a^2*(115*A+156*B+120*C)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^3*tan(d*x+c)/d+1/60*a*(5*A+12*B)*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^4*tan(d*x+c)/d+1/6*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^5*tan(d*x+c)/d,1],
[cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+a*cos(d*x+c)),x,8,-sqrt(2)*(A-B+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+4/315*(147*A-111*B+143*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*(21*A-3*B+19*C)*cos(d*x+c)^2*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/63*(9*B-C)*cos(d*x+c)^3*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/9*C*cos(d*x+c)^4*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-2/315*(21*A-93*B+29*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a/d,1],
[cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+a*cos(d*x+c)),x,7,sqrt(2)*(A-B+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-4/105*(35*A-49*B+37*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/35*(7*B-C)*cos(d*x+c)^2*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/7*C*cos(d*x+c)^3*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*(35*A-7*B+31*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a/d,1],
[cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+a*cos(d*x+c)),x,6,-sqrt(2)*(A-B+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+2/15*(15*A-10*B+14*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/5*C*cos(d*x+c)^2*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*(5*B-C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+a*cos(d*x+c)),x,4,sqrt(2)*(A-B+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+2/3*(3*B-2*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/3*C*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/sqrt(a+a*cos(d*x+c)),x,6,2*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-sqrt(2)*(A-B+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+2*C*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/sqrt(a+a*cos(d*x+c)),x,6,-(A-2*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+sqrt(2)*(A-B+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+A*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/sqrt(a+a*cos(d*x+c)),x,7,1/4*(7*A-4*B+8*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-sqrt(2)*(A-B+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-1/4*(A-4*B)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/2*A*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/sqrt(a+a*cos(d*x+c)),x,8,-1/8*(9*A-14*B+8*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+sqrt(2)*(A-B+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+1/8*(7*A-2*B+8*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/12*(A-6*B)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/3*A*sec(d*x+c)^2*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5/sqrt(a+a*cos(d*x+c)),x,9,1/64*(107*A-72*B+112*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-sqrt(2)*(A-B+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-1/64*(21*A-56*B+16*C)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/96*(43*A-8*B+48*C)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/24*(A-8*B)*sec(d*x+c)^2*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/4*A*sec(d*x+c)^3*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x,8,1/2*(11*A-15*B+19*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A-B+C)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)-1/105*(455*A-651*B+799*C)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/70*(35*A-63*B+67*C)*cos(d*x+c)^2*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))+1/14*(7*A-7*B+11*C)*cos(d*x+c)^3*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))+1/210*(245*A-273*B+397*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a^2/d,1],
[cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x,7,-1/2*(7*A-11*B+15*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A-B+C)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/15*(45*A-65*B+93*C)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))+1/10*(5*A-5*B+9*C)*cos(d*x+c)^2*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/30*(15*A-35*B+39*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a^2/d,1],
[cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x,6,1/2*(3*A-7*B+11*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A-B+C)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)-1/3*(3*A-9*B+13*C)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))+1/6*(3*A-3*B+7*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a^2/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x,4,1/2*(A+3*B-7*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d+1/2*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+2*C*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(3/2),x,6,2*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(3/2)/d-1/2*(5*A-B-3*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(3/2),x,7,-(3*A-2*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(3/2)/d+1/2*(9*A-5*B+C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A-B+C)*tan(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/2*(3*A-B+C)*tan(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(3/2),x,8,1/4*(19*A-12*B+8*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(3/2)/d-1/2*(13*A-9*B+5*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/4*(7*A-6*B+2*C)*tan(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/2*(A-B+C)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/2*(2*A-B+C)*sec(d*x+c)*tan(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+a*cos(d*x+c))^(3/2),x,9,-1/8*(47*A-38*B+24*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(3/2)/d+1/2*(17*A-13*B+9*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d+1/8*(21*A-14*B+12*C)*tan(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/12*(13*A-12*B+6*C)*sec(d*x+c)*tan(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/2*(A-B+C)*sec(d*x+c)^2*tan(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/6*(5*A-3*B+3*C)*sec(d*x+c)^2*tan(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x,8,-1/16*(75*A-163*B+283*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A-B+C)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(5*A-13*B+21*C)*cos(d*x+c)^3*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+1/120*(465*A-985*B+1729*C)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))+1/80*(45*A-85*B+157*C)*cos(d*x+c)^2*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))-1/240*(195*A-475*B+787*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a^3/d,1],
[cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x,7,1/16*(19*A-75*B+163*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A-B+C)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(A-9*B+17*C)*cos(d*x+c)^2*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)-1/24*(21*A-93*B+197*C)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))+1/48*(15*A-39*B+95*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a^3/d,1],
[cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x,6,1/16*(5*A+19*B-75*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A-B+C)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(3*A+5*B-13*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+1/4*(A-B+9*C)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x,4,1/16*(3*A+5*B+19*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d+1/4*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)+1/16*(3*A+5*B-13*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+a*cos(d*x+c))^(5/2),x,7,2*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(5/2)/d-1/16*(43*A-3*B-5*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(11*A-3*B-5*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+a*cos(d*x+c))^(5/2),x,8,-(5*A-2*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(5/2)/d+1/16*(115*A-43*B+3*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A-B+C)*tan(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(15*A-7*B-C)*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+1/16*(35*A-11*B+3*C)*tan(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+a*cos(d*x+c))^(5/2),x,9,1/4*(39*A-20*B+8*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(5/2)/d-1/16*(219*A-115*B+43*C)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/16*(63*A-35*B+11*C)*tan(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))-1/4*(A-B+C)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(19*A-11*B+3*C)*sec(d*x+c)*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+1/16*(31*A-15*B+7*C)*sec(d*x+c)*tan(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,6,6/5*B*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(7*A+5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*(7*A+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*B*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*C*cos(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,5,2/5*(5*A+3*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*B*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*B*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*C*cos(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,4,2*B*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(3*A+C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*C*sqrt(cos(d*x+c))*sin(d*x+c)/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,4,-2*(A-C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2*B*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2*A*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,5,-2*B*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(A+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*A*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2*B*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,6,-2/5*(3*A+5*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*B*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/5*A*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/3*B*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*(3*A+5*C)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,8,2/15*a*(9*A+7*B+7*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+10/231*a*(11*A+11*B+9*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+10/231*a*(11*A+11*B+9*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*a*(9*A+7*B+7*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/77*a*(11*A+11*B+9*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/9*a*(B+C)*cos(d*x+c)^(7/2)*sin(d*x+c)/d+2/11*a*C*cos(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,7,2/15*a*(9*A+9*B+7*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*a*(7*A+5*B+5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*a*(7*A+5*B+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*a*(9*A+9*B+7*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*a*(B+C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/9*a*C*cos(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,6,2/5*a*(5*A+3*B+3*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*a*(7*A+7*B+5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*a*(7*A+7*B+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*a*(B+C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*a*C*cos(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,5,2/5*a*(5*A+5*B+3*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*a*(3*A+B+C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*a*(B+C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*a*C*cos(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,5,-2*a*(A-B-C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*a*(3*A+3*B+C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2*a*A*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*a*C*sqrt(cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,5,-2*a*(A+B-C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*a*(A+3*B+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*a*A*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2*a*(A+B)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,6,-2/5*a*(3*A+5*B+5*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*a*(A+B+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/5*a*A*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/3*a*(A+B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*a*(3*A+5*B+5*C)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,7,-2/5*a*(3*A+3*B+5*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*a*(5*A+7*B+7*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/7*a*A*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/5*a*(A+B)*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/21*a*(5*A+7*B+7*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*a*(3*A+3*B+5*C)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,9,4/15*a^2*(9*A+8*B+7*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/231*a^2*(66*A+55*B+50*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/231*a^2*(66*A+55*B+50*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+4/45*a^2*(9*A+8*B+7*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/693*a^2*(99*A+121*B+89*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/11*C*cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+2/99*(11*B+4*C)*cos(d*x+c)^(5/2)*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,8,4/15*a^2*(12*A+9*B+8*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^2*(7*A+6*B+5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/21*a^2*(7*A+6*B+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/105*a^2*(21*A+27*B+19*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/9*C*cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+2/63*(9*B+4*C)*cos(d*x+c)^(3/2)*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,7,4/5*a^2*(5*A+4*B+3*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^2*(14*A+7*B+6*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/105*a^2*(35*A+49*B+33*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/7*C*sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+2/35*(7*B+4*C)*sqrt(cos(d*x+c))*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,7,4/5*a^2*(5*B+4*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/3*a^2*(3*A+2*B+C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-2/15*a^2*(15*A-5*B-7*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2*A*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(cos(d*x+c))-2/5*(5*A-C)*sqrt(cos(d*x+c))*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,7,-4*a^2*(A-C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/3*a^2*(2*A+3*B+2*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-2/3*a^2*(5*A+3*B-C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/3*A*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/3*(4*A+3*B)*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,7,-4/5*a^2*(4*A+5*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/3*a^2*(A+2*B+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/15*a^2*(17*A+25*B+15*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/5*A*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/15*(4*A+5*B)*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,8,-4/5*a^2*(3*A+4*B+5*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^2*(6*A+7*B+14*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/105*a^2*(33*A+49*B+35*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+4/5*a^2*(3*A+4*B+5*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/7*A*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/35*(4*A+7*B)*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,9,-4/15*a^2*(8*A+9*B+12*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^2*(5*A+6*B+7*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/105*a^2*(19*A+27*B+21*C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)+4/21*a^2*(5*A+6*B+7*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+4/15*a^2*(8*A+9*B+12*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/9*A*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(9/2)+2/63*(4*A+9*B)*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,10,4/195*a^3*(221*A+195*B+175*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/231*a^3*(121*A+105*B+95*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/231*a^3*(121*A+105*B+95*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+4/585*a^3*(221*A+195*B+175*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+20/9009*a^3*(286*A+273*B+236*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/13*C*cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+2/143*(13*B+6*C)*cos(d*x+c)^(5/2)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d+2/1287*(143*A+195*B+145*C)*cos(d*x+c)^(5/2)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,9,4/15*a^3*(21*A+17*B+15*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/231*a^3*(143*A+121*B+105*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/231*a^3*(143*A+121*B+105*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+4/1155*a^3*(264*A+253*B+210*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/11*C*cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+2/99*(11*B+6*C)*cos(d*x+c)^(3/2)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d+2/693*(99*A+143*B+105*C)*cos(d*x+c)^(3/2)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,8,4/15*a^3*(27*A+21*B+17*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^3*(21*A+13*B+11*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/105*a^3*(42*A+41*B+32*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/9*C*sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+2/21*(3*B+2*C)*sqrt(cos(d*x+c))*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d+2/315*(63*A+99*B+73*C)*sqrt(cos(d*x+c))*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,8,4/5*a^3*(5*A+9*B+7*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^3*(35*A+21*B+13*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-4/105*a^3*(35*A-42*B-41*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2*A*(a+a*cos(d*x+c))^3*sin(d*x+c)/d/sqrt(cos(d*x+c))-2/7*(7*A-C)*sqrt(cos(d*x+c))*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d-2/35*(35*A-7*B-11*C)*sqrt(cos(d*x+c))*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,8,-4/5*a^3*(5*A-5*B-9*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/3*a^3*(5*A+5*B+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-4/15*a^3*(20*A+5*B-6*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/3*A*(a+a*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2*(2*A+B)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d/sqrt(cos(d*x+c))-2/15*(35*A+15*B-3*C)*sqrt(cos(d*x+c))*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,8,-4/5*a^3*(9*A+5*B-5*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/3*a^3*(3*A+5*B+5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-4/15*a^3*(21*A+20*B+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*A*(a+a*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/15*(6*A+5*B)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)+2/15*(33*A+35*B+15*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,8,-4/5*a^3*(7*A+9*B+5*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^3*(13*A+21*B+35*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/105*a^3*(106*A+147*B+140*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/7*A*(a+a*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/35*(6*A+7*B)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)+2/15*(7*A+9*B+5*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,9,-4/15*a^3*(17*A+21*B+27*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^3*(11*A+13*B+21*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/105*a^3*(32*A+41*B+42*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+4/15*a^3*(17*A+21*B+27*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/9*A*(a+a*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(9/2)+2/21*(2*A+3*B)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d/cos(d*x+c)^(7/2)+2/315*(73*A+99*B+63*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x,10,-4/15*a^3*(15*A+17*B+21*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/231*a^3*(105*A+121*B+143*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/1155*a^3*(210*A+253*B+264*C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)+4/231*a^3*(105*A+121*B+143*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+4/15*a^3*(15*A+17*B+21*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/11*A*(a+a*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(11/2)+2/99*(6*A+11*B)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d/cos(d*x+c)^(9/2)+2/693*(105*A+143*B+99*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x,7,-3/5*(5*A-7*B+7*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d+5/21*(7*A-7*B+9*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d+5/21*(7*A-7*B+9*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d-1/5*(5*A-7*B+7*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/a/d+1/7*(7*A-7*B+9*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/a/d-(A-B+C)*cos(d*x+c)^(7/2)*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x,6,3/5*(5*A-5*B+7*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d-1/3*(3*A-5*B+5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d-1/3*(3*A-5*B+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d+1/5*(5*A-5*B+7*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/a/d-(A-B+C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c)),x,5,-(A-3*B+3*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d+1/3*(3*A-3*B+5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d+1/3*(3*A-3*B+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d-(A-B+C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+a*cos(d*x+c)),x,4,(A-B+3*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d+(A+B-C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d-(A-B+C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x,5,-(3*A-B+C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d-(A-B-C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d+(3*A-B+C)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))-(A-B+C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x,6,(3*A-3*B+C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d+1/3*(5*A-3*B+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d+1/3*(5*A-3*B+3*C)*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)-(3*A-3*B+C)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))-(A-B+C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c)),x,7,-3/5*(7*A-5*B+5*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d-1/3*(5*A-5*B+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d+1/5*(7*A-5*B+5*C)*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)-1/3*(5*A-5*B+3*C)*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)+3/5*(7*A-5*B+5*C)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))-(A-B+C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c)),1],
[cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,7,1/5*(20*A-35*B+56*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d-5/3*(A-2*B+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d-5/3*(A-2*B+3*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d+1/15*(20*A-35*B+56*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/a^2/d-(A-2*B+3*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A-B+C)*cos(d*x+c)^(7/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,6,-(A-4*B+7*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d+1/3*(2*A-5*B+10*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d+1/3*(2*A-5*B+10*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d-1/3*(A-4*B+7*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A-B+C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2,x,5,-(B-4*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d+1/3*(A+2*B-5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d+1/3*(A+2*B-5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A-B+C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^2,x,5,(A-C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d+1/3*(2*A+B+2*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d-(A-C)*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A-B+C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x,6,-(4*A-B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d-1/3*(5*A-2*B-C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d+(4*A-B)*sin(d*x+c)/a^2/d/sqrt(cos(d*x+c))-1/3*(5*A-2*B-C)*sin(d*x+c)/a^2/d/sqrt(cos(d*x+c))/(1+cos(d*x+c))-1/3*(A-B+C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^2,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x,7,(7*A-4*B+C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d+1/3*(10*A-5*B+2*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d+1/3*(10*A-5*B+2*C)*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2)-(7*A-4*B+C)*sin(d*x+c)/a^2/d/sqrt(cos(d*x+c))-1/3*(7*A-4*B+C)*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2)/(1+cos(d*x+c))-1/3*(A-B+C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,1],
[cos(d*x+c)^(7/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,8,7/10*(7*A-17*B+33*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d-1/6*(13*A-33*B+63*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d-1/6*(13*A-33*B+63*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a^3/d+7/30*(7*A-17*B+33*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/a^3/d-1/5*(A-B+C)*cos(d*x+c)^(9/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(2*A-7*B+12*C)*cos(d*x+c)^(7/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/10*(13*A-33*B+63*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,7,-1/10*(9*A-49*B+119*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d+1/6*(3*A-13*B+33*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d+1/6*(3*A-13*B+33*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a^3/d-1/5*(A-B+C)*cos(d*x+c)^(7/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/3*(B-2*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/30*(9*A-49*B+119*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,6,-1/10*(A+9*B-49*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d+1/6*(A+3*B-13*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d-1/5*(A-B+C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/15*(2*A+3*B-8*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+1/6*(A+3*B-13*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3,x,6,1/10*(A-B-9*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d+1/6*(A+B+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d-1/5*(A-B+C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/15*(4*A+B-6*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/10*(A-B-9*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^3,x,6,1/10*(9*A+B-C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d+1/6*(3*A+B+C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d-1/5*(A-B+C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(6*A-B-4*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/10*(9*A+B-C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x,7,-1/10*(49*A-9*B-C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d-1/6*(13*A-3*B-C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d+1/10*(49*A-9*B-C)*sin(d*x+c)/a^3/d/sqrt(cos(d*x+c))-1/5*(A-B+C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^3-1/15*(8*A-3*B-2*C)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^2-1/6*(13*A-3*B-C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/(a^3+a^3*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x,8,1/10*(119*A-49*B+9*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d+1/6*(33*A-13*B+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d+1/6*(33*A-13*B+3*C)*sin(d*x+c)/a^3/d/cos(d*x+c)^(3/2)-1/10*(119*A-49*B+9*C)*sin(d*x+c)/a^3/d/sqrt(cos(d*x+c))-1/5*(A-B+C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3-1/3*(2*A-B)*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2-1/30*(119*A-49*B+9*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/(a^3+a^3*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,6,1/64*sqrt(a)*(48*A+40*B+35*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/64*a*(48*A+40*B+35*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/96*a*(48*A+40*B+35*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/24*a*(8*B+C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/4*C*cos(d*x+c)^(5/2)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,5,1/8*sqrt(a)*(8*A+6*B+5*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/8*a*(8*A+6*B+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/12*a*(6*B+C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/3*C*cos(d*x+c)^(3/2)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,4,1/4*sqrt(a)*(8*A+4*B+3*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/4*a*(4*B+C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/2*C*sqrt(cos(d*x+c))*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,4,sqrt(a)*(2*B+C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-a*(2*A-C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2*A*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,4,2*sqrt(a)*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+2/3*a*(A+3*B)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/3*A*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,3,2/15*a*(A+5*B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+2/15*a*(8*A+10*B+15*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/5*A*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,4,2/35*a*(A+7*B)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+2/105*a*(24*A+28*B+35*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+4/105*a*(24*A+28*B+35*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/7*A*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,5,2/63*a*(A+9*B)*sin(d*x+c)/d/cos(d*x+c)^(7/2)/sqrt(a+a*cos(d*x+c))+2/105*a*(16*A+18*B+21*C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+8/315*a*(16*A+18*B+21*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+16/315*a*(16*A+18*B+21*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/9*A*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(9/2),1],
[cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,7,1/128*a^(3/2)*(176*A+150*B+133*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/128*a^2*(176*A+150*B+133*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/192*a^2*(176*A+150*B+133*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/240*a^2*(80*A+90*B+67*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/40*a*(10*B+3*C)*cos(d*x+c)^(5/2)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+1/5*C*cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,6,1/64*a^(3/2)*(112*A+88*B+75*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/64*a^2*(112*A+88*B+75*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/96*a^2*(48*A+56*B+39*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/24*a*(8*B+3*C)*cos(d*x+c)^(3/2)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+1/4*C*cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,5,1/8*a^(3/2)*(24*A+14*B+11*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/24*a^2*(24*A+30*B+19*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/4*a*(2*B+C)*sqrt(cos(d*x+c))*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+1/3*C*sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,5,1/4*a^(3/2)*(8*A+12*B+7*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/4*a^2*(8*A-4*B-5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/2*a*(4*A-C)*sqrt(cos(d*x+c))*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2*A*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,5,a^(3/2)*(2*B+3*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/3*a^2*(8*A+6*B-3*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2*a*(A+B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*A*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,5,2*a^(3/2)*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+2/15*a^2*(12*A+20*B+15*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/15*a*(3*A+5*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*A*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,4,2/15*a^2*(4*A+6*B+5*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+2/105*a^2*(104*A+126*B+175*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/35*a*(3*A+7*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/7*A*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,5,2/315*a^2*(52*A+72*B+63*C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+2/315*a^2*(136*A+156*B+189*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+4/315*a^2*(136*A+156*B+189*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/21*a*(A+3*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/9*A*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(9/2),1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x,6,2/693*a^2*(84*A+110*B+99*C)*sin(d*x+c)/d/cos(d*x+c)^(7/2)/sqrt(a+a*cos(d*x+c))+2/1155*a^2*(336*A+374*B+429*C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+8/3465*a^2*(336*A+374*B+429*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+16/3465*a^2*(336*A+374*B+429*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/99*a*(3*A+11*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(9/2)+2/11*A*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(11/2),1],
[cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,8,1/512*a^(5/2)*(1304*A+1132*B+1015*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/512*a^3*(1304*A+1132*B+1015*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/768*a^3*(1304*A+1132*B+1015*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/960*a^3*(680*A+628*B+545*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/480*a^2*(120*A+156*B+115*C)*cos(d*x+c)^(5/2)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+1/60*a*(12*B+5*C)*cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+1/6*C*cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,7,1/128*a^(5/2)*(400*A+326*B+283*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/128*a^3*(400*A+326*B+283*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/960*a^3*(1040*A+950*B+787*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/240*a^2*(80*A+110*B+79*C)*cos(d*x+c)^(3/2)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+1/8*a*(2*B+C)*cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+1/5*C*cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,6,1/64*a^(5/2)*(304*A+200*B+163*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/192*a^3*(432*A+392*B+299*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/32*a^2*(16*A+24*B+17*C)*sqrt(cos(d*x+c))*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+1/24*a*(8*B+5*C)*sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+1/4*C*sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,6,1/8*a^(5/2)*(40*A+38*B+25*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/24*a^3*(24*A-54*B-49*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/4*a^2*(8*A-2*B-3*C)*sqrt(cos(d*x+c))*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d-1/3*a*(6*A-C)*sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2*A*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,6,1/4*a^(5/2)*(8*A+20*B+19*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/12*a^3*(56*A+12*B-27*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/2*a^2*(8*A+4*B-C)*sqrt(cos(d*x+c))*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/3*a*(5*A+3*B)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*A*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,6,a^(5/2)*(2*B+5*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/15*a^3*(64*A+70*B+15*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/5*a^2*(8*A+10*B+5*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*a*(A+B)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*A*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,6,2*a^(5/2)*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+2/105*a^3*(160*A+224*B+245*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/105*a^2*(40*A+56*B+35*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/35*a*(5*A+7*B)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/7*A*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,5,2/15*a^3*(8*A+10*B+11*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+2/315*a^3*(584*A+690*B+903*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/315*a^2*(64*A+90*B+63*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/63*a*(5*A+9*B)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/9*A*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(9/2),1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x,6,2/3465*a^3*(1160*A+1364*B+1485*C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+2/3465*a^3*(2840*A+3212*B+3795*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+4/3465*a^3*(2840*A+3212*B+3795*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/231*a^2*(32*A+44*B+33*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/99*a*(5*A+11*B)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(9/2)+2/11*A*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(11/2),1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(15/2),x,7,2/9009*a^3*(2224*A+2522*B+2717*C)*sin(d*x+c)/d/cos(d*x+c)^(7/2)/sqrt(a+a*cos(d*x+c))+2/15015*a^3*(8368*A+9230*B+10439*C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+8/45045*a^3*(8368*A+9230*B+10439*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+16/45045*a^3*(8368*A+9230*B+10439*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/1287*a^2*(136*A+182*B+143*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(9/2)+2/143*a*(5*A+13*B)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(11/2)+2/13*A*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(13/2),1],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+a*cos(d*x+c)),x,8,-1/8*(8*A-14*B+9*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+sqrt(2)*(A-B+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+1/8*(8*A-2*B+7*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/12*(6*B-C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/3*C*cos(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+a*cos(d*x+c)),x,7,1/4*(8*A-4*B+7*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-sqrt(2)*(A-B+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+1/4*(4*B-C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/2*C*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),x,6,(2*B-C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+sqrt(2)*(A-B+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+C*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c)),x,6,2*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-sqrt(2)*(A-B+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+2*A*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c)),x,5,sqrt(2)*(A-B+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+2/3*A*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))-2/3*(A-3*B)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/sqrt(a+a*cos(d*x+c)),x,6,-sqrt(2)*(A-B+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+2/5*A*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))-2/15*(A-5*B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+2/15*(13*A-5*B+15*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/sqrt(a+a*cos(d*x+c)),x,7,sqrt(2)*(A-B+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+2/7*A*sin(d*x+c)/d/cos(d*x+c)^(7/2)/sqrt(a+a*cos(d*x+c))-2/35*(A-7*B)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+2/105*(31*A-7*B+35*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))-2/105*(43*A-91*B+35*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)^2)/sqrt(a+a*cos(d*x+c)),x,7,1/4*(8*A*a-4*A*b-4*B*a+7*B*b)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-sqrt(2)*(a-b)*(A-B)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+1/4*(4*A*b+4*B*a-B*b)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/2*b*B*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x,8,1/4*(8*A-12*B+19*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(3/2)/d-1/2*(5*A-9*B+13*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A-B+C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)-1/4*(2*A-6*B+7*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))+1/2*(A-B+2*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2),x,7,(2*B-3*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(3/2)/d+1/2*(A-5*B+9*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A-B+C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/2*(A-B+3*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x,6,2*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(3/2)/d+1/2*(3*A+B-5*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A-B+C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x,5,-1/2*(7*A-3*B-C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A-B+C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^(3/2)+1/2*(5*A-B+C)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x,6,1/2*(11*A-7*B+3*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A-B+C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2)+1/6*(7*A-3*B+3*C)*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))-1/6*(19*A-15*B+3*C)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x,7,-1/2*(15*A-11*B+7*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(3/2)/d-1/2*(A-B+C)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2)+1/10*(9*A-5*B+5*C)*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))-1/30*(39*A-35*B+15*C)*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+1/30*(147*A-95*B+75*C)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x,8,(2*B-5*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(5/2)/d+1/16*(3*A-43*B+115*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A-B+C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)+1/16*(A+7*B-15*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+1/16*(3*A-11*B+35*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2),x,7,2*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(5/2)/d+1/16*(5*A+3*B-43*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A-B+C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)+1/16*(5*A+3*B-11*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x,5,1/16*(19*A+5*B+3*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A-B+C)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(9*A-B-7*C)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x,6,-1/16*(75*A-19*B-5*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A-B+C)*sin(d*x+c)/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^(5/2)-1/16*(13*A-5*B-3*C)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^(3/2)+1/16*(49*A-9*B+C)*sin(d*x+c)/a^2/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x,7,1/16*(163*A-75*B+19*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-1/4*(A-B+C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2)-1/16*(17*A-9*B+C)*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2)+1/48*(95*A-39*B+15*C)*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))-1/48*(299*A-147*B+27*C)*sin(d*x+c)/a^2/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)^2*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,7,1/8*a*(4*A+3*C)*x+1/5*b*(5*A+4*C)*sin(d*x+c)/d+1/8*a*(4*A+3*C)*cos(d*x+c)*sin(d*x+c)/d+1/4*a*C*cos(d*x+c)^3*sin(d*x+c)/d+1/5*b*C*cos(d*x+c)^4*sin(d*x+c)/d-1/15*b*(5*A+4*C)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,3,1/8*b*(4*A+3*C)*x+1/3*a*(3*A+2*C)*sin(d*x+c)/d+1/8*b*(4*A+3*C)*cos(d*x+c)*sin(d*x+c)/d+1/3*a*C*cos(d*x+c)^2*sin(d*x+c)/d+1/4*b*C*cos(d*x+c)^3*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,2,1/2*a*(2*A+C)*x-1/3*(a^2*C-b^2*(3*A+2*C))*sin(d*x+c)/b/d-1/6*a*C*cos(d*x+c)*sin(d*x+c)/d+1/3*C*(a+b*cos(d*x+c))^2*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c),x,4,1/2*b*(2*A+C)*x+a*A*arctanh(sin(d*x+c))/d+a*C*sin(d*x+c)/d+1/2*b*C*cos(d*x+c)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,4,a*C*x+A*b*arctanh(sin(d*x+c))/d+b*C*sin(d*x+c)/d+a*A*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,4,b*C*x+1/2*a*(A+2*C)*arctanh(sin(d*x+c))/d+A*b*tan(d*x+c)/d+1/2*a*A*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,6,1/2*b*(A+2*C)*arctanh(sin(d*x+c))/d+1/3*a*(2*A+3*C)*tan(d*x+c)/d+1/2*A*b*sec(d*x+c)*tan(d*x+c)/d+1/3*a*A*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,7,1/8*a*(3*A+4*C)*arctanh(sin(d*x+c))/d+1/3*b*(2*A+3*C)*tan(d*x+c)/d+1/8*a*(3*A+4*C)*sec(d*x+c)*tan(d*x+c)/d+1/3*A*b*sec(d*x+c)^2*tan(d*x+c)/d+1/4*a*A*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,7,1/8*b*(3*A+4*C)*arctanh(sin(d*x+c))/d+1/5*a*(4*A+5*C)*tan(d*x+c)/d+1/8*b*(3*A+4*C)*sec(d*x+c)*tan(d*x+c)/d+1/4*A*b*sec(d*x+c)^3*tan(d*x+c)/d+1/5*a*A*sec(d*x+c)^4*tan(d*x+c)/d+1/15*a*(4*A+5*C)*tan(d*x+c)^3/d,1],
[cos(d*x+c)^2*(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x,8,1/16*(b^2*(6*A+5*C)+a^2*(8*A+6*C))*x+2/5*a*b*(5*A+4*C)*sin(d*x+c)/d+1/16*(b^2*(6*A+5*C)+a^2*(8*A+6*C))*cos(d*x+c)*sin(d*x+c)/d+1/24*(2*a^2*C+b^2*(6*A+5*C))*cos(d*x+c)^3*sin(d*x+c)/d+1/15*a*b*C*cos(d*x+c)^4*sin(d*x+c)/d+1/6*C*cos(d*x+c)^3*(a+b*cos(d*x+c))^2*sin(d*x+c)/d-2/15*a*b*(5*A+4*C)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x,4,1/4*a*b*(4*A+3*C)*x+1/15*(5*a^2*(3*A+2*C)+2*b^2*(5*A+4*C))*sin(d*x+c)/d+1/4*a*b*(4*A+3*C)*cos(d*x+c)*sin(d*x+c)/d+1/15*(2*a^2*C+b^2*(5*A+4*C))*cos(d*x+c)^2*sin(d*x+c)/d+1/10*a*b*C*cos(d*x+c)^3*sin(d*x+c)/d+1/5*C*cos(d*x+c)^2*(a+b*cos(d*x+c))^2*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x,3,1/8*(4*a^2*(2*A+C)+b^2*(4*A+3*C))*x+1/6*a*(12*A*b^2-C*a^2+8*C*b^2)*sin(d*x+c)/b/d-1/24*(2*a^2*C-3*b^2*(4*A+3*C))*cos(d*x+c)*sin(d*x+c)/d-1/12*a*C*(a+b*cos(d*x+c))^2*sin(d*x+c)/b/d+1/4*C*(a+b*cos(d*x+c))^3*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c),x,5,a*b*(2*A+C)*x+a^2*A*arctanh(sin(d*x+c))/d+1/3*(3*A*b^2+2*(a^2+b^2)*C)*sin(d*x+c)/d+1/3*a*b*C*cos(d*x+c)*sin(d*x+c)/d+1/3*C*(a+b*cos(d*x+c))^2*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,5,1/2*(2*A*b^2+(2*a^2+b^2)*C)*x+2*a*A*b*arctanh(sin(d*x+c))/d-2*a*b*(A-C)*sin(d*x+c)/d-1/2*b^2*(2*A-C)*cos(d*x+c)*sin(d*x+c)/d+A*(a+b*cos(d*x+c))^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,5,2*a*b*C*x+1/2*(2*A*b^2+a^2*(A+2*C))*arctanh(sin(d*x+c))/d-1/2*b^2*(A-2*C)*sin(d*x+c)/d+a*A*b*tan(d*x+c)/d+1/2*A*(a+b*cos(d*x+c))^2*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,5,b^2*C*x+a*b*(A+2*C)*arctanh(sin(d*x+c))/d+1/3*(2*A*b^2+a^2*(2*A+3*C))*tan(d*x+c)/d+1/3*a*A*b*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(a+b*cos(d*x+c))^2*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,7,1/8*(4*b^2*(A+2*C)+a^2*(3*A+4*C))*arctanh(sin(d*x+c))/d+2/3*a*b*(2*A+3*C)*tan(d*x+c)/d+1/8*(2*A*b^2+a^2*(3*A+4*C))*sec(d*x+c)*tan(d*x+c)/d+1/6*a*A*b*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a+b*cos(d*x+c))^2*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,8,1/4*a*b*(3*A+4*C)*arctanh(sin(d*x+c))/d+1/15*(5*b^2*(2*A+3*C)+2*a^2*(4*A+5*C))*tan(d*x+c)/d+1/4*a*b*(3*A+4*C)*sec(d*x+c)*tan(d*x+c)/d+1/15*(2*A*b^2+a^2*(4*A+5*C))*sec(d*x+c)^2*tan(d*x+c)/d+1/10*a*A*b*sec(d*x+c)^3*tan(d*x+c)/d+1/5*A*(a+b*cos(d*x+c))^2*sec(d*x+c)^4*tan(d*x+c)/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x,5,1/16*b*(6*a^2*(4*A+3*C)+b^2*(6*A+5*C))*x+1/15*a*(5*a^2*(3*A+2*C)+6*b^2*(5*A+4*C))*sin(d*x+c)/d+1/16*b*(6*a^2*(4*A+3*C)+b^2*(6*A+5*C))*cos(d*x+c)*sin(d*x+c)/d+1/15*a*(15*A*b^2+(a^2+12*b^2)*C)*cos(d*x+c)^2*sin(d*x+c)/d+1/120*b*(6*a^2*C+5*b^2*(6*A+5*C))*cos(d*x+c)^3*sin(d*x+c)/d+1/10*a*C*cos(d*x+c)^2*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+1/6*C*cos(d*x+c)^2*(a+b*cos(d*x+c))^3*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x,4,1/8*a*(4*a^2*(2*A+C)+3*b^2*(4*A+3*C))*x-1/30*(3*a^4*C-4*b^4*(5*A+4*C)-4*a^2*b^2*(20*A+13*C))*sin(d*x+c)/b/d+1/120*a*(100*A*b^2-6*C*a^2+71*C*b^2)*cos(d*x+c)*sin(d*x+c)/d-1/60*(3*a^2*C-4*b^2*(5*A+4*C))*(a+b*cos(d*x+c))^2*sin(d*x+c)/b/d-1/20*a*C*(a+b*cos(d*x+c))^3*sin(d*x+c)/b/d+1/5*C*(a+b*cos(d*x+c))^4*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c),x,6,1/8*b*(12*a^2*(2*A+C)+b^2*(4*A+3*C))*x+a^3*A*arctanh(sin(d*x+c))/d+1/2*a*(6*A*b^2+(a^2+4*b^2)*C)*sin(d*x+c)/d+1/8*b*(2*a^2*C+b^2*(4*A+3*C))*cos(d*x+c)*sin(d*x+c)/d+1/4*a*C*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+1/4*C*(a+b*cos(d*x+c))^3*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,6,1/2*a*(6*A*b^2+2*C*a^2+3*C*b^2)*x+3*a^2*A*b*arctanh(sin(d*x+c))/d-1/3*b*(a^2*(6*A-8*C)-b^2*(3*A+2*C))*sin(d*x+c)/d-1/6*a*b^2*(6*A-5*C)*cos(d*x+c)*sin(d*x+c)/d-1/3*b*(3*A-C)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+A*(a+b*cos(d*x+c))^3*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,6,1/2*b*(2*A*b^2+(6*a^2+b^2)*C)*x+1/2*a*(6*A*b^2+a^2*(A+2*C))*arctanh(sin(d*x+c))/d-3/2*a*b^2*(3*A-2*C)*sin(d*x+c)/d-1/2*b^3*(4*A-C)*cos(d*x+c)*sin(d*x+c)/d+3/2*A*b*(a+b*cos(d*x+c))^2*tan(d*x+c)/d+1/2*A*(a+b*cos(d*x+c))^3*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,6,3*a*b^2*C*x+1/2*b*(2*A*b^2+3*a^2*(A+2*C))*arctanh(sin(d*x+c))/d-1/6*b^3*(5*A-6*C)*sin(d*x+c)/d+1/3*a*(3*A*b^2+a^2*(2*A+3*C))*tan(d*x+c)/d+1/2*A*b*(a+b*cos(d*x+c))^2*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(a+b*cos(d*x+c))^3*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,6,b^3*C*x+1/8*a*(12*b^2*(A+2*C)+a^2*(3*A+4*C))*arctanh(sin(d*x+c))/d+1/2*b*(A*b^2+a^2*(4*A+6*C))*tan(d*x+c)/d+1/8*a*(2*A*b^2+a^2*(3*A+4*C))*sec(d*x+c)*tan(d*x+c)/d+1/4*A*b*(a+b*cos(d*x+c))^2*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a+b*cos(d*x+c))^3*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,8,1/8*b*(4*b^2*(A+2*C)+3*a^2*(3*A+4*C))*arctanh(sin(d*x+c))/d+1/15*a*(15*b^2*(2*A+3*C)+2*a^2*(4*A+5*C))*tan(d*x+c)/d+3/40*b*(2*A*b^2+5*a^2*(3*A+4*C))*sec(d*x+c)*tan(d*x+c)/d+1/30*a*(3*A*b^2+2*a^2*(4*A+5*C))*sec(d*x+c)^2*tan(d*x+c)/d+3/20*A*b*(a+b*cos(d*x+c))^2*sec(d*x+c)^3*tan(d*x+c)/d+1/5*A*(a+b*cos(d*x+c))^3*sec(d*x+c)^4*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,x,9,1/16*a*(6*b^2*(3*A+4*C)+a^2*(5*A+6*C))*arctanh(sin(d*x+c))/d+1/15*b*(5*b^2*(2*A+3*C)+6*a^2*(4*A+5*C))*tan(d*x+c)/d+1/16*a*(6*b^2*(3*A+4*C)+a^2*(5*A+6*C))*sec(d*x+c)*tan(d*x+c)/d+1/15*b*(A*b^2+3*a^2*(4*A+5*C))*sec(d*x+c)^2*tan(d*x+c)/d+1/120*a*(6*A*b^2+5*a^2*(5*A+6*C))*sec(d*x+c)^3*tan(d*x+c)/d+1/10*A*b*(a+b*cos(d*x+c))^2*sec(d*x+c)^4*tan(d*x+c)/d+1/6*A*(a+b*cos(d*x+c))^3*sec(d*x+c)^5*tan(d*x+c)/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x,6,1/4*a*b*(b^2*(6*A+5*C)+a^2*(8*A+6*C))*x+1/105*(35*a^4*(3*A+2*C)+84*a^2*b^2*(5*A+4*C)+8*b^4*(7*A+6*C))*sin(d*x+c)/d+1/4*a*b*(b^2*(6*A+5*C)+a^2*(8*A+6*C))*cos(d*x+c)*sin(d*x+c)/d+1/105*(4*a^4*C+4*b^4*(7*A+6*C)+3*a^2*b^2*(63*A+50*C))*cos(d*x+c)^2*sin(d*x+c)/d+1/210*a*b*(126*A*b^2+6*C*a^2+103*C*b^2)*cos(d*x+c)^3*sin(d*x+c)/d+1/35*(2*a^2*C+b^2*(7*A+6*C))*cos(d*x+c)^2*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+2/21*a*C*cos(d*x+c)^2*(a+b*cos(d*x+c))^3*sin(d*x+c)/d+1/7*C*cos(d*x+c)^2*(a+b*cos(d*x+c))^4*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x,5,1/16*(8*a^4*(2*A+C)+12*a^2*b^2*(4*A+3*C)+b^4*(6*A+5*C))*x-1/60*a*(4*a^4*C-32*b^4*(5*A+4*C)-a^2*b^2*(190*A+121*C))*sin(d*x+c)/b/d-1/240*(8*a^4*C-15*b^4*(6*A+5*C)-2*a^2*b^2*(130*A+89*C))*cos(d*x+c)*sin(d*x+c)/d+1/120*a*(70*A*b^2-4*C*a^2+53*C*b^2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/b/d-1/120*(4*a^2*C-5*b^2*(6*A+5*C))*(a+b*cos(d*x+c))^3*sin(d*x+c)/b/d-1/30*a*C*(a+b*cos(d*x+c))^4*sin(d*x+c)/b/d+1/6*C*(a+b*cos(d*x+c))^5*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c),x,7,1/2*a*b*(4*a^2*(2*A+C)+b^2*(4*A+3*C))*x+a^4*A*arctanh(sin(d*x+c))/d+1/15*(6*a^4*C+2*b^4*(5*A+4*C)+a^2*b^2*(85*A+56*C))*sin(d*x+c)/d+1/30*a*b*(40*A*b^2+6*C*a^2+29*C*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/15*(3*a^2*C+b^2*(5*A+4*C))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+1/5*a*C*(a+b*cos(d*x+c))^3*sin(d*x+c)/d+1/5*C*(a+b*cos(d*x+c))^4*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,7,1/8*(8*a^4*C+24*a^2*b^2*(2*A+C)+b^4*(4*A+3*C))*x+4*a^3*A*b*arctanh(sin(d*x+c))/d-1/6*a*b*(a^2*(12*A-19*C)-8*b^2*(3*A+2*C))*sin(d*x+c)/d-1/24*b^2*(a^2*(24*A-26*C)-3*b^2*(4*A+3*C))*cos(d*x+c)*sin(d*x+c)/d-1/12*a*b*(12*A-7*C)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d-1/4*b*(4*A-C)*(a+b*cos(d*x+c))^3*sin(d*x+c)/d+A*(a+b*cos(d*x+c))^4*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,7,2*a*b*(2*A*b^2+(2*a^2+b^2)*C)*x+1/2*a^2*(12*A*b^2+a^2*(A+2*C))*arctanh(sin(d*x+c))/d-1/6*b^2*(a^2*(39*A-34*C)-2*b^2*(3*A+2*C))*sin(d*x+c)/d-1/3*a*b^3*(9*A-4*C)*cos(d*x+c)*sin(d*x+c)/d-1/6*b^2*(15*A-2*C)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+2*A*b*(a+b*cos(d*x+c))^3*tan(d*x+c)/d+1/2*A*(a+b*cos(d*x+c))^4*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,7,1/2*b^2*(2*A*b^2+(12*a^2+b^2)*C)*x+2*a*b*(2*A*b^2+a^2*(A+2*C))*arctanh(sin(d*x+c))/d-2/3*a*b*(b^2*(11*A-6*C)+a^2*(2*A+3*C))*sin(d*x+c)/d-1/6*b^2*(3*b^2*(6*A-C)+a^2*(4*A+6*C))*cos(d*x+c)*sin(d*x+c)/d+1/3*(6*A*b^2+a^2*(2*A+3*C))*(a+b*cos(d*x+c))^2*tan(d*x+c)/d+2/3*A*b*(a+b*cos(d*x+c))^3*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,7,4*a*b^3*C*x+1/8*(8*A*b^4+24*a^2*b^2*(A+2*C)+a^4*(3*A+4*C))*arctanh(sin(d*x+c))/d-1/24*b^2*(2*b^2*(13*A-12*C)+3*a^2*(3*A+4*C))*sin(d*x+c)/d+1/12*a*b*(12*A*b^2+a^2*(23*A+36*C))*tan(d*x+c)/d+1/8*(4*A*b^2+a^2*(3*A+4*C))*(a+b*cos(d*x+c))^2*sec(d*x+c)*tan(d*x+c)/d+1/3*A*b*(a+b*cos(d*x+c))^3*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,7,b^4*C*x+1/2*a*b*(4*b^2*(A+2*C)+a^2*(3*A+4*C))*arctanh(sin(d*x+c))/d+1/15*(6*A*b^4+2*a^4*(4*A+5*C)+a^2*b^2*(56*A+85*C))*tan(d*x+c)/d+1/30*a*b*(6*A*b^2+a^2*(29*A+40*C))*sec(d*x+c)*tan(d*x+c)/d+1/15*(3*A*b^2+a^2*(4*A+5*C))*(a+b*cos(d*x+c))^2*sec(d*x+c)^2*tan(d*x+c)/d+1/5*A*b*(a+b*cos(d*x+c))^3*sec(d*x+c)^3*tan(d*x+c)/d+1/5*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^4*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^7,x,9,1/16*(8*b^4*(A+2*C)+12*a^2*b^2*(3*A+4*C)+a^4*(5*A+6*C))*arctanh(sin(d*x+c))/d+4/15*a*b*(5*b^2*(2*A+3*C)+2*a^2*(4*A+5*C))*tan(d*x+c)/d+1/240*(24*A*b^4+15*a^4*(5*A+6*C)+10*a^2*b^2*(49*A+66*C))*sec(d*x+c)*tan(d*x+c)/d+1/60*a*b*(4*A*b^2+a^2*(39*A+50*C))*sec(d*x+c)^2*tan(d*x+c)/d+1/120*(12*A*b^2+5*a^2*(5*A+6*C))*(a+b*cos(d*x+c))^2*sec(d*x+c)^3*tan(d*x+c)/d+2/15*A*b*(a+b*cos(d*x+c))^3*sec(d*x+c)^4*tan(d*x+c)/d+1/6*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^5*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^8,x,10,1/4*a*b*(2*b^2*(3*A+4*C)+a^2*(5*A+6*C))*arctanh(sin(d*x+c))/d+1/105*(35*b^4*(2*A+3*C)+84*a^2*b^2*(4*A+5*C)+8*a^4*(6*A+7*C))*tan(d*x+c)/d+1/4*a*b*(2*b^2*(3*A+4*C)+a^2*(5*A+6*C))*sec(d*x+c)*tan(d*x+c)/d+1/105*(4*A*b^4+4*a^4*(6*A+7*C)+3*a^2*b^2*(50*A+63*C))*sec(d*x+c)^2*tan(d*x+c)/d+1/210*a*b*(6*A*b^2+a^2*(103*A+126*C))*sec(d*x+c)^3*tan(d*x+c)/d+1/35*(2*A*b^2+a^2*(6*A+7*C))*(a+b*cos(d*x+c))^2*sec(d*x+c)^4*tan(d*x+c)/d+2/21*A*b*(a+b*cos(d*x+c))^3*sec(d*x+c)^5*tan(d*x+c)/d+1/7*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^6*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(a^2-b^2*cos(d*x+c)^2),x,5,1/8*a*(8*a^4+8*a^2*b^2-9*b^4)*x+1/30*b*(83*a^4-32*a^2*b^2-16*b^4)*sin(d*x+c)/d+1/120*a*b^2*(106*a^2-71*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/60*b*(23*a^2-16*b^2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+1/20*a*b*(a+b*cos(d*x+c))^3*sin(d*x+c)/d-1/5*b*(a+b*cos(d*x+c))^4*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(a^2-b^2*cos(d*x+c)^2),x,4,1/8*(8*a^4-3*b^4)*x+1/6*a*b*(13*a^2-8*b^2)*sin(d*x+c)/d+1/24*b^2*(14*a^2-9*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/12*a*b*(a+b*cos(d*x+c))^2*sin(d*x+c)/d-1/4*b*(a+b*cos(d*x+c))^3*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(a^2-b^2*cos(d*x+c)^2),x,3,1/2*a*(2*a^2-b^2)*x+2/3*b*(2*a^2-b^2)*sin(d*x+c)/d+1/6*a*b^2*cos(d*x+c)*sin(d*x+c)/d-1/3*b*(a+b*cos(d*x+c))^2*sin(d*x+c)/d,1],
[cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,7,1/8*(8*a^4*C+4*a^2*b^2*(2*A+C)+b^4*(4*A+3*C))*x/b^5-2*a^3*(A*b^2+C*a^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^5/sqrt(a+b)/d-1/3*a*(3*A*b^2+3*C*a^2+2*C*b^2)*sin(d*x+c)/b^4/d+1/8*(4*a^2*C+b^2*(4*A+3*C))*cos(d*x+c)*sin(d*x+c)/b^3/d-1/3*a*C*cos(d*x+c)^2*sin(d*x+c)/b^2/d+1/4*C*cos(d*x+c)^3*sin(d*x+c)/b/d,1],
[cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,6,-1/2*a*(2*A*b^2+(2*a^2+b^2)*C)*x/b^4+2*a^2*(A*b^2+C*a^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^4/sqrt(a+b)/d+1/3*(3*a^2*C+b^2*(3*A+2*C))*sin(d*x+c)/b^3/d-1/2*a*C*cos(d*x+c)*sin(d*x+c)/b^2/d+1/3*C*cos(d*x+c)^2*sin(d*x+c)/b/d,1],
[cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,5,1/2*(2*a^2*C+b^2*(2*A+C))*x/b^3-2*a*(A*b^2+C*a^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^3/sqrt(a+b)/d-a*C*sin(d*x+c)/b^2/d+1/2*C*cos(d*x+c)*sin(d*x+c)/b/d,1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,4,-a*C*x/b^2+2*(A*b^2+C*a^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^2/sqrt(a+b)/d+C*sin(d*x+c)/b/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c)),x,4,C*x/b-2*(A*b^2+C*a^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a/sqrt(a-b)/b/sqrt(a+b)/d+A*arctanh(sin(d*x+c))/a/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c)),x,5,2*(A*b^2+C*a^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^2/sqrt(a-b)/sqrt(a+b)/d-A*b*arctanh(sin(d*x+c))/a^2/d+A*tan(d*x+c)/a/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c)),x,6,-2*b*(A*b^2+C*a^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^3/sqrt(a-b)/sqrt(a+b)/d+1/2*(2*A*b^2+a^2*(A+2*C))*arctanh(sin(d*x+c))/a^3/d-A*b*tan(d*x+c)/a^2/d+1/2*A*sec(d*x+c)*tan(d*x+c)/a/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c)),x,7,2*b^2*(A*b^2+C*a^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^4/sqrt(a-b)/sqrt(a+b)/d-1/2*b*(2*A*b^2+a^2*(A+2*C))*arctanh(sin(d*x+c))/a^4/d+1/3*(3*A*b^2+a^2*(2*A+3*C))*tan(d*x+c)/a^3/d-1/2*A*b*sec(d*x+c)*tan(d*x+c)/a^2/d+1/3*A*sec(d*x+c)^2*tan(d*x+c)/a/d,1],
[cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,7,-a*(2*A*b^2+(4*a^2+b^2)*C)*x/b^5+2*a^2*(2*A*a^2*b^2-3*A*b^4+4*C*a^4-5*C*a^2*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/b^5/(a+b)^(3/2)/d+1/3*(a^2*b^2*(6*A-7*C)+12*a^4*C-b^4*(3*A+2*C))*sin(d*x+c)/b^4/(a^2-b^2)/d-a*(A*b^2+2*C*a^2-C*b^2)*cos(d*x+c)*sin(d*x+c)/b^3/(a^2-b^2)/d+1/3*(3*A*b^2+4*C*a^2-C*b^2)*cos(d*x+c)^2*sin(d*x+c)/b^2/(a^2-b^2)/d-(A*b^2+C*a^2)*cos(d*x+c)^3*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,6,1/2*(2*A*b^2+(6*a^2+b^2)*C)*x/b^4-2*a*(A*a^2*b^2-2*A*b^4+3*C*a^4-4*C*a^2*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/b^4/(a+b)^(3/2)/d-a*(A*b^2+3*C*a^2-2*C*b^2)*sin(d*x+c)/b^3/(a^2-b^2)/d+1/2*(2*A*b^2+3*C*a^2-C*b^2)*cos(d*x+c)*sin(d*x+c)/b^2/(a^2-b^2)/d-(A*b^2+C*a^2)*cos(d*x+c)^2*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,5,-2*a*C*x/b^3-2*(A*b^4-2*C*a^4+3*C*a^2*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/b^3/(a+b)^(3/2)/d+C*sin(d*x+c)/b^2/d+a*(A*b^2+C*a^2)*sin(d*x+c)/b^2/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,4,C*x/b^2+2*a*(A*b^2-C*a^2+2*C*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/b^2/(a+b)^(3/2)/d-(A*b^2+C*a^2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^2,x,5,-2*b*(2*A*a^2-A*b^2+C*a^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^2/(a-b)^(3/2)/(a+b)^(3/2)/d+A*arctanh(sin(d*x+c))/a^2/d+(A*b^2+C*a^2)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x,6,2*(3*A*a^2*b^2-2*A*b^4+C*a^4)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^3/(a-b)^(3/2)/(a+b)^(3/2)/d-2*A*b*arctanh(sin(d*x+c))/a^3/d-(2*A*b^2-a^2*(A-C))*tan(d*x+c)/a^2/(a^2-b^2)/d+(A*b^2+C*a^2)*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x,7,-2*b*(4*A*a^2*b^2-3*A*b^4+2*C*a^4-C*a^2*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^4/(a-b)^(3/2)/(a+b)^(3/2)/d+1/2*(6*A*b^2+a^2*(A+2*C))*arctanh(sin(d*x+c))/a^4/d+b*(3*A*b^2-a^2*(2*A-C))*tan(d*x+c)/a^3/(a^2-b^2)/d-1/2*(3*A*b^2-a^2*(A-2*C))*sec(d*x+c)*tan(d*x+c)/a^2/(a^2-b^2)/d+(A*b^2+C*a^2)*sec(d*x+c)*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^2,x,8,2*b^2*(5*A*a^2*b^2-4*A*b^4+3*C*a^4-2*C*a^2*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^5/(a-b)^(3/2)/(a+b)^(3/2)/d-b*(4*A*b^2+a^2*(A+2*C))*arctanh(sin(d*x+c))/a^5/d-1/3*(12*A*b^4-a^2*b^2*(7*A-6*C)-a^4*(2*A+3*C))*tan(d*x+c)/a^4/(a^2-b^2)/d+b*(2*A*b^2-a^2*(A-C))*sec(d*x+c)*tan(d*x+c)/a^3/(a^2-b^2)/d-1/3*(4*A*b^2-a^2*(A-3*C))*sec(d*x+c)^2*tan(d*x+c)/a^2/(a^2-b^2)/d+(A*b^2+C*a^2)*sec(d*x+c)^2*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,7,1/2*(2*A*b^2+(12*a^2+b^2)*C)*x/b^5-a*(6*A*b^6+a^4*b^2*(2*A-29*C)-5*a^2*b^4*(A-4*C)+12*a^6*C)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(5/2)/b^5/(a+b)^(5/2)/d-1/2*a*(a^2*b^2*(2*A-21*C)-b^4*(5*A-6*C)+12*a^4*C)*sin(d*x+c)/b^4/(a^2-b^2)^2/d+1/2*(a^2*b^2*(A-10*C)-b^4*(4*A-C)+6*a^4*C)*cos(d*x+c)*sin(d*x+c)/b^3/(a^2-b^2)^2/d-1/2*(A*b^2+C*a^2)*cos(d*x+c)^3*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/2*(3*A*b^4-4*C*a^4+7*C*a^2*b^2)*cos(d*x+c)^2*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,6,-3*a*C*x/b^4+(2*A*b^6+6*a^6*C-15*a^4*b^2*C+a^2*b^4*(A+12*C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(5/2)/b^4/(a+b)^(5/2)/d+1/2*(A*b^2+3*C*a^2-2*C*b^2)*sin(d*x+c)/b^3/(a^2-b^2)/d-1/2*(A*b^2+C*a^2)*cos(d*x+c)^2*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/2*a*(2*A*b^4-3*a^4*C+a^2*b^2*(A+6*C))*sin(d*x+c)/b^3/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,5,C*x/b^3-a*(3*A*b^4+(2*a^4-5*a^2*b^2+6*b^4)*C)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(5/2)/b^3/(a+b)^(5/2)/d+1/2*a*(A*b^2+C*a^2)*sin(d*x+c)/b^2/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/2*(2*A*b^4-3*a^4*C+a^2*b^2*(A+6*C))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,5,(a^2*(2*A+C)+b^2*(A+2*C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(5/2)/(a+b)^(5/2)/d-1/2*(A*b^2+C*a^2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/2*a*(3*A*b^2-C*a^2+4*C*b^2)*sin(d*x+c)/b/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^3,x,6,b*(5*a^2*A*b^2-2*A*b^4-3*a^4*(2*A+C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^3/(a-b)^(5/2)/(a+b)^(5/2)/d+A*arctanh(sin(d*x+c))/a^3/d+1/2*(A*b^2+C*a^2)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/2*(2*A*b^4-a^4*C-a^2*b^2*(5*A+2*C))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^3,x,7,-(15*a^2*A*b^4-6*A*b^6-2*a^6*C-a^4*b^2*(12*A+C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^4/(a-b)^(5/2)/(a+b)^(5/2)/d-3*A*b*arctanh(sin(d*x+c))/a^4/d-1/2*(11*a^2*A*b^2-6*A*b^4-a^4*(2*A-3*C))*tan(d*x+c)/a^3/(a^2-b^2)^2/d+1/2*(A*b^2+C*a^2)*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/2*(3*A*b^4-2*a^4*C-a^2*b^2*(6*A+C))*tan(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^3,x,8,-b*(12*A*b^6-a^2*b^4*(29*A-2*C)+5*a^4*b^2*(4*A-C)+6*a^6*C)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^5/(a-b)^(5/2)/(a+b)^(5/2)/d+1/2*(12*A*b^2+a^2*(A+2*C))*arctanh(sin(d*x+c))/a^5/d-1/2*b*(12*A*b^4+a^4*(6*A-5*C)-a^2*b^2*(21*A-2*C))*tan(d*x+c)/a^4/(a^2-b^2)^2/d+1/2*(6*A*b^4+a^4*(A-4*C)-a^2*b^2*(10*A-C))*sec(d*x+c)*tan(d*x+c)/a^3/(a^2-b^2)^2/d+1/2*(A*b^2+C*a^2)*sec(d*x+c)*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/2*(7*A*a^2*b^2-4*A*b^4+3*C*a^4)*sec(d*x+c)*tan(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^4*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x,8,1/2*(2*A*b^2+(20*a^2+b^2)*C)*x/b^6+(8*a*A*b^8-a^7*b^2*(2*A-69*C)+7*a^5*b^4*(A-12*C)-8*a^3*b^6*(A-5*C)-20*a^9*C)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^6/sqrt(a+b)/(a^2-b^2)^3/d-1/6*a*(a^4*b^2*(6*A-167*C)-a^2*b^4*(17*A-146*C)+2*b^6*(13*A-12*C)+60*a^6*C)*sin(d*x+c)/b^5/(a^2-b^2)^3/d+1/2*(a^4*b^2*(A-27*C)-a^2*b^4*(2*A-23*C)+b^6*(6*A-C)+10*a^6*C)*cos(d*x+c)*sin(d*x+c)/b^4/(a^2-b^2)^3/d-1/3*(A*b^2+C*a^2)*cos(d*x+c)^4*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^3+1/6*(4*A*b^4-5*a^4*C+a^2*b^2*(A+10*C))*cos(d*x+c)^3*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2-1/6*(12*A*b^6+a^4*b^2*(2*A-53*C)+20*a^6*C+a^2*b^4*(A+48*C))*cos(d*x+c)^2*sin(d*x+c)/b^3/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x,7,-4*a*C*x/b^5-(2*A*b^8-8*a^8*C+28*a^6*b^2*C-35*a^4*b^4*C+a^2*b^6*(3*A+20*C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(7/2)/b^5/(a+b)^(7/2)/d-1/6*(5*A*b^4-(12*a^4-23*a^2*b^2+6*b^4)*C)*sin(d*x+c)/b^4/(a^2-b^2)^2/d-1/3*(A*b^2+C*a^2)*cos(d*x+c)^3*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^3+1/6*(3*A*b^4-4*a^4*C+a^2*b^2*(2*A+9*C))*cos(d*x+c)^2*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2+1/2*a*(2*A*b^6+4*a^6*C-11*a^4*b^2*C+3*a^2*b^4*(A+4*C))*sin(d*x+c)/b^4/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x,6,C*x/b^4+a*(a^2*b^4*(A-8*C)-2*a^6*C+7*a^4*b^2*C+4*b^6*(A+2*C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(7/2)/b^4/(a+b)^(7/2)/d-1/3*(A*b^2+C*a^2)*cos(d*x+c)^2*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^3-1/6*a*(2*A*b^4-3*a^4*C+a^2*b^2*(3*A+8*C))*sin(d*x+c)/b^3/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2-1/6*(4*A*b^6+9*a^6*C+2*a^2*b^4*(7*A+17*C)-a^4*b^2*(3*A+28*C))*sin(d*x+c)/b^3/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x,6,-b*(b^2*(A+2*C)+a^2*(4*A+3*C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(7/2)/(a+b)^(7/2)/d+1/3*a*(A*b^2+C*a^2)*sin(d*x+c)/b^2/(a^2-b^2)/d/(a+b*cos(d*x+c))^3+1/6*(3*A*b^4-4*a^4*C+a^2*b^2*(2*A+9*C))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2+1/6*a*(a^2*b^2*(2*A-5*C)+2*a^4*C+b^4*(13*A+18*C))*sin(d*x+c)/b^2/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x,6,a*(a^2*(2*A+C)+b^2*(3*A+4*C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(7/2)/(a+b)^(7/2)/d-1/3*(A*b^2+C*a^2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^3-1/6*a*(5*A*b^2-C*a^2+6*C*b^2)*sin(d*x+c)/b/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2+1/6*(a^4*C-2*b^4*(2*A+3*C)-a^2*b^2*(11*A+10*C))*sin(d*x+c)/b/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^4,x,7,-b*(7*a^2*A*b^4-2*A*b^6-a^4*b^2*(8*A-C)+4*a^6*(2*A+C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^4/(a-b)^(7/2)/(a+b)^(7/2)/d+A*arctanh(sin(d*x+c))/a^4/d+1/3*(A*b^2+C*a^2)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^3-1/6*(3*A*b^4-2*a^4*C-a^2*b^2*(8*A+3*C))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2-1/6*(17*a^2*A*b^4-6*A*b^6-2*a^6*C-13*a^4*b^2*(2*A+C))*sin(d*x+c)/a^3/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^4,x,8,-(35*a^4*A*b^4-28*a^2*A*b^6+8*A*b^8-2*a^8*C-a^6*b^2*(20*A+3*C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^5/(a-b)^(7/2)/(a+b)^(7/2)/d-4*A*b*arctanh(sin(d*x+c))/a^5/d+1/6*(68*a^2*A*b^4-24*A*b^6+a^6*(6*A-11*C)-a^4*b^2*(65*A+4*C))*tan(d*x+c)/a^4/(a^2-b^2)^3/d+1/3*(A*b^2+C*a^2)*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^3-1/6*(4*A*b^4-3*a^4*C-a^2*b^2*(9*A+2*C))*tan(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2-1/2*(11*a^2*A*b^4-4*A*b^6-2*a^6*C-3*a^4*b^2*(4*A+C))*tan(d*x+c)/a^3/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^4,x,9,(20*A*b^9-a^2*b^7*(69*A-2*C)-8*a^6*b^3*(5*A-C)+7*a^4*b^5*(12*A-C)-8*a^8*b*C)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^6/sqrt(a-b)/sqrt(a+b)/(a^2-b^2)^3/d+1/2*(20*A*b^2+a^2*(A+2*C))*arctanh(sin(d*x+c))/a^6/d+1/6*b*(60*A*b^6-a^6*(24*A-26*C)+a^4*b^2*(146*A-17*C)-a^2*b^4*(167*A-6*C))*tan(d*x+c)/a^5/(a^2-b^2)^3/d-1/2*(10*A*b^6-a^6*(A-6*C)+a^4*b^2*(23*A-2*C)-a^2*b^4*(27*A-C))*sec(d*x+c)*tan(d*x+c)/a^4/(a^2-b^2)^3/d+1/3*(A*b^2+C*a^2)*sec(d*x+c)*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^3-1/6*(5*A*b^4-4*a^4*C-a^2*b^2*(10*A+C))*sec(d*x+c)*tan(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2+1/6*(20*A*b^6-a^2*b^4*(53*A-2*C)+12*a^6*C+a^4*b^2*(48*A+C))*sec(d*x+c)*tan(d*x+c)/a^3/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^3*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,7,-1/8*(8*a^4-4*a^2*b^2-b^4)*x/b^5+2*a^3*sqrt(a-b)*sqrt(a+b)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/b^5/d+1/3*a*(3*a^2-b^2)*sin(d*x+c)/b^4/d-1/8*(4*a^2-b^2)*cos(d*x+c)*sin(d*x+c)/b^3/d+1/3*a*cos(d*x+c)^2*sin(d*x+c)/b^2/d-1/4*cos(d*x+c)^3*sin(d*x+c)/b/d,1],
[cos(d*x+c)^2*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,6,1/2*a*(2*a^2-b^2)*x/b^4-2*a^2*sqrt(a-b)*sqrt(a+b)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/b^4/d-1/3*(3*a^2-b^2)*sin(d*x+c)/b^3/d+1/2*a*cos(d*x+c)*sin(d*x+c)/b^2/d-1/3*cos(d*x+c)^2*sin(d*x+c)/b/d,1],
[cos(d*x+c)*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,5,-1/2*(2*a^2-b^2)*x/b^3+2*a*sqrt(a-b)*sqrt(a+b)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/b^3/d+a*sin(d*x+c)/b^2/d-1/2*cos(d*x+c)*sin(d*x+c)/b/d,1],
[(1-cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,4,a*x/b^2-2*sqrt(a-b)*sqrt(a+b)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/b^2/d-sin(d*x+c)/b/d,1],
[(1-cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c)),x,4,-x/b+2*sqrt(a-b)*sqrt(a+b)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a/b/d+arctanh(sin(d*x+c))/a/d,1],
[(1-cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c)),x,5,-2*sqrt(a-b)*sqrt(a+b)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^2/d-b*arctanh(sin(d*x+c))/a^2/d+tan(d*x+c)/a/d,1],
[(1-cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c)),x,6,2*sqrt(a-b)*b*sqrt(a+b)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^3/d-1/2*(a^2-2*b^2)*arctanh(sin(d*x+c))/a^3/d-b*tan(d*x+c)/a^2/d+1/2*sec(d*x+c)*tan(d*x+c)/a/d,1],
[(1-cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c)),x,7,-2*sqrt(a-b)*b^2*sqrt(a+b)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^4/d+1/2*b*(a^2-2*b^2)*arctanh(sin(d*x+c))/a^4/d-1/3*(a^2-3*b^2)*tan(d*x+c)/a^3/d-1/2*b*sec(d*x+c)*tan(d*x+c)/a^2/d+1/3*sec(d*x+c)^2*tan(d*x+c)/a/d,1],
[cos(d*x+c)^4*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,8,-1/8*(40*a^4-12*a^2*b^2-b^4)*x/b^6+2*a^3*(5*a^2-4*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^6/sqrt(a+b)/d+1/3*a*(15*a^2-2*b^2)*sin(d*x+c)/b^5/d-1/8*(20*a^2-b^2)*cos(d*x+c)*sin(d*x+c)/b^4/d+5/3*a*cos(d*x+c)^2*sin(d*x+c)/b^3/d-5/4*cos(d*x+c)^3*sin(d*x+c)/b^2/d+cos(d*x+c)^4*sin(d*x+c)/b/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^3*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,7,a*(4*a^2-b^2)*x/b^5-2*a^2*(4*a^2-3*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^5/sqrt(a+b)/d-1/3*(12*a^2-b^2)*sin(d*x+c)/b^4/d+2*a*cos(d*x+c)*sin(d*x+c)/b^3/d-4/3*cos(d*x+c)^2*sin(d*x+c)/b^2/d+cos(d*x+c)^3*sin(d*x+c)/b/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^2*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,6,-1/2*(6*a^2-b^2)*x/b^4+2*a*(3*a^2-2*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^4/sqrt(a+b)/d+3*a*sin(d*x+c)/b^3/d-3/2*cos(d*x+c)*sin(d*x+c)/b^2/d+cos(d*x+c)^2*sin(d*x+c)/b/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,5,2*a*x/b^3-2*(2*a^2-b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^3/sqrt(a+b)/d-sin(d*x+c)/b^2/d-a*sin(d*x+c)/b^2/d/(a+b*cos(d*x+c)),1],
[(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,5,-x/b^2+2*a*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^2/sqrt(a+b)/d+sin(d*x+c)/b/d/(a+b*cos(d*x+c)),1],
[(1-cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^2,x,6,-2*b*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^2/sqrt(a-b)/sqrt(a+b)/d+arctanh(sin(d*x+c))/a^2/d-sin(d*x+c)/a/d/(a+b*cos(d*x+c)),1],
[(1-cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x,6,-2*(a^2-2*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^3/sqrt(a-b)/sqrt(a+b)/d-2*b*arctanh(sin(d*x+c))/a^3/d+2*tan(d*x+c)/a^2/d-tan(d*x+c)/a/d/(a+b*cos(d*x+c)),1],
[(1-cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x,7,2*b*(2*a^2-3*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^4/sqrt(a-b)/sqrt(a+b)/d-1/2*(a^2-6*b^2)*arctanh(sin(d*x+c))/a^4/d-3*b*tan(d*x+c)/a^3/d+3/2*sec(d*x+c)*tan(d*x+c)/a^2/d-sec(d*x+c)*tan(d*x+c)/a/d/(a+b*cos(d*x+c)),1],
[(1-cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^2,x,8,-2*b^2*(3*a^2-4*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^5/sqrt(a-b)/sqrt(a+b)/d+b*(a^2-4*b^2)*arctanh(sin(d*x+c))/a^5/d-1/3*(a^2-12*b^2)*tan(d*x+c)/a^4/d-2*b*sec(d*x+c)*tan(d*x+c)/a^3/d+4/3*sec(d*x+c)^2*tan(d*x+c)/a^2/d-sec(d*x+c)^2*tan(d*x+c)/a/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^4*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,8,1/2*a*(20*a^2-3*b^2)*x/b^6-a^2*(20*a^4-33*a^2*b^2+12*b^4)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/b^6/(a+b)^(3/2)/d-1/6*(60*a^4-59*a^2*b^2+2*b^4)*sin(d*x+c)/b^5/(a^2-b^2)/d+1/2*a*(10*a^2-9*b^2)*cos(d*x+c)*sin(d*x+c)/b^4/(a^2-b^2)/d-1/6*(20*a^2-17*b^2)*cos(d*x+c)^2*sin(d*x+c)/b^3/(a^2-b^2)/d+1/2*cos(d*x+c)^4*sin(d*x+c)/b/d/(a+b*cos(d*x+c))^2+1/2*(5*a^2-4*b^2)*cos(d*x+c)^3*sin(d*x+c)/b^2/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^3*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,7,-1/2*(12*a^2-b^2)*x/b^5+a*(12*a^4-19*a^2*b^2+6*b^4)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/b^5/(a+b)^(3/2)/d+1/2*a*(12*a^2-11*b^2)*sin(d*x+c)/b^4/(a^2-b^2)/d-1/2*(6*a^2-5*b^2)*cos(d*x+c)*sin(d*x+c)/b^3/(a^2-b^2)/d+1/2*cos(d*x+c)^3*sin(d*x+c)/b/d/(a+b*cos(d*x+c))^2+1/2*(4*a^2-3*b^2)*cos(d*x+c)^2*sin(d*x+c)/b^2/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^2*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,6,3*a*x/b^4-(6*a^4-9*a^2*b^2+2*b^4)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/b^4/(a+b)^(3/2)/d-3/2*sin(d*x+c)/b^3/d+1/2*cos(d*x+c)^2*sin(d*x+c)/b/d/(a+b*cos(d*x+c))^2-1/2*a*(3*a^2-2*b^2)*sin(d*x+c)/b^3/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)*(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,5,-x/b^3+a*(2*a^2-3*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/b^3/(a+b)^(3/2)/d-1/2*a*sin(d*x+c)/b^2/d/(a+b*cos(d*x+c))^2+1/2*(3*a^2-2*b^2)*sin(d*x+c)/b^2/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(1-cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,6,arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/(a+b)^(3/2)/d+1/2*sin(d*x+c)/b/d/(a+b*cos(d*x+c))^2-1/2*a*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(1-cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^3,x,6,-b*(3*a^2-2*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^3/(a-b)^(3/2)/(a+b)^(3/2)/d+arctanh(sin(d*x+c))/a^3/d-1/2*sin(d*x+c)/a/d/(a+b*cos(d*x+c))^2-1/2*(a^2-2*b^2)*sin(d*x+c)/a^2/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(1-cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^3,x,7,-(2*a^4-9*a^2*b^2+6*b^4)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^4/(a-b)^(3/2)/(a+b)^(3/2)/d-3*b*arctanh(sin(d*x+c))/a^4/d+1/2*(5*a^2-6*b^2)*tan(d*x+c)/a^3/(a^2-b^2)/d-1/2*tan(d*x+c)/a/d/(a+b*cos(d*x+c))^2-1/2*(2*a^2-3*b^2)*tan(d*x+c)/a^2/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(1-cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^3,x,8,b*(6*a^4-19*a^2*b^2+12*b^4)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^5/(a-b)^(3/2)/(a+b)^(3/2)/d-1/2*(a^2-12*b^2)*arctanh(sin(d*x+c))/a^5/d-1/2*b*(11*a^2-12*b^2)*tan(d*x+c)/a^4/(a^2-b^2)/d+1/2*(5*a^2-6*b^2)*sec(d*x+c)*tan(d*x+c)/a^3/(a^2-b^2)/d-1/2*sec(d*x+c)*tan(d*x+c)/a/d/(a+b*cos(d*x+c))^2-1/2*(3*a^2-4*b^2)*sec(d*x+c)*tan(d*x+c)/a^2/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(1-cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^3,x,9,-b^2*(12*a^4-33*a^2*b^2+20*b^4)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^6/(a-b)^(3/2)/(a+b)^(3/2)/d+1/2*b*(3*a^2-20*b^2)*arctanh(sin(d*x+c))/a^6/d-1/6*(2*a^4-59*a^2*b^2+60*b^4)*tan(d*x+c)/a^5/(a^2-b^2)/d-1/2*b*(9*a^2-10*b^2)*sec(d*x+c)*tan(d*x+c)/a^4/(a^2-b^2)/d+1/6*(17*a^2-20*b^2)*sec(d*x+c)^2*tan(d*x+c)/a^3/(a^2-b^2)/d-1/2*sec(d*x+c)^2*tan(d*x+c)/a/d/(a+b*cos(d*x+c))^2-1/2*(4*a^2-5*b^2)*sec(d*x+c)^2*tan(d*x+c)/a^2/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,3,a*x-b*sin(d*x+c)/d,1],
[(a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,4,-x+4*a*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/sqrt(a+b)/d,1],
[(a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,5,2*(a^2+b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/(a+b)^(3/2)/d-2*a*b*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x,6,2*a*(a^2+2*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(5/2)/(a+b)^(5/2)/d-a*b*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-b*(2*a^2+b^2)*sin(d*x+c)/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^2*sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,9,-2/315*(16*a^4*C+6*a^2*b^2*(7*A+4*C)-21*b^4*(9*A+7*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^4/d/sqrt((a+b*cos(d*x+c))/(a+b))+4/315*a*(a^2-b^2)*(21*A*b^2+8*C*a^2+18*C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^4/d/sqrt(a+b*cos(d*x+c))-4/315*a*(21*A*b^2+8*C*a^2+18*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/d+2/315*(24*a^2*C+7*b^2*(9*A+7*C))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^3/d-4/21*a*C*cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^2/d+2/9*C*cos(d*x+c)^2*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d,1],
[cos(d*x+c)*sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,8,2/105*a*(35*A*b^2+8*C*a^2+19*C*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^3/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/105*(a^2-b^2)*(35*A*b^2+8*C*a^2+25*C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^3/d/sqrt(a+b*cos(d*x+c))+2/105*(8*a^2*C+5*b^2*(7*A+5*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d-8/35*a*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^2/d+2/7*C*cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d,1],
[sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,7,-2/15*(2*a^2*C-3*b^2*(5*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/d/sqrt((a+b*cos(d*x+c))/(a+b))+4/15*a*(a^2-b^2)*C*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/d/sqrt(a+b*cos(d*x+c))-4/15*a*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+2/5*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d,1],
[sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c),x,9,2/3*a*C*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/3*(a^2*C-b^2*(3*A+C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b/d/sqrt(a+b*cos(d*x+c))+2*a*A*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+2/3*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,9,-(A-2*C)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+a*A*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+A*b*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+A*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,10,-1/4*A*b*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/4*b*(3*A+8*C)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-1/4*(A*b^2-4*a^2*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+1/4*A*b*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a/d+1/2*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,11,1/24*(3*A*b^2-8*a^2*(2*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-1/24*(A*b^2-8*a^2*(2*A+3*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+1/8*b*(A*b^2+4*a^2*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^2/d/sqrt(a+b*cos(d*x+c))-1/24*(3*A*b^2-8*a^2*(2*A+3*C))*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a^2/d+1/12*A*b*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/a/d+1/3*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d,1],
[cos(d*x+c)^2*(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x,10,-4/1155*a*(8*a^4*C+3*a^2*b^2*(11*A+6*C)-b^4*(451*A+348*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^4/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/1155*(a^2-b^2)*(16*a^4*C+6*a^2*b^2*(11*A+8*C)-25*b^4*(11*A+9*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^4/d/sqrt(a+b*cos(d*x+c))-2/1155*(16*a^4*C+6*a^2*b^2*(11*A+8*C)-25*b^4*(11*A+9*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/d-4/1155*a*(33*A*b^2+8*C*a^2+34*C*b^2)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^3/d+2/231*(8*a^2*C+3*b^2*(11*A+9*C))*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b^3/d-4/33*a*C*cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b^2/d+2/11*C*cos(d*x+c)^2*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x,9,2/315*(8*a^4*C+21*b^4*(9*A+7*C)+3*a^2*b^2*(21*A+11*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^3/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/315*a*(a^2-b^2)*(63*A*b^2+8*C*a^2+39*C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^3/d/sqrt(a+b*cos(d*x+c))+2/315*a*(63*A*b^2+8*C*a^2+39*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d+2/315*(8*a^2*C+7*b^2*(9*A+7*C))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^2/d-8/63*a*C*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b^2/d+2/9*C*cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x,8,4/105*a*(70*A*b^2-3*C*a^2+41*C*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/105*(a^2-b^2)*(35*A*b^2-6*C*a^2+25*C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/d/sqrt(a+b*cos(d*x+c))-2/105*(6*a^2*C-5*b^2*(7*A+5*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d-4/35*a*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d+2/7*C*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c),x,10,2/5*(a^2*C+b^2*(5*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/5*a*(5*A*b^2-(a^2-b^2)*C)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b/d/sqrt(a+b*cos(d*x+c))+2*a^2*A*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+2/5*a*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+2/5*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,10,-1/3*a*(3*A-8*C)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/3*(a^2*(3*A-2*C)+2*b^2*(3*A+C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+3*a*A*b*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-1/3*b*(3*A-2*C)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+A*(a+b*cos(d*x+c))^(3/2)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,10,-1/4*b*(5*A-8*C)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/4*a*b*(7*A+8*C)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+1/4*(3*A*b^2+4*a^2*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+3/4*A*b*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/d+1/2*A*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,11,-1/24*(3*A*b^2+8*a^2*(2*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/24*(8*a^2*(2*A+3*C)+b^2*(17*A+48*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-1/8*b*(A*b^2-12*a^2*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+1/24*(3*A*b^2+8*a^2*(2*A+3*C))*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a/d+1/4*A*b*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,12,1/64*b*(3*A*b^2-4*a^2*(13*A+20*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-1/64*b*(A*b^2-4*a^2*(19*A+28*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+1/64*(3*A*b^4+24*a^2*b^2*(A+2*C)+16*a^4*(3*A+4*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^2/d/sqrt(a+b*cos(d*x+c))-1/64*b*(3*A*b^2-4*a^2*(13*A+20*C))*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a^2/d+1/32*(A*b^2+4*a^2*(3*A+4*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/a/d+1/8*A*b*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^3*tan(d*x+c)/d,1],
[cos(d*x+c)^2*(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x,11,-2/45045*(240*a^6*C-1617*b^6*(13*A+11*C)+10*a^4*b^2*(143*A+76*C)-3*a^2*b^4*(13299*A+10223*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^4/d/sqrt((a+b*cos(d*x+c))/(a+b))+4/45045*a*(a^2-b^2)*(120*a^4*C+5*a^2*b^2*(143*A+94*C)-3*b^4*(2717*A+2174*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^4/d/sqrt(a+b*cos(d*x+c))-4/45045*a*(120*a^4*C+5*a^2*b^2*(143*A+94*C)-3*b^4*(2717*A+2174*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/d-2/45045*(240*a^4*C-539*b^4*(13*A+11*C)+10*a^2*b^2*(143*A+124*C))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^3/d-4/9009*a*(143*A*b^2+24*C*a^2+166*C*b^2)*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b^3/d+2/1287*(24*a^2*C+11*b^2*(13*A+11*C))*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b^3/d-12/143*a*C*cos(d*x+c)*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b^2/d+2/13*C*cos(d*x+c)^2*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x,10,2/693*a*(8*a^4*C+3*a^2*b^2*(33*A+17*C)+3*b^4*(319*A+247*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^3/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/693*(a^2-b^2)*(8*a^4*C+15*b^4*(11*A+9*C)+3*a^2*b^2*(33*A+19*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^3/d/sqrt(a+b*cos(d*x+c))+2/693*(8*a^4*C+15*b^4*(11*A+9*C)+3*a^2*b^2*(33*A+19*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d+2/693*a*(99*A*b^2+8*C*a^2+67*C*b^2)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^2/d+2/693*(8*a^2*C+9*b^2*(11*A+9*C))*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b^2/d-8/99*a*C*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b^2/d+2/11*C*cos(d*x+c)*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x,9,-2/315*(10*a^4*C-21*b^4*(9*A+7*C)-3*a^2*b^2*(161*A+93*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-4/315*a*(a^2-b^2)*(84*A*b^2-5*C*a^2+57*C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/d/sqrt(a+b*cos(d*x+c))+4/315*a*(84*A*b^2-5*C*a^2+57*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d-2/315*(10*a^2*C-7*b^2*(9*A+7*C))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d-4/63*a*C*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d+2/9*C*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c),x,11,2/21*a*(49*A*b^2+3*C*a^2+29*C*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/21*(2*a^2*b^2*(7*A-C)-3*a^4*C+b^4*(7*A+5*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b/d/sqrt(a+b*cos(d*x+c))+2*a^3*A*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+2/21*(3*a^2*C+b^2*(7*A+5*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+2/7*a*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/7*C*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,11,-1/15*(a^2*(15*A-46*C)-6*b^2*(5*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/15*a*(a^2*(15*A-16*C)+4*b^2*(15*A+4*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+5*a^2*A*b*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-1/15*a*b*(15*A-16*C)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d-1/5*b*(5*A-2*C)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d+A*(a+b*cos(d*x+c))^(5/2)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,11,-1/12*a*b*(27*A-56*C)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/12*b*(8*b^2*(3*A+C)+a^2*(33*A+16*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+1/4*a*(15*A*b^2+4*a^2*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-1/12*b^2*(21*A-8*C)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+5/4*A*b*(a+b*cos(d*x+c))^(3/2)*tan(d*x+c)/d+1/2*A*(a+b*cos(d*x+c))^(5/2)*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,11,-1/24*(3*b^2*(11*A-16*C)+8*a^2*(2*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/24*a*(8*a^2*(2*A+3*C)+b^2*(59*A+96*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+5/8*b*(A*b^2+4*a^2*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+1/24*(15*A*b^2+8*a^2*(2*A+3*C))*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/d+5/12*A*b*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,12,-1/192*b*(15*A*b^2+4*a^2*(71*A+108*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/192*b*(4*a^2*(89*A+132*C)+b^2*(133*A+384*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-1/64*(5*A*b^4-120*a^2*b^2*(A+2*C)-16*a^4*(3*A+4*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+1/192*b*(15*A*b^2+4*a^2*(71*A+108*C))*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a/d+1/32*(5*A*b^2+4*a^2*(3*A+4*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+5/24*A*b*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(a^2-b^2*cos(d*x+c)^2),x,9,4/105*a*(73*a^2-41*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/105*(41*a^4-66*a^2*b^2+25*b^4)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+2/105*b*(41*a^2-25*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+4/35*a*b*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d-2/7*b*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(a^2-b^2*cos(d*x+c)^2),x,8,2/15*(17*a^2-9*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))-4/15*a*(a^2-b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+4/15*a*b*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d-2/5*b*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c)),x,9,2/315*(128*a^4*C+21*b^4*(9*A+7*C)+12*a^2*b^2*(14*A+9*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^5/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/315*a*(128*a^4*C+4*a^2*b^2*(42*A+19*C)+3*b^4*(49*A+37*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^5/d/sqrt(a+b*cos(d*x+c))-4/315*a*(42*A*b^2+32*C*a^2+31*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^4/d+2/315*(48*a^2*C+7*b^2*(9*A+7*C))*cos(d*x+c)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/d-16/63*a*C*cos(d*x+c)^2*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d+2/9*C*cos(d*x+c)^3*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d,1],
[cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c)),x,8,-4/105*a*(35*A*b^2+24*C*a^2+22*C*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^4/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/105*(48*a^4*C+5*b^4*(7*A+5*C)+2*a^2*b^2*(35*A+16*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^4/d/sqrt(a+b*cos(d*x+c))+2/105*(24*a^2*C+5*b^2*(7*A+5*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/d-12/35*a*C*cos(d*x+c)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d+2/7*C*cos(d*x+c)^2*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d,1],
[cos(d*x+c)*(A+C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c)),x,7,2/15*(8*a^2*C+3*b^2*(5*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^3/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/15*a*(15*A*b^2+8*C*a^2+7*C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^3/d/sqrt(a+b*cos(d*x+c))-8/15*a*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d+2/5*C*cos(d*x+c)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d,1],
[(A+C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c)),x,6,-4/3*a*C*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/3*(2*a^2*C+b^2*(3*A+C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/d/sqrt(a+b*cos(d*x+c))+2/3*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)/sqrt(a+b*cos(d*x+c)),x,8,2*C*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b/d/sqrt((a+b*cos(d*x+c))/(a+b))-2*a*C*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b/d/sqrt(a+b*cos(d*x+c))+2*A*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^2/sqrt(a+b*cos(d*x+c)),x,9,-A*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a/d/sqrt((a+b*cos(d*x+c))/(a+b))+(A+2*C)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-A*b*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+A*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^3/sqrt(a+b*cos(d*x+c)),x,10,3/4*A*b*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-1/4*A*b*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+1/4*(3*A*b^2+4*a^2*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^2/d/sqrt(a+b*cos(d*x+c))-3/4*A*b*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a^2/d+1/2*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/a/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^4/sqrt(a+b*cos(d*x+c)),x,11,-1/24*(15*A*b^2+8*a^2*(2*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^3/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/24*(5*A*b^2+8*a^2*(2*A+3*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a^2/d/sqrt(a+b*cos(d*x+c))-1/8*b*(5*A*b^2+4*a^2*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^3/d/sqrt(a+b*cos(d*x+c))+1/24*(15*A*b^2+8*a^2*(2*A+3*C))*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a^3/d-5/12*A*b*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/a^2/d+1/3*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/a/d,1],
[cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x,9,-2/105*a*(4*a^2*b^2*(70*A-43*C)+384*a^4*C-b^4*(175*A+107*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^5/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/105*(384*a^4*C+5*b^4*(7*A+5*C)+4*a^2*b^2*(70*A+29*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^5/d/sqrt(a+b*cos(d*x+c))-2*(A*b^2+C*a^2)*cos(d*x+c)^3*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+2/105*(2*a^2*b^2*(70*A-31*C)+192*a^4*C-5*b^4*(7*A+5*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^4/(a^2-b^2)/d-2/35*a*(35*A*b^2+48*C*a^2-13*C*b^2)*cos(d*x+c)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)/d+2/7*(7*A*b^2+8*C*a^2-C*b^2)*cos(d*x+c)^2*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)/d,1],
[cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x,8,2/5*(2*a^2*b^2*(5*A-4*C)+16*a^4*C-b^4*(5*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^4/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))-4/5*a*(5*A*b^2+2*(4*a^2+b^2)*C)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^4/d/sqrt(a+b*cos(d*x+c))-2*(A*b^2+C*a^2)*cos(d*x+c)^2*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-2/5*a*(5*A*b^2+8*C*a^2-3*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)/d+2/5*(5*A*b^2+6*C*a^2-C*b^2)*cos(d*x+c)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)/d,1],
[cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x,7,-2/3*a*(3*A*b^2+8*C*a^2-5*C*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^3/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/3*(3*A*b^2+(8*a^2+b^2)*C)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^3/d/sqrt(a+b*cos(d*x+c))+2*a*(A*b^2+C*a^2)*sin(d*x+c)/b^2/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+2/3*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d,1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x,6,2*(A*b^2+2*C*a^2-C*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))-4*a*C*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/d/sqrt(a+b*cos(d*x+c))-2*(A*b^2+C*a^2)*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x,9,-2*(A*b^2+C*a^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a/b/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))+2*C*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b/d/sqrt(a+b*cos(d*x+c))+2*A*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+2*(A*b^2+C*a^2)*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x,10,(3*A*b^2-a^2*(A-2*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^2/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))+A*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))-3*A*b*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^2/d/sqrt(a+b*cos(d*x+c))-b*(3*A*b^2-a^2*(A-2*C))*sin(d*x+c)/a^2/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+A*tan(d*x+c)/a/d/sqrt(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x,11,-1/4*b*(15*A*b^2-a^2*(7*A-8*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^3/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))-5/4*A*b*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a^2/d/sqrt(a+b*cos(d*x+c))+1/4*(15*A*b^2+4*a^2*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^3/d/sqrt(a+b*cos(d*x+c))+1/4*b^2*(15*A*b^2-a^2*(7*A-8*C))*sin(d*x+c)/a^3/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-5/4*A*b*tan(d*x+c)/a^2/d/sqrt(a+b*cos(d*x+c))+1/2*A*sec(d*x+c)*tan(d*x+c)/a/d/sqrt(a+b*cos(d*x+c)),1],
[cos(d*x+c)^3*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,9,2/15*(4*a^4*b^2*(10*A-53*C)-5*a^2*b^4*(15*A-11*C)+128*a^6*C+3*b^6*(5*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^5/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/15*a*(4*a^2*b^2*(10*A-29*C)+128*a^4*C-b^4*(45*A+17*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^5/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-2/3*(A*b^2+C*a^2)*cos(d*x+c)^3*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+4/3*(3*A*b^4-a^2*b^2*(A-6*C)-4*a^4*C)*cos(d*x+c)^2*sin(d*x+c)/b^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c))-4/15*a*(a^2*b^2*(10*A-49*C)-b^4*(20*A-7*C)+32*a^4*C)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^4/(a^2-b^2)^2/d+2/15*(a^2*b^2*(15*A-71*C)-b^4*(35*A-3*C)+48*a^4*C)*cos(d*x+c)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)^2/d,1],
[cos(d*x+c)^2*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,8,-4/3*a*(a^2*b^2*(A-14*C)-b^4*(3*A-4*C)+8*a^4*C)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^4/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/3*(2*a^2*b^2*(A-8*C)+16*a^4*C-b^4*(3*A+C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^4/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-2/3*(A*b^2+C*a^2)*cos(d*x+c)^2*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)-4/3*a*(2*A*b^4-3*C*a^4+5*C*a^2*b^2)*sin(d*x+c)/b^3/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c))+2/3*(A*b^2+2*C*a^2-C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)/d,1],
[cos(d*x+c)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,7,-2/3*(3*b^4*(A-C)-8*a^4*C+a^2*b^2*(A+15*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^3/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/3*a*(A*b^2-8*C*a^2+9*C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^3/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+2/3*a*(A*b^2+C*a^2)*sin(d*x+c)/b^2/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+2/3*(3*A*b^4-5*a^4*C+a^2*b^2*(A+9*C))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,7,4/3*a*(2*A*b^2-(a^2-3*b^2)*C)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/3*(A*b^2-2*C*a^2+3*C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-2/3*(A*b^2+C*a^2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)-4/3*a*(2*A*b^2-C*a^2+3*C*b^2)*sin(d*x+c)/b/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x,10,2/3*(3*A*b^4-a^4*C-a^2*b^2*(7*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^2/b/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/3*(A*b^2+C*a^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+2*A*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^2/d/sqrt(a+b*cos(d*x+c))+2/3*(A*b^2+C*a^2)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)-2/3*(3*A*b^4-a^4*C-a^2*b^2*(7*A+3*C))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x,11,1/3*(26*a^2*A*b^2-15*A*b^4-a^4*(3*A-8*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^3/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-1/3*(5*A*b^2-a^2*(3*A-2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a^2/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-5*A*b*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^3/d/sqrt(a+b*cos(d*x+c))-1/3*b*(5*A*b^2-a^2*(3*A-2*C))*sin(d*x+c)/a^2/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)-1/3*b*(26*a^2*A*b^2-15*A*b^4-a^4*(3*A-8*C))*sin(d*x+c)/a^3/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c))+A*tan(d*x+c)/a/d/(a+b*cos(d*x+c))^(3/2),1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(7/2),x,8,-2/15*(2*a^4*C-3*b^4*(3*A+5*C)-a^2*b^2*(23*A+19*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/(a^2-b^2)^3/d/sqrt((a+b*cos(d*x+c))/(a+b))-4/15*a*(4*A*b^2-(a^2-5*b^2)*C)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c))-2/5*(A*b^2+C*a^2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(5/2)-4/15*a*(4*A*b^2-C*a^2+5*C*b^2)*sin(d*x+c)/b/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^(3/2)+2/15*(2*a^4*C-3*b^4*(3*A+5*C)-a^2*b^2*(23*A+19*C))*sin(d*x+c)/b/(a^2-b^2)^3/d/sqrt(a+b*cos(d*x+c)),1],
[(a^2-b^2*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c)),x,7,4/3*a*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/3*(a^2-b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-2/3*b*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[(a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x,6,-2*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+4*a*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c)),1],
[(a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,7,4*a*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))-2*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-4*a*b*sin(d*x+c)/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c)),1],
[(a^2-b^2*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(7/2),x,8,2/3*(5*a^2+3*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-4/3*a*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-4/3*a*b*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)-2/3*b*(5*a^2+3*b^2)*sin(d*x+c)/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,8,2/15*a*(9*A+7*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+10/231*b*(11*A+9*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+10/231*b*(11*A+9*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*a*(9*A+7*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/77*b*(11*A+9*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/9*a*C*cos(d*x+c)^(7/2)*sin(d*x+c)/d+2/11*b*C*cos(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,7,2/15*b*(9*A+7*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*a*(7*A+5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*a*(7*A+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*b*(9*A+7*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*a*C*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/9*b*C*cos(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,6,2/5*a*(5*A+3*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*b*(7*A+5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*b*(7*A+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*a*C*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*b*C*cos(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,5,2/5*b*(5*A+3*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*a*(3*A+C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*a*C*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*b*C*cos(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,5,-2*a*(A-C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*b*(3*A+C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2*a*A*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*b*C*sqrt(cos(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,5,-2*b*(A-C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*a*(A+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*a*A*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2*A*b*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,6,-2/5*a*(3*A+5*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*b*(A+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/5*a*A*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/3*A*b*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*a*(3*A+5*C)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,7,-2/5*b*(3*A+5*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*a*(5*A+7*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/7*a*A*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/5*A*b*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/21*a*(5*A+7*C)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*b*(3*A+5*C)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x,8,4/15*a*b*(9*A+7*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/231*(11*a^2*(7*A+5*C)+5*b^2*(11*A+9*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/231*(11*a^2*(7*A+5*C)+5*b^2*(11*A+9*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d+4/45*a*b*(9*A+7*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/77*(4*a^2*C+b^2*(11*A+9*C))*cos(d*x+c)^(5/2)*sin(d*x+c)/d+8/99*a*b*C*cos(d*x+c)^(7/2)*sin(d*x+c)/d+2/11*C*cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x,7,2/15*(3*a^2*(5*A+3*C)+b^2*(9*A+7*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a*b*(7*A+5*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/21*a*b*(7*A+5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*(4*a^2*C+b^2*(9*A+7*C))*cos(d*x+c)^(3/2)*sin(d*x+c)/d+8/63*a*b*C*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/9*C*cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,6,4/5*a*b*(5*A+3*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(7*a^2*(3*A+C)+b^2*(7*A+5*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*(4*a^2*C+b^2*(7*A+5*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d+8/35*a*b*C*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,6,-2/5*(5*a^2*(A-C)-b^2*(5*A+3*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/3*a*b*(3*A+C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-4/3*a*b*(3*A-C)*sqrt(cos(d*x+c))*sin(d*x+c)/d-2/5*b^2*(5*A-C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2*A*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,6,-4*a*b*(A-C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(b^2*(3*A+C)+a^2*(A+3*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+8/3*a*A*b*sin(d*x+c)/d/sqrt(cos(d*x+c))-2/3*b^2*(A-C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/3*A*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,6,-2/5*(5*b^2*(A-C)+a^2*(3*A+5*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/3*a*b*(A+3*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+8/15*a*A*b*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*(4*A*b^2+a^2*(3*A+5*C))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/5*A*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,7,-4/5*a*b*(3*A+5*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(7*b^2*(A+3*C)+a^2*(5*A+7*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+8/35*a*A*b*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/21*(4*A*b^2+a^2*(5*A+7*C))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+4/5*a*b*(3*A+5*C)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/7*A*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2),x,8,2/5*a*(a^2*(5*A+3*C)+b^2*(9*A+7*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/231*b*(33*a^2*(7*A+5*C)+5*b^2*(11*A+9*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/231*b*(33*a^2*(7*A+5*C)+5*b^2*(11*A+9*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/165*a*(99*A*b^2+8*C*a^2+77*C*b^2)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/231*b*(8*a^2*C+3*b^2*(11*A+9*C))*cos(d*x+c)^(5/2)*sin(d*x+c)/d+4/33*a*C*cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+2/11*C*cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^3*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,7,2/15*b*(9*a^2*(5*A+3*C)+b^2*(9*A+7*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*a*(7*a^2*(3*A+C)+3*b^2*(7*A+5*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/63*a*(63*A*b^2+8*C*a^2+45*C*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/315*b*(24*a^2*C+7*b^2*(9*A+7*C))*cos(d*x+c)^(3/2)*sin(d*x+c)/d+4/21*a*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+2/9*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^3*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,7,-2/5*a*(5*a^2*(A-C)-3*b^2*(5*A+3*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*b*(21*a^2*(3*A+C)+b^2*(7*A+5*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-2/21*b*(6*a^2*(7*A-3*C)-b^2*(7*A+5*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d-2/35*a*b^2*(35*A-11*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d-2/7*b*(7*A-C)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+2*A*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,7,-2/5*b*(15*a^2*(A-C)-b^2*(5*A+3*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*a*(3*b^2*(3*A+C)+a^2*(A+3*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-2*a*b^2*(5*A-C)*sqrt(cos(d*x+c))*sin(d*x+c)/d-2/15*b^3*(35*A-3*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+4*A*b*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*A*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,7,-2/5*a*(15*b^2*(A-C)+a^2*(3*A+5*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*b*(b^2*(3*A+C)+3*a^2*(A+3*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/5*a*(8*A*b^2+a^2*(3*A+5*C))*sin(d*x+c)/d/sqrt(cos(d*x+c))-2/15*b^3*(9*A-5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+4/5*A*b*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*A*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,7,-2/5*b*(5*b^2*(A-C)+3*a^2*(3*A+5*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*a*(21*b^2*(A+3*C)+a^2*(5*A+7*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/105*a*(24*A*b^2+5*a^2*(5*A+7*C))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+6/35*b*(8*A*b^2+7*a^2*(3*A+5*C))*sin(d*x+c)/d/sqrt(cos(d*x+c))+12/35*A*b*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/7*A*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,8,-2/15*a*(9*b^2*(3*A+5*C)+a^2*(7*A+9*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*b*(7*b^2*(A+3*C)+3*a^2*(5*A+7*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/315*a*(24*A*b^2+7*a^2*(7*A+9*C))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/63*b*(8*A*b^2+9*a^2*(5*A+7*C))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/15*a*(9*b^2*(3*A+5*C)+a^2*(7*A+9*C))*sin(d*x+c)/d/sqrt(cos(d*x+c))+4/21*A*b*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/9*A*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(9/2),1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2),x,9,2/195*(39*a^4*(5*A+3*C)+78*a^2*b^2*(9*A+7*C)+7*b^4*(13*A+11*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+8/231*a*b*(11*a^2*(7*A+5*C)+5*b^2*(11*A+9*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+8/231*a*b*(11*a^2*(7*A+5*C)+5*b^2*(11*A+9*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/6435*(192*a^4*C+77*b^4*(13*A+11*C)+11*a^2*b^2*(637*A+491*C))*cos(d*x+c)^(3/2)*sin(d*x+c)/d+4/9009*a*b*(1573*A*b^2+96*C*a^2+1259*C*b^2)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/1287*(48*a^2*C+11*b^2*(13*A+11*C))*cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+16/143*a*C*cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^3*sin(d*x+c)/d+2/13*C*cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^4*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,8,8/15*a*b*(3*a^2*(5*A+3*C)+b^2*(9*A+7*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/231*(77*a^4*(3*A+C)+66*a^2*b^2*(7*A+5*C)+5*b^4*(11*A+9*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/693*(64*a^4*C+15*b^4*(11*A+9*C)+9*a^2*b^2*(143*A+101*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d+4/3465*a*b*(891*A*b^2+96*C*a^2+673*C*b^2)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/231*(16*a^2*C+3*b^2*(11*A+9*C))*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+16/99*a*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^3*sin(d*x+c)/d+2/11*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^4*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,8,-2/15*(15*a^4*(A-C)-18*a^2*b^2*(5*A+3*C)-b^4*(9*A+7*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+8/21*a*b*(7*a^2*(3*A+C)+b^2*(7*A+5*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-4/63*a*b*(a^2*(63*A-31*C)-6*b^2*(7*A+5*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d-2/315*b^2*(3*a^2*(105*A-41*C)-7*b^2*(9*A+7*C))*cos(d*x+c)^(3/2)*sin(d*x+c)/d-2/21*a*b*(21*A-5*C)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d-2/9*b*(9*A-C)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^3*sin(d*x+c)/d+2*A*(a+b*cos(d*x+c))^4*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,8,-8/5*a*b*(5*a^2*(A-C)-b^2*(5*A+3*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(42*a^2*b^2*(3*A+C)+7*a^4*(A+3*C)+b^4*(7*A+5*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-2/21*b^2*(3*a^2*(49*A-13*C)-b^2*(7*A+5*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d-4/105*a*b^3*(175*A-27*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d-2/7*b^2*(21*A-C)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+16/3*A*b*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*A*(a+b*cos(d*x+c))^4*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,8,-2/5*(30*a^2*b^2*(A-C)-b^4*(5*A+3*C)+a^4*(3*A+5*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+8/3*a*b*(b^2*(3*A+C)+a^2*(A+3*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-4/15*a*b*(2*b^2*(33*A-5*C)+3*a^2*(3*A+5*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d-2/15*b^2*(b^2*(59*A-3*C)+3*a^2*(3*A+5*C))*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*(16*A*b^2+a^2*(3*A+5*C))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(cos(d*x+c))+16/15*A*b*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*A*(a+b*cos(d*x+c))^4*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,8,-8/5*a*b*(5*b^2*(A-C)+a^2*(3*A+5*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(7*b^4*(3*A+C)+42*a^2*b^2*(A+3*C)+a^4*(5*A+7*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/105*a*b*(96*A*b^2+a^2*(101*A+175*C))*sin(d*x+c)/d/sqrt(cos(d*x+c))-2/105*b^2*(b^2*(87*A-35*C)+5*a^2*(5*A+7*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/105*(48*A*b^2+5*a^2*(5*A+7*C))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(3/2)+16/35*A*b*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/7*A*(a+b*cos(d*x+c))^4*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,8,-2/15*(15*b^4*(A-C)+18*a^2*b^2*(3*A+5*C)+a^4*(7*A+9*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+8/21*a*b*(7*b^2*(A+3*C)+a^2*(5*A+7*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/315*a*b*(32*A*b^2+a^2*(101*A+147*C))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/315*(192*A*b^4+21*a^4*(7*A+9*C)+7*a^2*b^2*(155*A+261*C))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/315*(48*A*b^2+7*a^2*(7*A+9*C))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(5/2)+16/63*A*b*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/9*A*(a+b*cos(d*x+c))^4*sin(d*x+c)/d/cos(d*x+c)^(9/2),1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x,9,-8/15*a*b*(3*b^2*(3*A+5*C)+a^2*(7*A+9*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/231*(77*b^4*(A+3*C)+66*a^2*b^2*(5*A+7*C)+5*a^4*(9*A+11*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/3465*a*b*(96*A*b^2+a^2*(673*A+891*C))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/693*(64*A*b^4+15*a^4*(9*A+11*C)+9*a^2*b^2*(101*A+143*C))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+8/15*a*b*(3*b^2*(3*A+5*C)+a^2*(7*A+9*C))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/231*(16*A*b^2+3*a^2*(9*A+11*C))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(7/2)+16/99*A*b*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(9/2)+2/11*A*(a+b*cos(d*x+c))^4*sin(d*x+c)/d/cos(d*x+c)^(11/2),1],
[cos(d*x+c)^(7/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,9,2/15*(15*a^4*C+3*a^2*b^2*(5*A+3*C)+b^4*(9*A+7*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^5/d-2/21*a*(21*a^4*C+7*a^2*b^2*(3*A+C)+b^4*(7*A+5*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^6/d+2*a^4*(A*b^2+C*a^2)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b^6/(a+b)/d-2/21*a*(7*A*b^2+7*C*a^2+5*C*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/b^4/d+2/45*(9*a^2*C+b^2*(9*A+7*C))*cos(d*x+c)^(3/2)*sin(d*x+c)/b^3/d-2/7*a*C*cos(d*x+c)^(5/2)*sin(d*x+c)/b^2/d+2/9*C*cos(d*x+c)^(7/2)*sin(d*x+c)/b/d,1],
[cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,8,-2/5*a*(5*A*b^2+5*C*a^2+3*C*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^4/d+2/21*(21*a^4*C+7*a^2*b^2*(3*A+C)+b^4*(7*A+5*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^5/d-2*a^3*(A*b^2+C*a^2)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b^5/(a+b)/d+2/21*(7*a^2*C+b^2*(7*A+5*C))*sqrt(cos(d*x+c))*sin(d*x+c)/b^3/d-2/5*a*C*cos(d*x+c)^(3/2)*sin(d*x+c)/b^2/d+2/7*C*cos(d*x+c)^(5/2)*sin(d*x+c)/b/d,1],
[cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,7,2/5*(5*a^2*C+b^2*(5*A+3*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^3/d-2/3*a*(3*A*b^2+(3*a^2+b^2)*C)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^4/d+2*a^2*(A*b^2+C*a^2)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b^4/(a+b)/d-2/3*a*C*sqrt(cos(d*x+c))*sin(d*x+c)/b^2/d+2/5*C*cos(d*x+c)^(3/2)*sin(d*x+c)/b/d,1],
[sqrt(cos(d*x+c))*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,6,-2*a*C*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^2/d+2/3*(3*a^2*C+b^2*(3*A+C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^3/d-2*a*(A*b^2+C*a^2)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b^3/(a+b)/d+2/3*C*sqrt(cos(d*x+c))*sin(d*x+c)/b/d,1],
[(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+b*cos(d*x+c)),x,5,2*C*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b/d-2*a*C*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^2/d+2*(A*b^2+C*a^2)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b^2/(a+b)/d,1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x,6,-2*A*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d+2*C*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b/d-2*(A*b^2+C*a^2)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a/b/(a+b)/d+2*A*sin(d*x+c)/a/d/sqrt(cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x,7,2*A*b*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d+2/3*A*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d+2*(A*b^2+C*a^2)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^2/(a+b)/d+2/3*A*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)-2*A*b*sin(d*x+c)/a^2/d/sqrt(cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x,8,-2/5*(5*A*b^2+a^2*(3*A+5*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d-2/3*A*b*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d-2*b*(A*b^2+C*a^2)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^3/(a+b)/d+2/5*A*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)-2/3*A*b*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2)+2/5*(5*A*b^2+a^2*(3*A+5*C))*sin(d*x+c)/a^3/d/sqrt(cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c)),x,9,2/5*b*(5*A*b^2+a^2*(3*A+5*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^4/d+2/21*(7*A*b^2+a^2*(5*A+7*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d+2*b^2*(A*b^2+C*a^2)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^4/(a+b)/d+2/7*A*sin(d*x+c)/a/d/cos(d*x+c)^(7/2)-2/5*A*b*sin(d*x+c)/a^2/d/cos(d*x+c)^(5/2)+2/21*(7*A*b^2+a^2*(5*A+7*C))*sin(d*x+c)/a^3/d/cos(d*x+c)^(3/2)-2/5*b*(5*A*b^2+a^2*(3*A+5*C))*sin(d*x+c)/a^4/d/sqrt(cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2)/(a+b*cos(d*x+c)),x,10,-2/15*(15*A*b^4+3*a^2*b^2*(3*A+5*C)+a^4*(7*A+9*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^5/d-2/21*b*(7*A*b^2+a^2*(5*A+7*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^4/d-2*b^3*(A*b^2+C*a^2)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^5/(a+b)/d+2/9*A*sin(d*x+c)/a/d/cos(d*x+c)^(9/2)-2/7*A*b*sin(d*x+c)/a^2/d/cos(d*x+c)^(7/2)+2/45*(9*A*b^2+a^2*(7*A+9*C))*sin(d*x+c)/a^3/d/cos(d*x+c)^(5/2)-2/21*b*(7*A*b^2+a^2*(5*A+7*C))*sin(d*x+c)/a^4/d/cos(d*x+c)^(3/2)+2/15*(15*A*b^4+3*a^2*b^2*(3*A+5*C)+a^4*(7*A+9*C))*sin(d*x+c)/a^5/d/sqrt(cos(d*x+c)),1],
[cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,8,1/5*(3*a^2*b^2*(5*A-8*C)+35*a^4*C-2*b^4*(5*A+3*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^4/(a^2-b^2)/d-1/3*a*(a^2*b^2*(9*A-20*C)+21*a^4*C-4*b^4*(3*A+C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^5/(a^2-b^2)/d-a^2*(5*A*b^4-3*a^2*b^2*(A-3*C)-7*a^4*C)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a-b)/b^5/(a+b)^2/d-1/3*a*(3*A*b^2+7*C*a^2-4*C*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)/d+1/5*(5*A*b^2+7*C*a^2-2*C*b^2)*cos(d*x+c)^(3/2)*sin(d*x+c)/b^2/(a^2-b^2)/d-(A*b^2+C*a^2)*cos(d*x+c)^(5/2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,7,-a*(A*b^2+5*C*a^2-4*C*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^3/(a^2-b^2)/d+1/3*(a^2*b^2*(3*A-16*C)+15*a^4*C-2*b^4*(3*A+C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^4/(a^2-b^2)/d+a*(3*A*b^4-a^2*b^2*(A-7*C)-5*a^4*C)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a-b)/b^4/(a+b)^2/d+1/3*(3*A*b^2+5*C*a^2-2*C*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)/d-(A*b^2+C*a^2)*cos(d*x+c)^(3/2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,6,(A*b^2+3*C*a^2-2*C*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^2/(a^2-b^2)/d+a*(A*b^2-3*C*a^2+4*C*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^3/(a^2-b^2)/d-(A*b^4-3*a^4*C+a^2*b^2*(A+5*C))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a-b)/b^3/(a+b)^2/d-(A*b^2+C*a^2)*sqrt(cos(d*x+c))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^2,x,6,-(A*b^2+C*a^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/b/(a^2-b^2)/d-(A*b^2-C*a^2+2*C*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^2/(a^2-b^2)/d-(A*b^4+a^4*C-3*a^2*b^2*(A+C))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a/(a-b)/b^2/(a+b)^2/d+(A*b^2+C*a^2)*sqrt(cos(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x,7,(3*A*b^2-a^2*(2*A-C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/(a^2-b^2)/d+(A*b^2+C*a^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/b/(a^2-b^2)/d+(3*A*b^4-a^4*C-a^2*b^2*(5*A+C))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^2/(a-b)/b/(a+b)^2/d-(3*A*b^2-a^2*(2*A-C))*sin(d*x+c)/a^2/(a^2-b^2)/d/sqrt(cos(d*x+c))+(A*b^2+C*a^2)*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(cos(d*x+c))/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x,8,-b*(5*A*b^2-a^2*(4*A-C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/(a^2-b^2)/d-1/3*(5*A*b^2-a^2*(2*A-3*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/(a^2-b^2)/d-(5*A*b^4-a^2*b^2*(7*A-C)-3*a^4*C)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^3/(a-b)/(a+b)^2/d-1/3*(5*A*b^2-a^2*(2*A-3*C))*sin(d*x+c)/a^2/(a^2-b^2)/d/cos(d*x+c)^(3/2)+b*(5*A*b^2-a^2*(4*A-C))*sin(d*x+c)/a^3/(a^2-b^2)/d/sqrt(cos(d*x+c))+(A*b^2+C*a^2)*sin(d*x+c)/a/(a^2-b^2)/d/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^2,x,9,1/5*(35*A*b^4-3*a^2*b^2*(8*A-5*C)-2*a^4*(3*A+5*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^4/(a^2-b^2)/d+1/3*b*(7*A*b^2-a^2*(4*A-3*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/(a^2-b^2)/d+b*(7*A*b^4-3*a^2*b^2*(3*A-C)-5*a^4*C)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^4/(a-b)/(a+b)^2/d-1/5*(7*A*b^2-a^2*(2*A-5*C))*sin(d*x+c)/a^2/(a^2-b^2)/d/cos(d*x+c)^(5/2)+1/3*b*(7*A*b^2-a^2*(4*A-3*C))*sin(d*x+c)/a^3/(a^2-b^2)/d/cos(d*x+c)^(3/2)-1/5*(35*A*b^4-3*a^2*b^2*(8*A-5*C)-2*a^4*(3*A+5*C))*sin(d*x+c)/a^4/(a^2-b^2)/d/sqrt(cos(d*x+c))+(A*b^2+C*a^2)*sin(d*x+c)/a/(a^2-b^2)/d/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^(5/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,8,-1/4*a*(a^2*b^2*(3*A-65*C)-3*b^4*(3*A-8*C)+35*a^4*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^4/(a^2-b^2)^2/d+1/12*(a^4*b^2*(9*A-223*C)-a^2*b^4*(15*A-128*C)+105*a^6*C+8*b^6*(3*A+C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^5/(a^2-b^2)^2/d-1/4*a*(15*A*b^6+a^4*b^2*(3*A-86*C)-3*a^2*b^4*(2*A-21*C)+35*a^6*C)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a-b)^2/b^5/(a+b)^3/d+1/12*(a^2*b^2*(3*A-61*C)-b^4*(21*A-8*C)+35*a^4*C)*sqrt(cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)^2/d-1/2*(A*b^2+C*a^2)*cos(d*x+c)^(5/2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/4*(5*A*b^4-7*a^4*C+a^2*b^2*(A+13*C))*cos(d*x+c)^(3/2)*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,7,-1/4*(b^4*(5*A-8*C)-15*a^4*C+a^2*b^2*(A+29*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^3/(a^2-b^2)^2/d-1/4*a*(15*a^4*C+b^4*(7*A+24*C)-a^2*b^2*(A+33*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^4/(a^2-b^2)^2/d+1/4*(3*A*b^6+15*a^6*C+5*a^2*b^4*(2*A+7*C)-a^4*b^2*(A+38*C))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a-b)^2/b^4/(a+b)^3/d-1/2*(A*b^2+C*a^2)*cos(d*x+c)^(3/2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/4*(3*A*b^4-5*a^4*C+a^2*b^2*(3*A+11*C))*sqrt(cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,7,1/4*(A*b^4-3*a^4*C+a^2*b^2*(5*A+9*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/b^2/(a^2-b^2)^2/d+1/4*(a^2*b^2*(3*A-5*C)+3*a^4*C+b^4*(3*A+8*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^3/(a^2-b^2)^2/d+1/4*(A*b^6-3*a^4*b^2*(A-2*C)-3*a^6*C-5*a^2*b^4*(2*A+3*C))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a/(a-b)^2/b^3/(a+b)^3/d-1/2*(A*b^2+C*a^2)*sqrt(cos(d*x+c))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/4*(A*b^4-3*a^4*C+a^2*b^2*(5*A+9*C))*sqrt(cos(d*x+c))*sin(d*x+c)/a/b/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^3,x,7,1/4*(3*A*b^4-a^4*C-a^2*b^2*(9*A+5*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/b/(a^2-b^2)^2/d+1/4*(A*b^4+a^4*C-7*a^2*b^2*(A+C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/b^2/(a^2-b^2)^2/d+1/4*(3*A*b^6-3*a^2*b^4*(2*A-C)-a^6*C+5*a^4*b^2*(3*A+2*C))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^2/(a-b)^2/b^2/(a+b)^3/d+1/2*(A*b^2+C*a^2)*sqrt(cos(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/4*(3*A*b^4-a^4*C-a^2*b^2*(9*A+5*C))*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x,8,-1/4*(15*A*b^4+a^4*(8*A-5*C)-a^2*b^2*(29*A+C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/(a^2-b^2)^2/d-1/4*(5*A*b^4-3*a^4*C-a^2*b^2*(11*A+3*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/b/(a^2-b^2)^2/d-1/4*(15*A*b^6+3*a^6*C-a^2*b^4*(38*A+C)+5*a^4*b^2*(7*A+2*C))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^3/(a-b)^2/b/(a+b)^3/d+1/4*(15*A*b^4+a^4*(8*A-5*C)-a^2*b^2*(29*A+C))*sin(d*x+c)/a^3/(a^2-b^2)^2/d/sqrt(cos(d*x+c))+1/2*(A*b^2+C*a^2)*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^2-1/4*(5*A*b^4-3*a^4*C-a^2*b^2*(11*A+3*C))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/sqrt(cos(d*x+c))/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x,9,1/4*b*(35*A*b^4+3*a^4*(8*A-3*C)-a^2*b^2*(65*A-3*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^4/(a^2-b^2)^2/d+1/12*(35*A*b^4+a^4*(8*A-21*C)-a^2*b^2*(61*A-3*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/(a^2-b^2)^2/d+1/4*(35*A*b^6-a^2*b^4*(86*A-3*C)+3*a^4*b^2*(21*A-2*C)+15*a^6*C)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^4/(a-b)^2/(a+b)^3/d+1/12*(35*A*b^4+a^4*(8*A-21*C)-a^2*b^2*(61*A-3*C))*sin(d*x+c)/a^3/(a^2-b^2)^2/d/cos(d*x+c)^(3/2)-1/4*b*(35*A*b^4+3*a^4*(8*A-3*C)-a^2*b^2*(65*A-3*C))*sin(d*x+c)/a^4/(a^2-b^2)^2/d/sqrt(cos(d*x+c))+1/2*(A*b^2+C*a^2)*sin(d*x+c)/a/(a^2-b^2)/d/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2-1/4*(7*A*b^4-5*a^4*C-a^2*b^2*(13*A+C))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,8,1/24*(a-b)*sqrt(a+b)*(3*a^2*C-8*b^2*(3*A+2*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/d-1/24*sqrt(a+b)*(3*a^2*C-2*a*b*C-8*b^2*(3*A+2*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d-1/8*a*sqrt(a+b)*(8*A*b^2+(a^2+4*b^2)*C)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d-1/24*(3*a^2*C-8*b^2*(3*A+2*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d/sqrt(cos(d*x+c))-1/4*a*C*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+1/3*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d,1],
[sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,7,-1/4*(a-b)*sqrt(a+b)*C*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d+1/4*sqrt(a+b)*(8*A*b+(a+2*b)*C)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d+1/4*sqrt(a+b)*(a^2*C-4*b^2*(2*A+C))*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+1/4*a*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(cos(d*x+c))+1/2*C*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,7,(a-b)*sqrt(a+b)*(2*A-C)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-sqrt(a+b)*(2*A*a-2*A*b-C*a)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-a*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d+2*A*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))-(2*A-C)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,6,2/3*A*(a-b)*b*sqrt(a+b)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d-2/3*sqrt(a+b)*(A*b-a*(A+3*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-2*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d+2/3*A*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,5,-2/15*(a-b)*sqrt(a+b)*(2*A*b^2-3*a^2*(3*A+5*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d-2/15*(a-b)*sqrt(a+b)*(9*A*a+2*A*b+15*C*a)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d+2/5*A*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/15*A*b*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(3/2),1],
[sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,6,2/105*(a-b)*b*sqrt(a+b)*(8*A*b^2+a^2*(19*A+35*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d+2/105*(a-b)*sqrt(a+b)*(6*a*A*b+8*A*b^2+5*a^2*(5*A+7*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d+2/7*A*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/35*A*b*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)-2/105*(4*A*b^2-5*a^2*(5*A+7*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2),1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2),x,9,-1/64*(a-b)*sqrt(a+b)*(80*A*b^2-3*C*a^2+52*C*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d-1/64*sqrt(a+b)*(3*a^3*C-2*a^2*b*C-8*b^3*(4*A+3*C)-4*a*b^2*(20*A+13*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d-1/64*sqrt(a+b)*(3*a^4*C+24*a^2*b^2*(2*A+C)+16*b^4*(4*A+3*C))*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d+1/64*a*(80*A*b^2-3*C*a^2+52*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d/sqrt(cos(d*x+c))-1/32*(3*a^2*C-4*b^2*(4*A+3*C))*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d-1/8*a*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d+1/4*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,8,-1/24*(a-b)*sqrt(a+b)*(3*a^2*C+8*b^2*(3*A+2*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d+1/24*sqrt(a+b)*(48*A*a*b+24*A*b^2+3*C*a^2+14*C*a*b+16*C*b^2)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d-1/8*a*sqrt(a+b)*(24*A*b^2-C*a^2+12*C*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+1/24*(3*a^2*C+8*b^2*(3*A+2*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(cos(d*x+c))+1/4*a*C*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+1/3*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,8,1/4*(a-b)*sqrt(a+b)*(8*A-5*C)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d-1/4*sqrt(a+b)*(8*A*a-16*A*b-5*C*a-2*C*b)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d-1/4*sqrt(a+b)*(8*A*b^2+3*C*a^2+4*C*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d-1/4*a*(8*A-5*C)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))-1/2*b*(4*A-C)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+2*A*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,8,1/3*(a-b)*b*sqrt(a+b)*(8*A-3*C)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d+1/3*sqrt(a+b)*(6*A*b^2+2*a^2*(A+3*C)-a*(8*A*b-3*C*b))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-3*a*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d+2*A*b*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))-1/3*b*(8*A-3*C)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*A*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,7,2/5*(a-b)*sqrt(a+b)*(A*b^2+a^2*(3*A+5*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d-2/5*sqrt(a+b)*(A*b^2-2*a*b*(2*A+5*C)+a^2*(3*A+5*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-2*b*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d+2/5*A*b*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*A*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,6,-4/105*(a-b)*b*sqrt(a+b)*(3*A*b^2-a^2*(41*A+70*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d+2/105*(a-b)*sqrt(a+b)*(25*A*a^2-57*A*a*b-6*A*b^2+35*C*a^2-105*C*a*b)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d+6/35*A*b*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/105*(3*A*b^2+5*a^2*(5*A+7*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)+2/7*A*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,7,2/315*(a-b)*sqrt(a+b)*(8*A*b^4+21*a^4*(7*A+9*C)+3*a^2*b^2*(11*A+21*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d+2/315*(a-b)*sqrt(a+b)*(6*a*A*b^2+8*A*b^3-21*a^3*(7*A+9*C)+a^2*(39*A*b+63*C*b))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d+2/21*A*b*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/315*(3*A*b^2+7*a^2*(7*A+9*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)-4/315*b*(2*A*b^2-a^2*(44*A+63*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2)+2/9*A*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(9/2),1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2),x,10,1/1920*(a-b)*sqrt(a+b)*(45*a^4*C-256*b^4*(5*A+4*C)-12*a^2*b^2*(220*A+141*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/d-1/1920*sqrt(a+b)*(45*a^4*C-30*a^3*b*C-256*b^4*(5*A+4*C)-12*a^2*b^2*(220*A+141*C)-8*a*b^3*(260*A+193*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d-1/128*a*sqrt(a+b)*(3*a^4*C+40*a^2*b^2*(2*A+C)+80*b^4*(4*A+3*C))*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d-1/1920*(45*a^4*C-256*b^4*(5*A+4*C)-12*a^2*b^2*(220*A+141*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d/sqrt(cos(d*x+c))+1/320*a*(240*A*b^2-15*C*a^2+172*C*b^2)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d-1/240*(15*a^2*C-16*b^2*(5*A+4*C))*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d-3/40*a*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d+1/5*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,9,-1/192*(a-b)*sqrt(a+b)*(432*A*b^2+15*C*a^2+284*C*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d+1/192*sqrt(a+b)*(15*a^3*C+24*b^3*(4*A+3*C)+2*a^2*b*(192*A+59*C)+4*a*b^2*(108*A+71*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d+1/64*sqrt(a+b)*(5*a^4*C-120*a^2*b^2*(2*A+C)-16*b^4*(4*A+3*C))*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+1/192*a*(432*A*b^2+15*C*a^2+284*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(cos(d*x+c))+1/32*(5*a^2*C+4*b^2*(4*A+3*C))*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+5/24*a*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d+1/4*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,9,1/24*(a-b)*sqrt(a+b)*(a^2*(48*A-33*C)-8*b^2*(3*A+2*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-1/24*sqrt(a+b)*(a^2*(48*A-33*C)-8*b^2*(3*A+2*C)-2*a*b*(72*A+13*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d-5/8*a*sqrt(a+b)*(8*A*b^2+(a^2+4*b^2)*C)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d-1/24*(a^2*(48*A-33*C)-8*b^2*(3*A+2*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))-1/4*a*b*(8*A-3*C)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d-1/3*b*(6*A-C)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2*A*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,9,1/12*(a-b)*b*sqrt(a+b)*(56*A-27*C)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d+1/12*sqrt(a+b)*(6*b^2*(12*A+C)+8*a^2*(A+3*C)-a*(56*A*b-27*C*b))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d-1/4*sqrt(a+b)*(8*A*b^2+15*C*a^2+4*C*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d-1/12*a*b*(56*A-27*C)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))-1/2*b^2*(8*A-C)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+10/3*A*b*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*A*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,9,1/15*(a-b)*sqrt(a+b)*(b^2*(46*A-15*C)+6*a^2*(3*A+5*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d+1/15*sqrt(a+b)*(30*A*b^3-a*b^2*(46*A-15*C)-6*a^3*(3*A+5*C)+a^2*(34*A*b+90*C*b))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-5*a*b*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d+2/5*(5*A*b^2+a^2*(3*A+5*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))-1/15*(b^2*(46*A-15*C)+6*a^2*(3*A+5*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*A*b*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*A*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,8,2/21*(a-b)*b*sqrt(a+b)*(3*A*b^2+a^2*(29*A+49*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d-2/21*sqrt(a+b)*(3*A*b^3-9*a*b^2*(3*A+7*C)-a^3*(5*A+7*C)+a^2*b*(29*A+49*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-2*b^2*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d+2/21*(3*A*b^2+a^2*(5*A+7*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/7*A*b*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/7*A*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,7,-2/315*(a-b)*sqrt(a+b)*(10*A*b^4-21*a^4*(7*A+9*C)-3*a^2*b^2*(93*A+161*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d-2/315*(a-b)*sqrt(a+b)*(10*A*b^3+21*a^3*(7*A+9*C)+15*a*b^2*(11*A+21*C)-6*a^2*b*(19*A+28*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d+2/315*(15*A*b^2+7*a^2*(7*A+9*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/315*b*(5*A*b^2+a^2*(163*A+231*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)+10/63*A*b*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/9*A*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(9/2),1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x,8,2/693*(a-b)*b*sqrt(a+b)*(8*A*b^4+3*a^2*b^2*(17*A+33*C)+a^4*(741*A+957*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d+2/693*(a-b)*sqrt(a+b)*(6*a*A*b^3+8*A*b^4+15*a^4*(9*A+11*C)+3*a^2*b^2*(19*A+33*C)-6*a^3*b*(101*A+132*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d+2/231*(5*A*b^2+3*a^2*(9*A+11*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/693*b*(3*A*b^2+a^2*(229*A+297*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)-2/693*(4*A*b^4-15*a^4*(9*A+11*C)-a^2*b^2*(205*A+297*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2)+10/99*A*b*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(9/2)+2/11*A*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(11/2),1],
[cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c)),x,8,-1/24*(a-b)*sqrt(a+b)*(15*a^2*C+8*b^2*(3*A+2*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^3/d+1/24*sqrt(a+b)*(15*a^2*C-10*a*b*C+8*b^2*(3*A+2*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d+1/8*a*sqrt(a+b)*(8*A*b^2+5*C*a^2+4*C*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^4/d+1/24*(15*a^2*C+8*b^2*(3*A+2*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/d/sqrt(cos(d*x+c))-5/12*a*C*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d+1/3*C*cos(d*x+c)^(3/2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d,1],
[sqrt(cos(d*x+c))*(A+C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c)),x,7,3/4*(a-b)*sqrt(a+b)*C*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d-1/4*(3*a-2*b)*sqrt(a+b)*C*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d-1/4*sqrt(a+b)*(3*a^2*C+4*b^2*(2*A+C))*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d-3/4*a*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d/sqrt(cos(d*x+c))+1/2*C*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d,1],
[(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),x,6,-(a-b)*sqrt(a+b)*C*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d+sqrt(a+b)*(2*A*b+C*a)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d+a*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/sqrt(a+b*cos(d*x+c)),x,6,2*A*(a-b)*sqrt(a+b)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d-2*A*sqrt(a+b)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-2*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d,1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/sqrt(a+b*cos(d*x+c)),x,4,-4/3*A*(a-b)*b*sqrt(a+b)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d+2/3*sqrt(a+b)*(2*A*b+a*(A+3*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d+2/3*A*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(3/2),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/sqrt(a+b*cos(d*x+c)),x,5,2/15*(a-b)*sqrt(a+b)*(8*A*b^2+3*a^2*(3*A+5*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d+2/15*sqrt(a+b)*(2*a*A*b-8*A*b^2-3*a^2*(3*A+5*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d+2/5*A*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)-8/15*A*b*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/sqrt(a+b*cos(d*x+c)),x,6,-4/105*(a-b)*b*sqrt(a+b)*(24*A*b^2+a^2*(22*A+35*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^5/d-2/105*sqrt(a+b)*(12*a*A*b^2-48*A*b^3-5*a^3*(5*A+7*C)-a^2*(44*A*b+70*C*b))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d+2/7*A*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(7/2)-12/35*A*b*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^2/d/cos(d*x+c)^(5/2)+2/105*(24*A*b^2+5*a^2*(5*A+7*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^3/d/cos(d*x+c)^(3/2),1],
[cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x,8,1/4*(8*A*b^2+15*C*a^2-7*C*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/sqrt(a+b)/d-1/4*(8*A*b^2+(15*a^2+5*a*b-2*b^2)*C)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/sqrt(a+b)/d-1/4*sqrt(a+b)*(8*A*b^2+15*C*a^2+4*C*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^4/d-2*(A*b^2+C*a^2)*cos(d*x+c)^(3/2)*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-1/4*a*(8*A*b^2+15*C*a^2-7*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)/d/sqrt(cos(d*x+c))+1/2*(4*A*b^2+5*C*a^2-C*b^2)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)/d,1],
[sqrt(cos(d*x+c))*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x,7,-(2*A*b^2+3*C*a^2-C*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/sqrt(a+b)/d+(2*A*b^2+a*(3*a+b)*C)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/sqrt(a+b)/d+3*a*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d-2*(A*b^2+C*a^2)*sqrt(cos(d*x+c))*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+(2*A*b^2+3*C*a^2-C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)/d/sqrt(cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x,6,2*(A*b^2+C*a^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/b/sqrt(a+b)/d+2*(A*b-C*a)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/sqrt(a+b)/d-2*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d-2*(A*b^2+C*a^2)*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x,4,-2*(2*A*b^2-a^2*(A-C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/sqrt(a+b)/d-2*(2*A*b+a*(A-C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/sqrt(a+b)/d+2*(A*b^2+C*a^2)*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x,5,2/3*b*(8*A*b^2-a^2*(5*A-3*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/sqrt(a+b)/d+2/3*(6*a*A*b+8*A*b^2+a^2*(A+3*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/sqrt(a+b)/d+2*(A*b^2+C*a^2)*sin(d*x+c)/a/(a^2-b^2)/d/cos(d*x+c)^(3/2)/sqrt(a+b*cos(d*x+c))-2/3*(4*A*b^2-a^2*(A-3*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^2/(a^2-b^2)/d/cos(d*x+c)^(3/2),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x,6,-2/5*(16*A*b^4-2*a^2*b^2*(4*A-5*C)-a^4*(3*A+5*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^5/sqrt(a+b)/d-2/5*(12*a*A*b^2+16*A*b^3+2*a^2*b*(2*A+5*C)+a^3*(3*A+5*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/sqrt(a+b)/d+2*(A*b^2+C*a^2)*sin(d*x+c)/a/(a^2-b^2)/d/cos(d*x+c)^(5/2)/sqrt(a+b*cos(d*x+c))-2/5*(6*A*b^2-a^2*(A-5*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^2/(a^2-b^2)/d/cos(d*x+c)^(5/2)+2/5*b*(8*A*b^2-a^2*(3*A-5*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^3/(a^2-b^2)/d/cos(d*x+c)^(3/2),1],
[cos(d*x+c)^(3/2)*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,8,1/3*(8*A*b^4-15*C*a^4+26*C*a^2*b^2-3*C*b^4)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/(a-b)/b^3/(a+b)^(3/2)/d+1/3*(2*A*a*b^3-6*A*b^4+15*C*a^4+5*C*a^3*b-21*C*a^2*b^2-3*C*a*b^3)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/(a-b)/b^3/(a+b)^(3/2)/d+5*a*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^4/d-2/3*(A*b^2+C*a^2)*cos(d*x+c)^(3/2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+2/3*(3*A*b^4-5*a^4*C+a^2*b^2*(A+9*C))*sqrt(cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c))-1/3*(8*A*b^4-(15*a^4-26*a^2*b^2+3*b^4)*C)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)^2/d/sqrt(cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,7,-2/3*(A*b^4-3*a^4*C+a^2*b^2*(3*A+7*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/b^2/sqrt(a+b)/(a^2-b^2)/d+2/3*(3*A*a*b^2-A*b^3-3*C*a^3-C*a^2*b+6*C*a*b^2)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/(a-b)/b^2/(a+b)^(3/2)/d-2*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d-2/3*(A*b^2+C*a^2)*sqrt(cos(d*x+c))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+2/3*(A*b^4-3*a^4*C+a^2*b^2*(3*A+7*C))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x,5,4/3*b*(3*A*a^2-A*b^2+2*C*a^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/(a-b)/(a+b)^(3/2)/d-2/3*(2*A*b^2+3*a*b*(A+C)-a^2*(3*A+C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/sqrt(a+b)/(a^2-b^2)/d+2/3*(A*b^2+C*a^2)*sqrt(cos(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+4/3*b*(A*b^2-a^2*(3*A+2*C))*sin(d*x+c)/a/(a^2-b^2)^2/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x,5,2/3*(8*A*b^4+3*a^4*(A-C)-a^2*b^2*(15*A+C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/sqrt(a+b)/(a^2-b^2)/d+2/3*(6*a*A*b^2+8*A*b^3-3*a^3*(A-C)-a^2*b*(9*A+C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/sqrt(a+b)/(a^2-b^2)/d+2/3*(A*b^2+C*a^2)*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^(3/2)-4/3*(2*A*b^4-a^4*C-a^2*b^2*(4*A+C))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x,6,-4/3*b*(8*A*b^4+a^4*(4*A-3*C)-a^2*b^2*(14*A-C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^5/sqrt(a+b)/(a^2-b^2)/d-2/3*(12*a*A*b^3+16*A*b^4-2*a^2*b^2*(8*A-C)-a^4*(A+3*C)-a^3*(9*A*b-3*C*b))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/sqrt(a+b)/(a^2-b^2)/d+2/3*(A*b^2+C*a^2)*sin(d*x+c)/a/(a^2-b^2)/d/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2)+4/3*(5*A*a^2*b^2-3*A*b^4+2*C*a^4)*sin(d*x+c)/a^2/(a^2-b^2)^2/d/cos(d*x+c)^(3/2)/sqrt(a+b*cos(d*x+c))+2/3*(8*A*b^4+a^4*(A-5*C)-a^2*b^2*(13*A-C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^3/(a^2-b^2)^2/d/cos(d*x+c)^(3/2),1],
[cos(d*x+c)^m*(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2),x,6,(2*a^2*C+b^2*(C*(3+m)+A*(4+m)))*cos(d*x+c)^(1+m)*sin(d*x+c)/d/(2+m)/(4+m)+2*a*b*C*cos(d*x+c)^(2+m)*sin(d*x+c)/d/(3+m)/(4+m)+C*cos(d*x+c)^(1+m)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/(4+m)-(a^2*(4+m)*(C*(1+m)+A*(2+m))+b^2*(1+m)*(C*(3+m)+A*(4+m)))*cos(d*x+c)^(1+m)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],cos(d*x+c)^2)*sin(d*x+c)/d/(1+m)/(2+m)/(4+m)/sqrt(sin(d*x+c)^2)-2*a*b*(C*(2+m)+A*(3+m))*cos(d*x+c)^(2+m)*hypergeom([1/2, 1+1/2*m],[2+1/2*m],cos(d*x+c)^2)*sin(d*x+c)/d/(2+m)/(3+m)/sqrt(sin(d*x+c)^2),1],
[cos(d*x+c)^m*(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2),x,5,a*C*cos(d*x+c)^(1+m)*sin(d*x+c)/d/(2+m)+b*C*cos(d*x+c)^(2+m)*sin(d*x+c)/d/(3+m)-a*(C*(1+m)+A*(2+m))*cos(d*x+c)^(1+m)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],cos(d*x+c)^2)*sin(d*x+c)/d/(1+m)/(2+m)/sqrt(sin(d*x+c)^2)-b*(C*(2+m)+A*(3+m))*cos(d*x+c)^(2+m)*hypergeom([1/2, 1+1/2*m],[2+1/2*m],cos(d*x+c)^2)*sin(d*x+c)/d/(2+m)/(3+m)/sqrt(sin(d*x+c)^2),1],
[cos(d*x+c)^m*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,10,a*(A*b^2+C*a^2)*AppellF1(1/2,1/2-1/2*m,1,3/2,sin(d*x+c)^2,-b^2*sin(d*x+c)^2/(a^2-b^2))*cos(d*x+c)^(-1+m)*(cos(d*x+c)^2)^(1/2-1/2*m)*sin(d*x+c)/b^2/(a^2-b^2)/d-(A*b^2+C*a^2)*AppellF1(1/2,-1/2*m,1,3/2,sin(d*x+c)^2,-b^2*sin(d*x+c)^2/(a^2-b^2))*cos(d*x+c)^m*sin(d*x+c)/b/(a^2-b^2)/d/((cos(d*x+c)^2)^(1/2*m))+a*C*cos(d*x+c)^(1+m)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],cos(d*x+c)^2)*sin(d*x+c)/b^2/d/(1+m)/sqrt(sin(d*x+c)^2)-C*cos(d*x+c)^(2+m)*hypergeom([1/2, 1+1/2*m],[2+1/2*m],cos(d*x+c)^2)*sin(d*x+c)/b/d/(2+m)/sqrt(sin(d*x+c)^2),1],
[cos(d*x+c)^m*(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,11,(A*b^4*m-a^4*C*(1+m)+a^2*b^2*(A-A*m+C*(2+m)))*AppellF1(1/2,1/2-1/2*m,1,3/2,sin(d*x+c)^2,-b^2*sin(d*x+c)^2/(a^2-b^2))*cos(d*x+c)^(-1+m)*(cos(d*x+c)^2)^(1/2-1/2*m)*sin(d*x+c)/b^2/(a^2-b^2)^2/d-(A*b^4*m-a^4*C*(1+m)+a^2*b^2*(A-A*m+C*(2+m)))*AppellF1(1/2,-1/2*m,1,3/2,sin(d*x+c)^2,-b^2*sin(d*x+c)^2/(a^2-b^2))*cos(d*x+c)^m*sin(d*x+c)/a/b/(a^2-b^2)^2/d/((cos(d*x+c)^2)^(1/2*m))+(A*b^2+C*a^2)*cos(d*x+c)^(1+m)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))-(a^2*C*(1+m)-b^2*(-A*m+C))*cos(d*x+c)^(1+m)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],cos(d*x+c)^2)*sin(d*x+c)/b^2/(a^2-b^2)/d/(1+m)/sqrt(sin(d*x+c)^2)+(A*b^2+C*a^2)*(1+m)*cos(d*x+c)^(2+m)*hypergeom([1/2, 1+1/2*m],[2+1/2*m],cos(d*x+c)^2)*sin(d*x+c)/a/b/(a^2-b^2)/d/(2+m)/sqrt(sin(d*x+c)^2),1],
[cos(d*x+c)*(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,8,1/8*(4*B*a+3*C*b)*x+(B*b+C*a)*sin(d*x+c)/d+1/8*(4*B*a+3*C*b)*cos(d*x+c)*sin(d*x+c)/d+1/4*b*C*cos(d*x+c)^3*sin(d*x+c)/d-1/3*(B*b+C*a)*sin(d*x+c)^3/d,1],
[(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,2,1/2*(B*b+C*a)*x+1/3*(3*B*a+2*C*b)*sin(d*x+c)/d+1/2*(B*b+C*a)*cos(d*x+c)*sin(d*x+c)/d+1/3*b*C*cos(d*x+c)^2*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,2,1/2*(2*B*a+C*b)*x+(B*b+C*a)*sin(d*x+c)/d+1/2*b*C*cos(d*x+c)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,5,(B*b+C*a)*x+a*B*arctanh(sin(d*x+c))/d+b*C*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,5,b*C*x+(B*b+C*a)*arctanh(sin(d*x+c))/d+a*B*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,7,1/2*(B*a+2*C*b)*arctanh(sin(d*x+c))/d+(B*b+C*a)*tan(d*x+c)/d+1/2*a*B*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,8,1/2*(B*b+C*a)*arctanh(sin(d*x+c))/d+1/3*(2*B*a+3*C*b)*tan(d*x+c)/d+1/2*(B*b+C*a)*sec(d*x+c)*tan(d*x+c)/d+1/3*a*B*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,8,1/8*(3*B*a+4*C*b)*arctanh(sin(d*x+c))/d+(B*b+C*a)*tan(d*x+c)/d+1/8*(3*B*a+4*C*b)*sec(d*x+c)*tan(d*x+c)/d+1/4*a*B*sec(d*x+c)^3*tan(d*x+c)/d+1/3*(B*b+C*a)*tan(d*x+c)^3/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,8,1/8*(4*B*a^2+3*B*b^2+6*C*a*b)*x+1/5*(4*b^2*C+5*a*(2*B*b+C*a))*sin(d*x+c)/d+1/8*(4*B*a^2+3*B*b^2+6*C*a*b)*cos(d*x+c)*sin(d*x+c)/d+1/20*b*(5*B*b+6*C*a)*cos(d*x+c)^3*sin(d*x+c)/d+1/5*b*C*cos(d*x+c)^3*(a+b*cos(d*x+c))*sin(d*x+c)/d-1/15*(4*b^2*C+5*a*(2*B*b+C*a))*sin(d*x+c)^3/d,1],
[(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,3,1/8*(8*B*a*b+4*C*a^2+3*C*b^2)*x+1/6*(4*B*a^2*b+4*B*b^3-C*a^3+8*C*a*b^2)*sin(d*x+c)/b/d+1/24*(8*B*a*b-2*C*a^2+9*C*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/12*(4*B*b-C*a)*(a+b*cos(d*x+c))^2*sin(d*x+c)/b/d+1/4*C*(a+b*cos(d*x+c))^3*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,3,1/2*(2*B*a^2+B*b^2+2*C*a*b)*x+2/3*(3*B*a*b+C*a^2+C*b^2)*sin(d*x+c)/d+1/6*b*(3*B*b+2*C*a)*cos(d*x+c)*sin(d*x+c)/d+1/3*C*(a+b*cos(d*x+c))^2*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,5,1/2*(4*B*a*b+2*C*a^2+C*b^2)*x+a^2*B*arctanh(sin(d*x+c))/d+1/2*b*(2*B*b+3*C*a)*sin(d*x+c)/d+1/2*b*C*(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,5,b*(B*b+2*C*a)*x+a*(2*B*b+C*a)*arctanh(sin(d*x+c))/d+b^2*C*sin(d*x+c)/d+a^2*B*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,5,b^2*C*x+1/2*(B*a^2+2*B*b^2+4*C*a*b)*arctanh(sin(d*x+c))/d+a*(2*B*b+C*a)*tan(d*x+c)/d+1/2*a^2*B*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,7,1/2*(2*B*a*b+C*a^2+2*C*b^2)*arctanh(sin(d*x+c))/d+1/3*(2*B*a^2+3*B*b^2+6*C*a*b)*tan(d*x+c)/d+1/2*a*(2*B*b+C*a)*sec(d*x+c)*tan(d*x+c)/d+1/3*a^2*B*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,8,1/8*(3*B*a^2+4*B*b^2+8*C*a*b)*arctanh(sin(d*x+c))/d+1/3*(4*B*a*b+2*C*a^2+3*C*b^2)*tan(d*x+c)/d+1/8*(3*B*a^2+4*B*b^2+8*C*a*b)*sec(d*x+c)*tan(d*x+c)/d+1/3*a*(2*B*b+C*a)*sec(d*x+c)^2*tan(d*x+c)/d+1/4*a^2*B*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,4,1/8*(12*B*a^2*b+3*B*b^3+4*C*a^3+9*C*a*b^2)*x+1/30*(15*B*a^3*b+60*B*a*b^3-3*C*a^4+52*C*a^2*b^2+16*C*b^4)*sin(d*x+c)/b/d+1/120*(30*B*a^2*b+45*B*b^3-6*C*a^3+71*C*a*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/60*(15*B*a*b-3*C*a^2+16*C*b^2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/b/d+1/20*(5*B*b-C*a)*(a+b*cos(d*x+c))^3*sin(d*x+c)/b/d+1/5*C*(a+b*cos(d*x+c))^4*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,4,1/8*(8*B*a^3+12*B*a*b^2+12*C*a^2*b+3*C*b^3)*x+1/6*(16*B*a^2*b+4*B*b^3+3*C*a^3+12*C*a*b^2)*sin(d*x+c)/d+1/24*b*(20*B*a*b+6*C*a^2+9*C*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/12*(4*B*b+3*C*a)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+1/4*C*(a+b*cos(d*x+c))^3*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,6,1/2*(6*B*a^2*b+B*b^3+2*C*a^3+3*C*a*b^2)*x+a^3*B*arctanh(sin(d*x+c))/d+1/3*b*(9*B*a*b+8*C*a^2+2*C*b^2)*sin(d*x+c)/d+1/6*b^2*(3*B*b+5*C*a)*cos(d*x+c)*sin(d*x+c)/d+1/3*b*C*(a+b*cos(d*x+c))^2*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,6,1/2*b*(6*B*a*b+6*C*a^2+C*b^2)*x+a^2*(3*B*b+C*a)*arctanh(sin(d*x+c))/d-b*(2*B*a^2-B*b^2-3*C*a*b)*sin(d*x+c)/d-1/2*b^2*(2*B*a-C*b)*cos(d*x+c)*sin(d*x+c)/d+a*B*(a+b*cos(d*x+c))^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,6,b^2*(B*b+3*C*a)*x+1/2*a*(B*a^2+6*B*b^2+6*C*a*b)*arctanh(sin(d*x+c))/d-1/2*b^2*(B*a-2*C*b)*sin(d*x+c)/d+a^2*(2*B*b+C*a)*tan(d*x+c)/d+1/2*a*B*(a+b*cos(d*x+c))^2*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,6,b^3*C*x+1/2*(3*B*a^2*b+2*B*b^3+C*a^3+6*C*a*b^2)*arctanh(sin(d*x+c))/d+1/3*a*(2*B*a^2+8*B*b^2+9*C*a*b)*tan(d*x+c)/d+1/6*a^2*(5*B*b+3*C*a)*sec(d*x+c)*tan(d*x+c)/d+1/3*a*B*(a+b*cos(d*x+c))^2*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,8,1/8*(3*B*a^3+12*B*a*b^2+12*C*a^2*b+8*C*b^3)*arctanh(sin(d*x+c))/d+1/3*(6*B*a^2*b+3*B*b^3+2*C*a^3+9*C*a*b^2)*tan(d*x+c)/d+1/8*a*(3*B*a^2+10*B*b^2+12*C*a*b)*sec(d*x+c)*tan(d*x+c)/d+1/6*a^2*(3*B*b+2*C*a)*sec(d*x+c)^2*tan(d*x+c)/d+1/4*a*B*(a+b*cos(d*x+c))^2*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x,9,1/8*(9*B*a^2*b+4*B*b^3+3*C*a^3+12*C*a*b^2)*arctanh(sin(d*x+c))/d+1/15*(8*B*a^3+30*B*a*b^2+30*C*a^2*b+15*C*b^3)*tan(d*x+c)/d+1/8*(9*B*a^2*b+4*B*b^3+3*C*a^3+12*C*a*b^2)*sec(d*x+c)*tan(d*x+c)/d+1/15*a*(4*B*a^2+12*B*b^2+15*C*a*b)*sec(d*x+c)^2*tan(d*x+c)/d+1/20*a^2*(7*B*b+5*C*a)*sec(d*x+c)^3*tan(d*x+c)/d+1/5*a*B*(a+b*cos(d*x+c))^2*sec(d*x+c)^4*tan(d*x+c)/d,1],
[cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,7,1/2*(2*a^2+b^2)*(B*b-C*a)*x/b^4-2*a^3*(B*b-C*a)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^4/sqrt(a+b)/d-1/3*(3*B*a*b-3*C*a^2-2*C*b^2)*sin(d*x+c)/b^3/d+1/2*(B*b-C*a)*cos(d*x+c)*sin(d*x+c)/b^2/d+1/3*C*cos(d*x+c)^2*sin(d*x+c)/b/d,1],
[cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,6,-1/2*(2*B*a*b-2*C*a^2-C*b^2)*x/b^3+2*a^2*(B*b-C*a)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^3/sqrt(a+b)/d+(B*b-C*a)*sin(d*x+c)/b^2/d+1/2*C*cos(d*x+c)*sin(d*x+c)/b/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,5,(B*b-C*a)*x/b^2-2*a*(B*b-C*a)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^2/sqrt(a+b)/d+C*sin(d*x+c)/b/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c)),x,4,C*x/b+2*(B*b-C*a)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b/sqrt(a+b)/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c)),x,5,-2*(B*b-C*a)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a/sqrt(a-b)/sqrt(a+b)/d+B*arctanh(sin(d*x+c))/a/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c)),x,7,2*b*(B*b-C*a)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^2/sqrt(a-b)/sqrt(a+b)/d-(B*b-C*a)*arctanh(sin(d*x+c))/a^2/d+B*tan(d*x+c)/a/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c)),x,7,-2*b^2*(B*b-C*a)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^3/sqrt(a-b)/sqrt(a+b)/d+1/2*(B*a^2+2*B*b^2-2*C*a*b)*arctanh(sin(d*x+c))/a^3/d-(B*b-C*a)*tan(d*x+c)/a^2/d+1/2*B*sec(d*x+c)*tan(d*x+c)/a/d,1],
[cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,7,-1/2*(4*B*a*b-6*C*a^2-C*b^2)*x/b^4+2*a^2*(2*B*a^2*b-3*B*b^3-3*C*a^3+4*C*a*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/b^4/(a+b)^(3/2)/d+(2*B*a^2*b-B*b^3-3*C*a^3+2*C*a*b^2)*sin(d*x+c)/b^3/(a^2-b^2)/d-1/2*(2*B*a*b-3*C*a^2+C*b^2)*cos(d*x+c)*sin(d*x+c)/b^2/(a^2-b^2)/d+a*(B*b-C*a)*cos(d*x+c)^2*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,6,(B*b-2*C*a)*x/b^3-2*a*(B*a^2*b-2*B*b^3-2*C*a^3+3*C*a*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/b^3/(a+b)^(3/2)/d+C*sin(d*x+c)/b^2/d-a^2*(B*b-C*a)*sin(d*x+c)/b^2/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,4,C*x/b^2-2*(B*b^3+C*a^3-2*C*a*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/b^2/(a+b)^(3/2)/d+a*(B*b-C*a)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^2,x,5,2*(B*a-C*b)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/(a+b)^(3/2)/d-(B*b-C*a)*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x,6,-2*(2*B*a^2*b-B*b^3-C*a^3)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^2/(a-b)^(3/2)/(a+b)^(3/2)/d+B*arctanh(sin(d*x+c))/a^2/d+b*(B*b-C*a)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x,7,2*b*(3*B*a^2*b-2*B*b^3-2*C*a^3+C*a*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^3/(a-b)^(3/2)/(a+b)^(3/2)/d-(2*B*b-C*a)*arctanh(sin(d*x+c))/a^3/d+(B*a^2-2*B*b^2+C*a*b)*tan(d*x+c)/a^2/(a^2-b^2)/d+b*(B*b-C*a)*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,8,-1/2*(6*B*a*b-12*C*a^2-C*b^2)*x/b^5+a^2*(6*B*a^4*b-15*B*a^2*b^3+12*B*b^5-12*C*a^5+29*C*a^3*b^2-20*C*a*b^4)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(5/2)/b^5/(a+b)^(5/2)/d+1/2*(6*B*a^4*b-11*B*a^2*b^3+2*B*b^5-12*C*a^5+21*C*a^3*b^2-6*C*a*b^4)*sin(d*x+c)/b^4/(a^2-b^2)^2/d-1/2*(3*B*a^3*b-6*B*a*b^3-6*C*a^4+10*C*a^2*b^2-C*b^4)*cos(d*x+c)*sin(d*x+c)/b^3/(a^2-b^2)^2/d+1/2*a*(B*b-C*a)*cos(d*x+c)^3*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/2*a*(2*B*a^2*b-5*B*b^3-4*C*a^3+7*C*a*b^2)*cos(d*x+c)^2*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,7,(B*b-3*C*a)*x/b^4-a*(2*B*a^4*b-5*B*a^2*b^3+6*B*b^5-6*C*a^5+15*C*a^3*b^2-12*C*a*b^4)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(5/2)/b^4/(a+b)^(5/2)/d-1/2*(B*a*b-3*C*a^2+2*C*b^2)*sin(d*x+c)/b^3/(a^2-b^2)/d+1/2*a*(B*b-C*a)*cos(d*x+c)^2*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/2*a^2*(B*a^2*b-4*B*b^3-3*C*a^3+6*C*a*b^2)*sin(d*x+c)/b^3/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,6,C*x/b^3+(B*a^2*b^3+2*B*b^5-2*C*a^5+5*C*a^3*b^2-6*C*a*b^4)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(5/2)/b^3/(a+b)^(5/2)/d-1/2*a^2*(B*b-C*a)*sin(d*x+c)/b^2/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/2*a*(B*a^2*b-4*B*b^3-3*C*a^3+6*C*a*b^2)*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,5,-(3*B*a*b-C*a^2-2*C*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(5/2)/(a+b)^(5/2)/d+1/2*a*(B*b-C*a)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/2*(B*a^2*b+2*B*b^3+C*a^3-4*C*a*b^2)*sin(d*x+c)/b/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^3,x,6,(2*B*a^2+B*b^2-3*C*a*b)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(5/2)/(a+b)^(5/2)/d-1/2*(B*b-C*a)*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/2*(3*B*a*b-C*a^2-2*C*b^2)*sin(d*x+c)/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^3,x,7,-(6*B*a^4*b-5*B*a^2*b^3+2*B*b^5-2*C*a^5-C*a^3*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^3/(a-b)^(5/2)/(a+b)^(5/2)/d+B*arctanh(sin(d*x+c))/a^3/d+1/2*b*(B*b-C*a)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/2*b*(5*B*a^2*b-2*B*b^3-3*C*a^3)*sin(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^3,x,8,b*(12*B*a^4*b-15*B*a^2*b^3+6*B*b^5-6*C*a^5+5*C*a^3*b^2-2*C*a*b^4)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^4/(a-b)^(5/2)/(a+b)^(5/2)/d-(3*B*b-C*a)*arctanh(sin(d*x+c))/a^4/d+1/2*(2*B*a^4-11*B*a^2*b^2+6*B*b^4+5*C*a^3*b-2*C*a*b^3)*tan(d*x+c)/a^3/(a^2-b^2)^2/d+1/2*b*(B*b-C*a)*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/2*b*(6*B*a^2*b-3*B*b^3-4*C*a^3+C*a*b^2)*tan(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)*sqrt(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,9,-2/105*(14*B*a^2*b-63*B*b^3-8*C*a^3-19*C*a*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^3/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/105*(a^2-b^2)*(14*B*a*b-8*C*a^2-25*C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^3/d/sqrt(a+b*cos(d*x+c))-2/105*(14*B*a*b-8*C*a^2-25*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d+2/35*(7*B*b-4*C*a)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^2/d+2/7*C*cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d,1],
[sqrt(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,7,2/15*(5*B*a*b-2*C*a^2+9*C*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/15*(a^2-b^2)*(5*B*b-2*C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/d/sqrt(a+b*cos(d*x+c))+2/15*(5*B*b-2*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+2/5*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d,1],
[sqrt(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,7,2/3*(3*B*b+C*a)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/3*(a^2-b^2)*C*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b/d/sqrt(a+b*cos(d*x+c))+2/3*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,9,2*C*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+2*b*B*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+2*a*B*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c)),1],
[sqrt(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,10,-B*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+(B*a+2*C*b)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+(B*b+2*C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+B*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,11,-1/4*(B*b+4*C*a)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/4*(3*B*b+4*C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+1/4*(4*B*a^2-B*b^2+4*C*a*b)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+1/4*(B*b+4*C*a)*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a/d+1/2*B*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,10,-2/315*(18*B*a^3*b-246*B*a*b^3-8*C*a^4-33*C*a^2*b^2-147*C*b^4)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^3/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/315*(a^2-b^2)*(18*B*a^2*b-75*B*b^3-8*C*a^3-39*C*a*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^3/d/sqrt(a+b*cos(d*x+c))-2/315*(18*B*a^2*b-75*B*b^3-8*C*a^3-39*C*a*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d-2/315*(18*B*a*b-8*C*a^2-49*C*b^2)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^2/d+2/63*(9*B*b-4*C*a)*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b^2/d+2/9*C*cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,8,2/105*(21*B*a^2*b+63*B*b^3-6*C*a^3+82*C*a*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/105*(a^2-b^2)*(21*B*a*b-6*C*a^2+25*C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/d/sqrt(a+b*cos(d*x+c))+2/105*(21*B*a*b-6*C*a^2+25*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+2/35*(7*B*b-2*C*a)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d+2/7*C*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,8,2/15*(20*B*a*b+3*C*a^2+9*C*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/15*(a^2-b^2)*(5*B*b+3*C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b/d/sqrt(a+b*cos(d*x+c))+2/15*(5*B*b+3*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+2/5*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,10,2/3*(3*B*b+4*C*a)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/3*(3*B*a*b-C*a^2+C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+2*a^2*B*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+2/3*b*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,10,-(B*a-2*C*b)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+(B*a^2+2*B*b^2+2*C*a*b)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+a*(3*B*b+2*C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+a*B*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,11,-1/4*(5*B*b+4*C*a)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/4*(7*B*a*b+4*C*a^2+8*C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+1/4*(4*B*a^2+3*B*b^2+12*C*a*b)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+1/4*(5*B*b+4*C*a)*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/d+1/2*a*B*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,12,-1/24*(16*B*a^2+3*B*b^2+30*C*a*b)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/24*(16*B*a^2+17*B*b^2+42*C*a*b)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+1/8*(12*B*a^2*b-B*b^3+8*C*a^3+6*C*a*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+1/24*(16*B*a^2+3*B*b^2+30*C*a*b)*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a/d+1/12*(7*B*b+6*C*a)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/3*a*B*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,11,-2/3465*(110*B*a^4*b-3069*B*a^2*b^3-1617*B*b^5-40*C*a^5-255*C*a^3*b^2-3705*C*a*b^4)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^3/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/3465*(a^2-b^2)*(110*B*a^3*b-1254*B*a*b^3-40*C*a^4-285*C*a^2*b^2-675*C*b^4)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^3/d/sqrt(a+b*cos(d*x+c))-2/3465*(110*B*a^3*b-1254*B*a*b^3-40*C*a^4-285*C*a^2*b^2-675*C*b^4)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d-2/3465*(110*B*a^2*b-539*B*b^3-40*C*a^3-335*C*a*b^2)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^2/d-2/693*(22*B*a*b-8*C*a^2-81*C*b^2)*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b^2/d+2/99*(11*B*b-4*C*a)*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b^2/d+2/11*C*cos(d*x+c)*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,9,2/315*(45*B*a^3*b+435*B*a*b^3-10*C*a^4+279*C*a^2*b^2+147*C*b^4)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/315*(a^2-b^2)*(45*B*a^2*b+75*B*b^3-10*C*a^3+114*C*a*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/d/sqrt(a+b*cos(d*x+c))+2/315*(45*B*a^2*b+75*B*b^3-10*C*a^3+114*C*a*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+2/315*(45*B*a*b-10*C*a^2+49*C*b^2)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d+2/63*(9*B*b-2*C*a)*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d+2/9*C*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,9,2/105*(161*B*a^2*b+63*B*b^3+15*C*a^3+145*C*a*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/105*(a^2-b^2)*(56*B*a*b+15*C*a^2+25*C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b/d/sqrt(a+b*cos(d*x+c))+2/105*(56*B*a*b+15*C*a^2+25*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+2/35*(7*B*b+5*C*a)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/7*C*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,11,2/15*(35*B*a*b+23*C*a^2+9*C*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/15*(10*B*a^2*b+5*B*b^3-8*C*a^3+8*C*a*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+2*a^3*B*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+2/15*b*(5*B*b+8*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+2/5*b*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,11,-1/3*(3*B*a^2-6*B*b^2-14*C*a*b)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/3*(3*B*a^3+12*B*a*b^2+4*C*a^2*b+2*C*b^3)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+a^2*(5*B*b+2*C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-1/3*b*(3*B*a-2*C*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+a*B*(a+b*cos(d*x+c))^(3/2)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,11,-1/4*(9*B*a*b+4*C*a^2-8*C*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/4*(11*B*a^2*b+8*B*b^3+4*C*a^3+16*C*a*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+1/4*a*(4*B*a^2+15*B*b^2+20*C*a*b)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+1/4*a*(7*B*b+4*C*a)*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/d+1/2*a*B*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,12,-1/24*(16*B*a^2+33*B*b^2+54*C*a*b)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/24*(16*B*a^3+59*B*a*b^2+66*C*a^2*b+48*C*b^3)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+1/8*(20*B*a^2*b+5*B*b^3+8*C*a^3+30*C*a*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+1/24*(16*B*a^2+33*B*b^2+54*C*a*b)*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/d+1/4*a*(3*B*b+2*C*a)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/3*a*B*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,13,-1/192*(284*B*a^2*b+15*B*b^3+128*C*a^3+264*C*a*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/192*(356*B*a^2*b+133*B*b^3+128*C*a^3+472*C*a*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+1/64*(48*B*a^4+120*B*a^2*b^2-5*B*b^4+160*C*a^3*b+40*C*a*b^3)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+1/192*(284*B*a^2*b+15*B*b^3+128*C*a^3+264*C*a*b^2)*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a/d+1/96*(36*B*a^2+59*B*b^2+104*C*a*b)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/24*a*(11*B*b+8*C*a)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d+1/4*a*B*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^3*tan(d*x+c)/d,1],
[cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c)),x,8,-2/15*(10*B*a*b-8*C*a^2-9*C*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^3/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/15*(10*B*a^2*b+5*B*b^3-8*C*a^3-7*C*a*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^3/d/sqrt(a+b*cos(d*x+c))+2/15*(5*B*b-4*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d+2/5*C*cos(d*x+c)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c)),x,6,2/3*(3*B*b-2*C*a)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/3*(3*B*a*b-2*C*a^2-C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/d/sqrt(a+b*cos(d*x+c))+2/3*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/sqrt(a+b*cos(d*x+c)),x,6,2*C*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b/d/sqrt((a+b*cos(d*x+c))/(a+b))+2*(B*b-C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b/d/sqrt(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/sqrt(a+b*cos(d*x+c)),x,6,2*C*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+2*B*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/sqrt(a+b*cos(d*x+c)),x,10,-B*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a/d/sqrt((a+b*cos(d*x+c))/(a+b))+B*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-(B*b-2*C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+B*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/sqrt(a+b*cos(d*x+c)),x,11,1/4*(3*B*b-4*C*a)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-1/4*(B*b-4*C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+1/4*(4*B*a^2+3*B*b^2-4*C*a*b)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^2/d/sqrt(a+b*cos(d*x+c))-1/4*(3*B*b-4*C*a)*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a^2/d+1/2*B*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/a/d,1],
[cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x,9,-2/15*(40*B*a^3*b-25*B*a*b^3-48*C*a^4+24*C*a^2*b^2+9*C*b^4)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^4/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/15*(40*B*a^2*b+5*B*b^3-48*C*a^3-12*C*a*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^4/d/sqrt(a+b*cos(d*x+c))+2*a*(B*b-C*a)*cos(d*x+c)^2*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+2/15*(20*B*a^2*b-5*B*b^3-24*C*a^3+9*C*a*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)/d-2/5*(5*B*a*b-6*C*a^2+C*b^2)*cos(d*x+c)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)/d,1],
[cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x,8,2/3*(6*B*a^2*b-3*B*b^3-8*C*a^3+5*C*a*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^3/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/3*(6*B*a*b-8*C*a^2-C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^3/d/sqrt(a+b*cos(d*x+c))-2*a^2*(B*b-C*a)*sin(d*x+c)/b^2/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+2/3*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x,6,-2*(B*a*b-2*C*a^2+C*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))+2*(B*b-2*C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/d/sqrt(a+b*cos(d*x+c))+2*a*(B*b-C*a)*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x,7,2*(B*b-C*a)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))+2*C*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b/d/sqrt(a+b*cos(d*x+c))-2*(B*b-C*a)*sin(d*x+c)/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x,8,-2*(B*b-C*a)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))+2*B*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+2*b*(B*b-C*a)*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x,11,-(B*a^2-3*B*b^2+2*C*a*b)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^2/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))+B*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))-(3*B*b-2*C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^2/d/sqrt(a+b*cos(d*x+c))+b*(B*a^2-3*B*b^2+2*C*a*b)*sin(d*x+c)/a^2/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+B*tan(d*x+c)/a/d/sqrt(a+b*cos(d*x+c)),1],
[cos(d*x+c)^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,9,2/3*(8*B*a^4*b-15*B*a^2*b^3+3*B*b^5-16*C*a^5+28*C*a^3*b^2-8*C*a*b^4)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^4/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/3*(8*B*a^3*b-9*B*a*b^3-16*C*a^4+16*C*a^2*b^2+C*b^4)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^4/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+2/3*a*(B*b-C*a)*cos(d*x+c)^2*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)-2/3*a^2*(3*B*a^2*b-7*B*b^3-6*C*a^3+10*C*a*b^2)*sin(d*x+c)/b^3/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c))-2/3*(B*a*b-2*C*a^2+C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)/d,1],
[cos(d*x+c)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,8,-2/3*(2*B*a^3*b-6*B*a*b^3-8*C*a^4+15*C*a^2*b^2-3*C*b^4)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^3/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/3*(2*B*a^2*b-3*B*b^3-8*C*a^3+9*C*a*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^3/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-2/3*a^2*(B*b-C*a)*sin(d*x+c)/b^2/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+2/3*a*(2*B*a^2*b-6*B*b^3-5*C*a^3+9*C*a*b^2)*sin(d*x+c)/b^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,7,-2/3*(B*a^2*b+3*B*b^3+2*C*a^3-6*C*a*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/3*(B*a*b+2*C*a^2-3*C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+2/3*a*(B*b-C*a)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+2/3*(B*a^2*b+3*B*b^3+2*C*a^3-6*C*a*b^2)*sin(d*x+c)/b/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x,8,2/3*(4*B*a*b-C*a^2-3*C*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/3*(B*b-C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-2/3*(B*b-C*a)*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)-2/3*(4*B*a*b-C*a^2-3*C*b^2)*sin(d*x+c)/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x,11,-2/3*(7*B*a^2*b-3*B*b^3-4*C*a^3)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^2/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/3*(B*b-C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+2*B*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^2/d/sqrt(a+b*cos(d*x+c))+2/3*b*(B*b-C*a)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+2/3*b*(7*B*a^2*b-3*B*b^3-4*C*a^3)*sin(d*x+c)/a^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(5/2),x,12,-1/3*(3*B*a^4-26*B*a^2*b^2+15*B*b^4+14*C*a^3*b-6*C*a*b^3)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^3/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/3*(3*B*a^2-5*B*b^2+2*C*a*b)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a^2/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-(5*B*b-2*C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^3/d/sqrt(a+b*cos(d*x+c))+1/3*b*(3*B*a^2-5*B*b^2+2*C*a*b)*sin(d*x+c)/a^2/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+1/3*b*(3*B*a^4-26*B*a^2*b^2+15*B*b^4+14*C*a^3*b-6*C*a*b^3)*sin(d*x+c)/a^3/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c))+B*tan(d*x+c)/a/d/(a+b*cos(d*x+c))^(3/2),1],
[cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,9,2/15*(9*B*a+7*C*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+10/21*(B*b+C*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+10/21*(B*b+C*a)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*(9*B*a+7*C*b)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*(B*b+C*a)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/9*b*C*cos(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,8,6/5*(B*b+C*a)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(7*B*a+5*C*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*(7*B*a+5*C*b)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*(B*b+C*a)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*b*C*cos(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,7,2/5*(5*B*a+3*C*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(B*b+C*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*(B*b+C*a)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*b*C*cos(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,6,2*(B*b+C*a)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(3*B*a+C*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*b*C*sqrt(cos(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,6,-2*(B*a-C*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2*(B*b+C*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2*a*B*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,7,-2*(B*b+C*a)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(B*a+3*C*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*a*B*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2*(B*b+C*a)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,8,-2/5*(3*B*a+5*C*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(B*b+C*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/5*a*B*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/3*(B*b+C*a)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*(3*B*a+5*C*b)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,9,2/15*(9*B*a^2+7*B*b^2+14*C*a*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+10/231*(9*b^2*C+11*a*(2*B*b+C*a))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+10/231*(9*b^2*C+11*a*(2*B*b+C*a))*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*(9*B*a^2+7*B*b^2+14*C*a*b)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/77*(9*b^2*C+11*a*(2*B*b+C*a))*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/99*b*(11*B*b+13*C*a)*cos(d*x+c)^(7/2)*sin(d*x+c)/d+2/11*b*C*cos(d*x+c)^(7/2)*(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,8,2/15*(7*b^2*C+9*a*(2*B*b+C*a))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(7*B*a^2+5*B*b^2+10*C*a*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*(7*B*a^2+5*B*b^2+10*C*a*b)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*(7*b^2*C+9*a*(2*B*b+C*a))*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/63*b*(9*B*b+11*C*a)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/9*b*C*cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,7,2/5*(5*B*a^2+3*B*b^2+6*C*a*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(5*b^2*C+7*a*(2*B*b+C*a))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*(5*b^2*C+7*a*(2*B*b+C*a))*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/35*b*(7*B*b+9*C*a)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*b*C*cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,6,2/5*(3*b^2*C+5*a*(2*B*b+C*a))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(3*B*a^2+B*b^2+2*C*a*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/15*b*(5*B*b+7*C*a)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*b*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,6,-2*(B*a^2-B*b^2-2*C*a*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(6*B*a*b+3*C*a^2+C*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2*a^2*B*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*b^2*C*sqrt(cos(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,6,-2*(2*B*a*b+C*a^2-C*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(B*a^2+3*B*b^2+6*C*a*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*a^2*B*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2*a*(2*B*b+C*a)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,7,-2/5*(3*B*a^2+5*B*b^2+10*C*a*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(2*B*a*b+C*a^2+3*C*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/5*a^2*B*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/3*a*(2*B*b+C*a)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*(3*B*a^2+5*B*b^2+10*C*a*b)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))^2*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,8,-2/5*(6*B*a*b+3*C*a^2+5*C*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(5*B*a^2+7*B*b^2+14*C*a*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/7*a^2*B*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/5*a*(2*B*b+C*a)*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/21*(5*B*a^2+7*B*b^2+14*C*a*b)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*(6*B*a*b+3*C*a^2+5*C*b^2)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,9,2/15*(27*B*a^2*b+7*B*b^3+9*C*a^3+21*C*a*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/231*(77*B*a^3+165*B*a*b^2+165*C*a^2*b+45*C*b^3)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/231*(77*B*a^3+165*B*a*b^2+165*C*a^2*b+45*C*b^3)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*(27*B*a^2*b+7*B*b^3+9*C*a^3+21*C*a*b^2)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/77*b*(33*B*a*b+26*C*a^2+9*C*b^2)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/99*b^2*(11*B*b+15*C*a)*cos(d*x+c)^(7/2)*sin(d*x+c)/d+2/11*b*C*cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,8,2/15*(15*B*a^3+27*B*a*b^2+27*C*a^2*b+7*C*b^3)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(21*B*a^2*b+5*B*b^3+7*C*a^3+15*C*a*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*(21*B*a^2*b+5*B*b^3+7*C*a^3+15*C*a*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*b*(27*B*a*b+22*C*a^2+7*C*b^2)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/63*b^2*(9*B*b+13*C*a)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/9*b*C*cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,7,2/5*(15*B*a^2*b+3*B*b^3+5*C*a^3+9*C*a*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(21*B*a^3+21*B*a*b^2+21*C*a^2*b+5*C*b^3)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*b*(21*B*a*b+18*C*a^2+5*C*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/35*b^2*(7*B*b+11*C*a)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*b*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,7,-2/5*(5*B*a^3-15*B*a*b^2-15*C*a^2*b-3*C*b^3)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(9*B*a^2*b+B*b^3+3*C*a^3+3*C*a*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-2/3*b*(6*B*a^2-B*b^2-3*C*a*b)*sqrt(cos(d*x+c))*sin(d*x+c)/d-2/5*b^2*(5*B*a-C*b)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2*a*B*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,7,-2*(3*B*a^2*b-B*b^3+C*a^3-3*C*a*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(B*a^3+9*B*a*b^2+9*C*a^2*b+C*b^3)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*a^2*(7*B*b+3*C*a)*sin(d*x+c)/d/sqrt(cos(d*x+c))-2/3*b^2*(B*a-C*b)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/3*a*B*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,7,-2/5*(3*B*a^3+15*B*a*b^2+15*C*a^2*b-5*C*b^3)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(3*B*a^2*b+3*B*b^3+C*a^3+9*C*a*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/15*a^2*(9*B*b+5*C*a)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*a*(3*B*a^2+14*B*b^2+15*C*a*b)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/5*a*B*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,8,-2/5*(9*B*a^2*b+5*B*b^3+3*C*a^3+15*C*a*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(5*B*a^3+21*B*a*b^2+21*C*a^2*b+21*C*b^3)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/35*a^2*(11*B*b+7*C*a)*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/21*a*(5*B*a^2+18*B*b^2+21*C*a*b)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*(9*B*a^2*b+5*B*b^3+3*C*a^3+15*C*a*b^2)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/7*a*B*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[(a+b*cos(d*x+c))^3*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x,9,-2/15*(7*B*a^3+27*B*a*b^2+27*C*a^2*b+15*C*b^3)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(15*B*a^2*b+7*B*b^3+5*C*a^3+21*C*a*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/63*a^2*(13*B*b+9*C*a)*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/45*a*(7*B*a^2+22*B*b^2+27*C*a*b)*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/21*(15*B*a^2*b+7*B*b^3+5*C*a^3+21*C*a*b^2)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/15*(7*B*a^3+27*B*a*b^2+27*C*a^2*b+15*C*b^3)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/9*a*B*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(9/2),1],
[cos(d*x+c)^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,9,2/5*(5*a^2+3*b^2)*(B*b-C*a)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^4/d-2/21*(21*B*a^3*b+7*B*a*b^3-21*C*a^4-7*C*a^2*b^2-5*C*b^4)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^5/d+2*a^4*(B*b-C*a)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b^5/(a+b)/d-2/21*(7*B*a*b-7*C*a^2-5*C*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/b^3/d+2/5*(B*b-C*a)*cos(d*x+c)^(3/2)*sin(d*x+c)/b^2/d+2/7*C*cos(d*x+c)^(5/2)*sin(d*x+c)/b/d,1],
[cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,8,-2/5*(5*B*a*b-5*C*a^2-3*C*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^3/d+2/3*(3*a^2+b^2)*(B*b-C*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^4/d-2*a^3*(B*b-C*a)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b^4/(a+b)/d+2/3*(B*b-C*a)*sqrt(cos(d*x+c))*sin(d*x+c)/b^2/d+2/5*C*cos(d*x+c)^(3/2)*sin(d*x+c)/b/d,1],
[sqrt(cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,7,2*(B*b-C*a)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^2/d-2/3*(3*B*a*b-3*C*a^2-C*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^3/d+2*a^2*(B*b-C*a)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b^3/(a+b)/d+2/3*C*sqrt(cos(d*x+c))*sin(d*x+c)/b/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+b*cos(d*x+c)),x,6,2*C*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b/d+2*(B*b-C*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^2/d-2*a*(B*b-C*a)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b^2/(a+b)/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x,4,2*C*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b/d+2*(B*b-C*a)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b/(a+b)/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x,6,-2*B*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d-2*(B*b-C*a)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a/(a+b)/d+2*B*sin(d*x+c)/a/d/sqrt(cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x,8,2*(B*b-C*a)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d+2/3*B*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d+2*b*(B*b-C*a)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^2/(a+b)/d+2/3*B*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)-2*(B*b-C*a)*sin(d*x+c)/a^2/d/sqrt(cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c)),x,9,-2/5*(3*B*a^2+5*B*b^2-5*C*a*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d-2/3*(B*b-C*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d-2*b^2*(B*b-C*a)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^3/(a+b)/d+2/5*B*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)-2/3*(B*b-C*a)*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2)+2/5*(3*B*a^2+5*B*b^2-5*C*a*b)*sin(d*x+c)/a^3/d/sqrt(cos(d*x+c)),1],
[cos(d*x+c)^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,9,-1/5*(25*B*a^3*b-20*B*a*b^3-35*C*a^4+24*C*a^2*b^2+6*C*b^4)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^4/(a^2-b^2)/d+1/3*(15*B*a^4*b-16*B*a^2*b^3-2*B*b^5-21*C*a^5+20*C*a^3*b^2+4*C*a*b^4)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^5/(a^2-b^2)/d-a^3*(5*B*a^2*b-7*B*b^3-7*C*a^3+9*C*a*b^2)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a-b)/b^5/(a+b)^2/d+1/3*(5*B*a^2*b-2*B*b^3-7*C*a^3+4*C*a*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)/d-1/5*(5*B*a*b-7*C*a^2+2*C*b^2)*cos(d*x+c)^(3/2)*sin(d*x+c)/b^2/(a^2-b^2)/d+a*(B*b-C*a)*cos(d*x+c)^(5/2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,8,(3*B*a^2*b-2*B*b^3-5*C*a^3+4*C*a*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^3/(a^2-b^2)/d-1/3*(9*B*a^3*b-12*B*a*b^3-15*C*a^4+16*C*a^2*b^2+2*C*b^4)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^4/(a^2-b^2)/d+a^2*(3*B*a^2*b-5*B*b^3-5*C*a^3+7*C*a*b^2)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a-b)/b^4/(a+b)^2/d-1/3*(3*B*a*b-5*C*a^2+2*C*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)/d+a*(B*b-C*a)*cos(d*x+c)^(3/2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,7,-(B*a*b-3*C*a^2+2*C*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^2/(a^2-b^2)/d+(B*a^2*b-2*B*b^3-3*C*a^3+4*C*a*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^3/(a^2-b^2)/d-a*(B*a^2*b-3*B*b^3-3*C*a^3+5*C*a*b^2)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a-b)/b^3/(a+b)^2/d+a*(B*b-C*a)*sqrt(cos(d*x+c))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^2,x,7,(B*b-C*a)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b/(a^2-b^2)/d+(B*a*b+C*a^2-2*C*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^2/(a^2-b^2)/d-(B*a^2*b+B*b^3+C*a^3-3*C*a*b^2)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a-b)/b^2/(a+b)^2/d-(B*b-C*a)*sqrt(cos(d*x+c))*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x,7,-(B*b-C*a)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/(a^2-b^2)/d-(B*b-C*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b/(a^2-b^2)/d+(3*B*a^2*b-B*b^3-C*a^3-C*a*b^2)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a/(a-b)/b/(a+b)^2/d+b*(B*b-C*a)*sqrt(cos(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x,8,-(2*B*a^2-3*B*b^2+C*a*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/(a^2-b^2)/d+(B*b-C*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/(a^2-b^2)/d-(5*B*a^2*b-3*B*b^3-3*C*a^3+C*a*b^2)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^2/(a-b)/(a+b)^2/d+(2*B*a^2-3*B*b^2+C*a*b)*sin(d*x+c)/a^2/(a^2-b^2)/d/sqrt(cos(d*x+c))+b*(B*b-C*a)*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(cos(d*x+c))/(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^2,x,9,(4*B*a^2*b-5*B*b^3-2*C*a^3+3*C*a*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/(a^2-b^2)/d+1/3*(2*B*a^2-5*B*b^2+3*C*a*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/(a^2-b^2)/d+b*(7*B*a^2*b-5*B*b^3-5*C*a^3+3*C*a*b^2)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^3/(a-b)/(a+b)^2/d+1/3*(2*B*a^2-5*B*b^2+3*C*a*b)*sin(d*x+c)/a^2/(a^2-b^2)/d/cos(d*x+c)^(3/2)-(4*B*a^2*b-5*B*b^3-2*C*a^3+3*C*a*b^2)*sin(d*x+c)/a^3/(a^2-b^2)/d/sqrt(cos(d*x+c))+b*(B*b-C*a)*sin(d*x+c)/a/(a^2-b^2)/d/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,9,1/4*(15*B*a^4*b-29*B*a^2*b^3+8*B*b^5-35*C*a^5+65*C*a^3*b^2-24*C*a*b^4)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^4/(a^2-b^2)^2/d-1/12*(45*B*a^5*b-99*B*a^3*b^3+72*B*a*b^5-105*C*a^6+223*C*a^4*b^2-128*C*a^2*b^4-8*C*b^6)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^5/(a^2-b^2)^2/d+1/4*a^2*(15*B*a^4*b-38*B*a^2*b^3+35*B*b^5-35*C*a^5+86*C*a^3*b^2-63*C*a*b^4)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a-b)^2/b^5/(a+b)^3/d-1/12*(15*B*a^3*b-33*B*a*b^3-35*C*a^4+61*C*a^2*b^2-8*C*b^4)*sqrt(cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)^2/d+1/2*a*(B*b-C*a)*cos(d*x+c)^(5/2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/4*a*(3*B*a^2*b-9*B*b^3-7*C*a^3+13*C*a*b^2)*cos(d*x+c)^(3/2)*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,8,-1/4*(3*B*a^3*b-9*B*a*b^3-15*C*a^4+29*C*a^2*b^2-8*C*b^4)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^3/(a^2-b^2)^2/d+1/4*(3*B*a^4*b-5*B*a^2*b^3+8*B*b^5-15*C*a^5+33*C*a^3*b^2-24*C*a*b^4)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^4/(a^2-b^2)^2/d-1/4*a*(3*B*a^4*b-6*B*a^2*b^3+15*B*b^5-15*C*a^5+38*C*a^3*b^2-35*C*a*b^4)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a-b)^2/b^4/(a+b)^3/d+1/2*a*(B*b-C*a)*cos(d*x+c)^(3/2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/4*a*(B*a^2*b-7*B*b^3-5*C*a^3+11*C*a*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,8,-1/4*(B*a^2*b+5*B*b^3+3*C*a^3-9*C*a*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^2/(a^2-b^2)^2/d+1/4*(B*a^3*b-7*B*a*b^3+3*C*a^4-5*C*a^2*b^2+8*C*b^4)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^3/(a^2-b^2)^2/d-1/4*(B*a^4*b-10*B*a^2*b^3-3*B*b^5+3*C*a^5-6*C*a^3*b^2+15*C*a*b^4)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a-b)^2/b^3/(a+b)^3/d+1/2*a*(B*b-C*a)*sqrt(cos(d*x+c))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/4*(B*a^2*b+5*B*b^3+3*C*a^3-9*C*a*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/b/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^3,x,8,1/4*(5*B*a^2*b+B*b^3-C*a^3-5*C*a*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/b/(a^2-b^2)^2/d+1/4*(3*B*a^2*b+3*B*b^3+C*a^3-7*C*a*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^2/(a^2-b^2)^2/d-1/4*(3*B*a^4*b+10*B*a^2*b^3-B*b^5+C*a^5-10*C*a^3*b^2-3*C*a*b^4)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a/(a-b)^2/b^2/(a+b)^3/d-1/2*(B*b-C*a)*sqrt(cos(d*x+c))*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/4*(5*B*a^2*b+B*b^3-C*a^3-5*C*a*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/a/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x,8,-1/4*(9*B*a^2*b-3*B*b^3-5*C*a^3-C*a*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/(a^2-b^2)^2/d-1/4*(7*B*a^2*b-B*b^3-3*C*a^3-3*C*a*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/b/(a^2-b^2)^2/d+1/4*(15*B*a^4*b-6*B*a^2*b^3+3*B*b^5-3*C*a^5-10*C*a^3*b^2+C*a*b^4)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^2/(a-b)^2/b/(a+b)^3/d+1/2*b*(B*b-C*a)*sqrt(cos(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/4*b*(9*B*a^2*b-3*B*b^3-5*C*a^3-C*a*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x,9,-1/4*(8*B*a^4-29*B*a^2*b^2+15*B*b^4+9*C*a^3*b-3*C*a*b^3)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/(a^2-b^2)^2/d+1/4*(11*B*a^2*b-5*B*b^3-7*C*a^3+C*a*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/(a^2-b^2)^2/d-1/4*(35*B*a^4*b-38*B*a^2*b^3+15*B*b^5-15*C*a^5+6*C*a^3*b^2-3*C*a*b^4)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^3/(a-b)^2/(a+b)^3/d+1/4*(8*B*a^4-29*B*a^2*b^2+15*B*b^4+9*C*a^3*b-3*C*a*b^3)*sin(d*x+c)/a^3/(a^2-b^2)^2/d/sqrt(cos(d*x+c))+1/2*b*(B*b-C*a)*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^2+1/4*b*(11*B*a^2*b-5*B*b^3-7*C*a^3+C*a*b^2)*sin(d*x+c)/a^2/(a^2-b^2)^2/d/sqrt(cos(d*x+c))/(a+b*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,9,-1/24*(a-b)*sqrt(a+b)*(6*B*a*b-3*C*a^2+16*C*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/d+1/24*sqrt(a+b)*(a+2*b)*(6*B*b-3*C*a+8*C*b)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+1/8*sqrt(a+b)*(2*B*a^2*b-8*B*b^3-C*a^3-4*C*a*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d+1/24*(6*B*a*b-3*C*a^2+16*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d/sqrt(cos(d*x+c))+1/4*(2*B*b-C*a)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+1/3*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d,1],
[sqrt(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,8,-1/4*(a-b)*sqrt(a+b)*(4*B*b+C*a)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d+1/4*sqrt(a+b)*(a*C+2*b*(2*B+C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d-1/4*sqrt(a+b)*(4*B*a*b-C*a^2+4*C*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+1/4*(4*B*b+C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(cos(d*x+c))+1/2*C*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,7,-(a-b)*sqrt(a+b)*C*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d+sqrt(a+b)*(2*B+C)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d-sqrt(a+b)*(2*B*b+C*a)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d+C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[sqrt(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,6,2*(a-b)*sqrt(a+b)*B*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d+2*sqrt(a+b)*(b*B-a*(B-C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-2*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d,1],
[sqrt(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,5,2/3*(a-b)*sqrt(a+b)*(B*b+3*C*a)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d+2/3*(a-b)*sqrt(a+b)*(B-3*C)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d+2/3*B*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[sqrt(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,6,2/15*(a-b)*sqrt(a+b)*(9*B*a^2-2*B*b^2+5*C*a*b)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d-2/15*(a-b)*sqrt(a+b)*(9*B*a+2*B*b-5*C*a)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d+2/5*B*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/15*(B*b+5*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(3/2),1],
[sqrt(a+b*cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,7,2/105*(a-b)*sqrt(a+b)*(19*B*a^2*b+8*B*b^3+63*C*a^3-14*C*a*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d+2/105*(a-b)*sqrt(a+b)*(8*b^2*B+a^2*(25*B-63*C)+2*a*b*(3*B-7*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d+2/7*B*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/35*(B*b+7*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)+2/105*(25*B*a^2-4*B*b^2+7*C*a*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2),1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,10,-1/192*(a-b)*sqrt(a+b)*(24*B*a^2*b+128*B*b^3-9*C*a^3+156*C*a*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/d-1/192*sqrt(a+b)*(9*a^3*C-6*a^2*b*(4*B+C)-8*b^3*(16*B+9*C)-4*a*b^2*(28*B+39*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+1/64*sqrt(a+b)*(8*B*a^3*b-96*B*a*b^3-3*C*a^4-24*C*a^2*b^2-48*C*b^4)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d+1/192*(24*B*a^2*b+128*B*b^3-9*C*a^3+156*C*a*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d/sqrt(cos(d*x+c))+1/32*(8*B*a*b-3*C*a^2+12*C*b^2)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+1/24*(8*B*b-3*C*a)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d+1/4*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,9,-1/24*(a-b)*sqrt(a+b)*(30*B*a*b+3*C*a^2+16*C*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d+1/24*sqrt(a+b)*(30*B*a*b+12*B*b^2+3*C*a^2+14*C*a*b+16*C*b^2)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d-1/8*sqrt(a+b)*(6*B*a^2*b+8*B*b^3-C*a^3+12*C*a*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+1/24*(30*B*a*b+3*C*a^2+16*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(cos(d*x+c))+1/12*(6*B*b+7*C*a)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+1/3*b*C*cos(d*x+c)^(3/2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,8,-1/4*(a-b)*sqrt(a+b)*(4*B*b+5*C*a)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d+1/4*sqrt(a+b)*(8*B*a+4*B*b+5*C*a+2*C*b)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d-1/4*sqrt(a+b)*(12*B*a*b+3*C*a^2+4*C*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d+1/4*(4*B*b+5*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))+1/2*b*C*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,8,(a-b)*sqrt(a+b)*(2*B*a-C*b)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-sqrt(a+b)*(2*a*(B-C)-b*(4*B+C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d-sqrt(a+b)*(2*B*b+3*C*a)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d+2*a*B*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))-(2*B*a-C*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,7,2/3*(a-b)*sqrt(a+b)*(4*B*b+3*C*a)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d+2/3*sqrt(a+b)*(3*b^2*B-a*b*(4*B-6*C)+a^2*(B-3*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-2*b*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d+2/3*a*B*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,6,2/15*(a-b)*sqrt(a+b)*(9*B*a^2+3*B*b^2+20*C*a*b)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d-2/15*(a-b)*sqrt(a+b)*(9*B*a-3*B*b-5*C*a+15*C*b)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d+2/5*a*B*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/15*(6*B*b+5*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+b*cos(d*x+c))^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,7,2/105*(a-b)*sqrt(a+b)*(82*B*a^2*b-6*B*b^3+63*C*a^3+21*C*a*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d-2/105*(a-b)*sqrt(a+b)*(6*b^2*B-a^2*(25*B-63*C)+3*a*b*(19*B-7*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d+2/7*a*B*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/35*(8*B*b+7*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/105*(25*B*a^2+3*B*b^2+42*C*a*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(3/2),1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2),x,11,-1/1920*(a-b)*sqrt(a+b)*(150*B*a^3*b+2840*B*a*b^3-45*C*a^4+1692*C*a^2*b^2+1024*C*b^4)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/d-1/1920*sqrt(a+b)*(45*a^4*C-30*a^3*b*(5*B+C)-16*b^4*(45*B+64*C)-8*a*b^3*(355*B+193*C)-4*a^2*b^2*(295*B+423*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+1/128*sqrt(a+b)*(10*B*a^4*b-240*B*a^2*b^3-96*B*b^5-3*C*a^5-40*C*a^3*b^2-240*C*a*b^4)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d+1/1920*(150*B*a^3*b+2840*B*a*b^3-45*C*a^4+1692*C*a^2*b^2+1024*C*b^4)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d/sqrt(cos(d*x+c))+1/320*(50*B*a^2*b+120*B*b^3-15*C*a^3+172*C*a*b^2)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+1/240*(50*B*a*b-15*C*a^2+64*C*b^2)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d+1/40*(10*B*b-3*C*a)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d+1/5*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,10,-1/192*(a-b)*sqrt(a+b)*(264*B*a^2*b+128*B*b^3+15*C*a^3+284*C*a*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d+1/192*sqrt(a+b)*(15*a^3*C+8*b^3*(16*B+9*C)+2*a^2*b*(132*B+59*C)+4*a*b^2*(52*B+71*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d-1/64*sqrt(a+b)*(40*B*a^3*b+160*B*a*b^3-5*C*a^4+120*C*a^2*b^2+48*C*b^4)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+1/192*(264*B*a^2*b+128*B*b^3+15*C*a^3+284*C*a*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(cos(d*x+c))+1/32*(24*B*a*b+5*C*a^2+12*C*b^2)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+1/24*(8*B*b+11*C*a)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d+1/4*b*C*cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,9,-1/24*(a-b)*sqrt(a+b)*(54*B*a*b+33*C*a^2+16*C*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d+1/24*sqrt(a+b)*(4*b^2*(3*B+4*C)+a*b*(54*B+26*C)+a^2*(48*B+33*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d-1/8*sqrt(a+b)*(30*B*a^2*b+8*B*b^3+5*C*a^3+20*C*a*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d+1/24*(54*B*a*b+33*C*a^2+16*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))+1/4*b*(2*B*b+3*C*a)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+1/3*b*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,9,1/4*(a-b)*sqrt(a+b)*(8*B*a^2-4*B*b^2-9*C*a*b)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-1/4*sqrt(a+b)*(8*a^2*(B-C)-2*b^2*(2*B+C)-3*a*b*(8*B+3*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d-1/4*sqrt(a+b)*(20*B*a*b+15*C*a^2+4*C*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d-1/4*(8*B*a^2-4*B*b^2-9*C*a*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))-1/2*b*(4*B*a-C*b)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+2*a*B*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,9,1/3*(a-b)*sqrt(a+b)*(14*B*a*b+6*C*a^2-3*C*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-1/3*sqrt(a+b)*(2*a*b*(7*B-9*C)-2*a^2*(B-3*C)-3*b^2*(6*B+C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d-b*sqrt(a+b)*(2*B*b+5*C*a)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d+2*a*(2*B*b+C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))-1/3*(14*B*a*b+6*C*a^2-3*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*a*B*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,8,2/15*(a-b)*sqrt(a+b)*(9*B*a^2+23*B*b^2+35*C*a*b)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d+2/15*sqrt(a+b)*(15*b^3*B-a*b^2*(23*B-45*C)+a^2*b*(17*B-35*C)-a^3*(9*B-5*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-2*b^2*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d+2/15*a*(8*B*b+5*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*a*B*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,7,2/105*(a-b)*sqrt(a+b)*(145*B*a^2*b+15*B*b^3+63*C*a^3+161*C*a*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d+2/105*(a-b)*sqrt(a+b)*(a^2*(25*B-63*C)+15*b^2*(B-7*C)-8*a*b*(15*B-7*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d+2/35*a*(10*B*b+7*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/105*(25*B*a^2+45*B*b^2+77*C*a*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/7*a*B*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x,8,2/315*(a-b)*sqrt(a+b)*(147*B*a^4+279*B*a^2*b^2-10*B*b^4+435*C*a^3*b+45*C*a*b^3)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d-2/315*(a-b)*sqrt(a+b)*(10*b^3*B-6*a^2*b*(19*B-60*C)+3*a^3*(49*B-25*C)+15*a*b^2*(11*B-3*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d+2/21*a*(4*B*b+3*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/315*(49*B*a^2+75*B*b^2+135*C*a*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/315*(163*B*a^2*b+5*B*b^3+75*C*a^3+135*C*a*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)+2/9*a*B*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(9/2),1],
[(a+b*cos(d*x+c))^(5/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(15/2),x,9,2/3465*(a-b)*sqrt(a+b)*(3705*B*a^4*b+255*B*a^2*b^3+40*B*b^5+1617*C*a^5+3069*C*a^3*b^2-110*C*a*b^4)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d+2/3465*(a-b)*sqrt(a+b)*(40*b^4*B+3*a^4*(225*B-539*C)-6*a^3*b*(505*B-209*C)+15*a^2*b^2*(19*B-121*C)+10*a*b^3*(3*B-11*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d+2/99*a*(14*B*b+11*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(9/2)+2/693*(81*B*a^2+113*B*b^2+209*C*a*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/3465*(1145*B*a^2*b+15*B*b^3+539*C*a^3+825*C*a*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)+2/3465*(675*B*a^4+1025*B*a^2*b^2-20*B*b^4+1793*C*a^3*b+55*C*a*b^3)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2)+2/11*a*B*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(11/2),1],
[cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c)),x,9,1/24*(a-b)*sqrt(a+b)*(18*B*a*b-15*C*a^2-16*C*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^3/d-1/24*sqrt(a+b)*(18*B*a*b-12*B*b^2-15*C*a^2+10*C*a*b-16*C*b^2)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d-1/8*sqrt(a+b)*(6*B*a^2*b+8*B*b^3-5*C*a^3-4*C*a*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^4/d-1/24*(18*B*a*b-15*C*a^2-16*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/d/sqrt(cos(d*x+c))+1/12*(6*B*b-5*C*a)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d+1/3*C*cos(d*x+c)^(3/2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d,1],
[sqrt(cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c)),x,8,-1/4*(a-b)*sqrt(a+b)*(4*B*b-3*C*a)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/d-1/4*sqrt(a+b)*(3*a*C-2*b*(2*B+C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+1/4*sqrt(a+b)*(4*B*a*b-3*C*a^2-4*C*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d+1/4*(4*B*b-3*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d/sqrt(cos(d*x+c))+1/2*C*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),x,9,-(a-b)*sqrt(a+b)*C*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d+sqrt(a+b)*C*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d-sqrt(a+b)*(2*B*b-C*a)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/sqrt(a+b*cos(d*x+c)),x,4,2*sqrt(a+b)*B*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-2*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/sqrt(a+b*cos(d*x+c)),x,4,2*(a-b)*sqrt(a+b)*B*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d-2*sqrt(a+b)*(B-C)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/sqrt(a+b*cos(d*x+c)),x,5,-2/3*(a-b)*sqrt(a+b)*(2*B*b-3*C*a)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d+2/3*sqrt(a+b)*(2*b*B+a*(B-3*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d+2/3*B*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(3/2),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/sqrt(a+b*cos(d*x+c)),x,6,2/15*(a-b)*sqrt(a+b)*(9*B*a^2+8*B*b^2-10*C*a*b)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d-2/15*sqrt(a+b)*(8*b^2*B+a^2*(9*B-5*C)-2*a*b*(B+5*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d+2/5*B*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)-2/15*(4*B*b-5*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2),1],
[cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x,9,-1/4*(12*B*a^2*b-4*B*b^3-15*C*a^3+7*C*a*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^3/sqrt(a+b)/d+1/4*(a*b*(12*B-5*C)-15*a^2*C+2*b^2*(2*B+C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/sqrt(a+b)/d+1/4*sqrt(a+b)*(12*B*a*b-15*C*a^2-4*C*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^4/d+2*a*(B*b-C*a)*cos(d*x+c)^(3/2)*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+1/4*(12*B*a^2*b-4*B*b^3-15*C*a^3+7*C*a*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)/d/sqrt(cos(d*x+c))-1/2*(4*B*a*b-5*C*a^2+C*b^2)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)/d,1],
[sqrt(cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x,8,(2*B*a*b-3*C*a^2+C*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/sqrt(a+b)/d-(2*B*b-3*C*a-C*b)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/sqrt(a+b)/d-sqrt(a+b)*(2*B*b-3*C*a)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d+2*a*(B*b-C*a)*sqrt(cos(d*x+c))*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-(2*B*a*b-3*C*a^2+C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)/d/sqrt(cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x,7,-2*(B*b-C*a)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/sqrt(a+b)/d+2*(B*b-C*a)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/sqrt(a+b)/d-2*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+2*a*(B*b-C*a)*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x,5,2*(B*b-C*a)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/sqrt(a+b)/d+2*(B+C)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/sqrt(a+b)/d-2*(B*b-C*a)*sin(d*x+c)/(a^2-b^2)/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x,5,2*(B*a^2-2*B*b^2+C*a*b)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/sqrt(a+b)/d-2*(2*b*B+a*(B-C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/sqrt(a+b)/d+2*b*(B*b-C*a)*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x,6,-2/3*(5*B*a^2*b-8*B*b^3-3*C*a^3+6*C*a*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/sqrt(a+b)/d+2/3*(a+2*b)*(4*b*B+a*(B-3*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/sqrt(a+b)/d+2*b*(B*b-C*a)*sin(d*x+c)/a/(a^2-b^2)/d/cos(d*x+c)^(3/2)/sqrt(a+b*cos(d*x+c))+2/3*(B*a^2-4*B*b^2+3*C*a*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^2/(a^2-b^2)/d/cos(d*x+c)^(3/2),1],
[cos(d*x+c)^(3/2)*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,9,1/3*(6*B*a^3*b-14*B*a*b^3-15*C*a^4+26*C*a^2*b^2-3*C*b^4)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/(a-b)/b^3/(a+b)^(3/2)/d-1/3*(a^2*b*(6*B-5*C)-3*b^3*(4*B-C)-15*a^3*C+a*b^2*(2*B+21*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/sqrt(a+b)/(a^2-b^2)/d-sqrt(a+b)*(2*B*b-5*C*a)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^4/d+2/3*a*(B*b-C*a)*cos(d*x+c)^(3/2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+2/3*a*(2*B*a^2*b-6*B*b^3-5*C*a^3+9*C*a*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c))-1/3*(6*B*a^3*b-14*B*a*b^3-15*C*a^4+26*C*a^2*b^2-3*C*b^4)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)^2/d/sqrt(cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,8,2/3*(4*B*b^3+3*C*a^3-7*C*a*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/(a-b)/b^2/(a+b)^(3/2)/d-2/3*(3*b^3*B+3*a^3*C+a^2*b*C-a*b^2*(B+6*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/(a-b)/b^2/(a+b)^(3/2)/d-2*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d+2/3*a*(B*b-C*a)*sqrt(cos(d*x+c))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)-2/3*a*(4*B*b^3+3*C*a^3-7*C*a*b^2)*sin(d*x+c)/b^2/(a^2-b^2)^2/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x,6,-2/3*(3*B*a^2+B*b^2-4*C*a*b)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/(a-b)/(a+b)^(3/2)/d+2/3*(a*(3*B+C)-b*(B+3*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/(a-b)/(a+b)^(3/2)/d-2/3*(B*b-C*a)*sqrt(cos(d*x+c))*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+2/3*(3*B*a^2+B*b^2-4*C*a*b)*sin(d*x+c)/(a^2-b^2)^2/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x,6,2/3*(6*B*a^2*b-2*B*b^3-3*C*a^3-C*a*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/(a-b)/(a+b)^(3/2)/d-2/3*(2*b^2*B-3*a^2*(B+C)+a*b*(3*B+C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/sqrt(a+b)/(a^2-b^2)/d+2/3*b*(B*b-C*a)*sqrt(cos(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)-2/3*(6*B*a^2*b-2*B*b^3-3*C*a^3-C*a*b^2)*sin(d*x+c)/a/(a^2-b^2)^2/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x,6,2/3*(3*B*a^4-15*B*a^2*b^2+8*B*b^4+6*C*a^3*b-2*C*a*b^3)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/(a-b)/(a+b)^(3/2)/d+2/3*(8*b^3*B-3*a^3*(B-C)+2*a*b^2*(3*B-C)-3*a^2*b*(3*B+C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/sqrt(a+b)/(a^2-b^2)/d+2/3*b*(B*b-C*a)*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^(3/2)+2/3*b*(8*B*a^2*b-4*B*b^3-5*C*a^3+C*a*b^2)*sin(d*x+c)/a^2/(a^2-b^2)^2/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),1],
[cos(d*x+c)^2*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,7,1/8*(4*A*a+3*B*b+3*C*a)*x+1/5*(5*A*b+5*B*a+4*C*b)*sin(d*x+c)/d+1/8*(4*A*a+3*B*b+3*C*a)*cos(d*x+c)*sin(d*x+c)/d+1/4*(B*b+C*a)*cos(d*x+c)^3*sin(d*x+c)/d+1/5*b*C*cos(d*x+c)^4*sin(d*x+c)/d-1/15*(5*A*b+5*B*a+4*C*b)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,3,1/8*(4*A*b+4*B*a+3*C*b)*x+1/3*(3*A*a+2*B*b+2*C*a)*sin(d*x+c)/d+1/8*(4*A*b+4*B*a+3*C*b)*cos(d*x+c)*sin(d*x+c)/d+1/3*(B*b+C*a)*cos(d*x+c)^2*sin(d*x+c)/d+1/4*b*C*cos(d*x+c)^3*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,2,1/2*(b*B+a*(2*A+C))*x+(A*b+B*a+C*b)*sin(d*x+c)/d+1/2*(B*b+C*a)*cos(d*x+c)*sin(d*x+c)/d-1/3*b*C*sin(d*x+c)^3/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,4,1/2*(2*A*b+2*B*a+C*b)*x+a*A*arctanh(sin(d*x+c))/d+(B*b+C*a)*sin(d*x+c)/d+1/2*b*C*cos(d*x+c)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,4,(B*b+C*a)*x+(A*b+B*a)*arctanh(sin(d*x+c))/d+b*C*sin(d*x+c)/d+a*A*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,4,b*C*x+1/2*(2*b*B+a*(A+2*C))*arctanh(sin(d*x+c))/d+(A*b+B*a)*tan(d*x+c)/d+1/2*a*A*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,6,1/2*(A*b+B*a+2*C*b)*arctanh(sin(d*x+c))/d+1/3*(2*A*a+3*B*b+3*C*a)*tan(d*x+c)/d+1/2*(A*b+B*a)*sec(d*x+c)*tan(d*x+c)/d+1/3*a*A*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,7,1/8*(3*A*a+4*B*b+4*C*a)*arctanh(sin(d*x+c))/d+1/3*(2*A*b+2*B*a+3*C*b)*tan(d*x+c)/d+1/8*(3*A*a+4*B*b+4*C*a)*sec(d*x+c)*tan(d*x+c)/d+1/3*(A*b+B*a)*sec(d*x+c)^2*tan(d*x+c)/d+1/4*a*A*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,7,1/8*(3*A*b+3*B*a+4*C*b)*arctanh(sin(d*x+c))/d+1/5*(4*A*a+5*B*b+5*C*a)*tan(d*x+c)/d+1/8*(3*A*b+3*B*a+4*C*b)*sec(d*x+c)*tan(d*x+c)/d+1/4*(A*b+B*a)*sec(d*x+c)^3*tan(d*x+c)/d+1/5*a*A*sec(d*x+c)^4*tan(d*x+c)/d+1/15*(4*A*a+5*B*b+5*C*a)*tan(d*x+c)^3/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,4,1/8*(8*A*a*b+4*B*a^2+3*B*b^2+6*C*a*b)*x+1/15*(20*a*b*B+5*a^2*(3*A+2*C)+2*b^2*(5*A+4*C))*sin(d*x+c)/d+1/8*(8*A*a*b+4*B*a^2+3*B*b^2+6*C*a*b)*cos(d*x+c)*sin(d*x+c)/d+1/15*(5*A*b^2+10*B*a*b+2*C*a^2+4*C*b^2)*cos(d*x+c)^2*sin(d*x+c)/d+1/20*b*(5*B*b+2*C*a)*cos(d*x+c)^3*sin(d*x+c)/d+1/5*C*cos(d*x+c)^2*(a+b*cos(d*x+c))^2*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,3,1/8*(8*a*b*B+4*a^2*(2*A+C)+b^2*(4*A+3*C))*x+1/6*(4*a^2*b*B+4*b^3*B-a^3*C+4*a*b^2*(3*A+2*C))*sin(d*x+c)/b/d+1/24*(12*A*b^2+8*B*a*b-2*C*a^2+9*C*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/12*(4*B*b-C*a)*(a+b*cos(d*x+c))^2*sin(d*x+c)/b/d+1/4*C*(a+b*cos(d*x+c))^3*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,5,1/2*(2*a^2*B+b^2*B+2*a*b*(2*A+C))*x+a^2*A*arctanh(sin(d*x+c))/d+1/3*(3*A*b^2+6*B*a*b+2*C*a^2+2*C*b^2)*sin(d*x+c)/d+1/6*b*(3*B*b+2*C*a)*cos(d*x+c)*sin(d*x+c)/d+1/3*C*(a+b*cos(d*x+c))^2*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,5,1/2*(2*A*b^2+4*B*a*b+2*C*a^2+C*b^2)*x+a*(2*A*b+B*a)*arctanh(sin(d*x+c))/d-b*(2*A*a-B*b-2*C*a)*sin(d*x+c)/d-1/2*b^2*(2*A-C)*cos(d*x+c)*sin(d*x+c)/d+A*(a+b*cos(d*x+c))^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,5,b*(B*b+2*C*a)*x+1/2*(2*A*b^2+4*a*b*B+a^2*(A+2*C))*arctanh(sin(d*x+c))/d-1/2*b^2*(A-2*C)*sin(d*x+c)/d+a*(A*b+B*a)*tan(d*x+c)/d+1/2*A*(a+b*cos(d*x+c))^2*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,5,b^2*C*x+1/2*(a^2*B+2*b^2*B+2*a*b*(A+2*C))*arctanh(sin(d*x+c))/d+1/3*(2*A*b^2+6*a*b*B+a^2*(2*A+3*C))*tan(d*x+c)/d+1/6*a*(2*A*b+3*B*a)*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(a+b*cos(d*x+c))^2*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,7,1/8*(8*a*b*B+4*b^2*(A+2*C)+a^2*(3*A+4*C))*arctanh(sin(d*x+c))/d+1/3*(4*A*a*b+2*B*a^2+3*B*b^2+6*C*a*b)*tan(d*x+c)/d+1/8*(2*A*b^2+8*a*b*B+a^2*(3*A+4*C))*sec(d*x+c)*tan(d*x+c)/d+1/6*a*(A*b+2*B*a)*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a+b*cos(d*x+c))^2*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,8,1/8*(6*A*a*b+3*B*a^2+4*B*b^2+8*C*a*b)*arctanh(sin(d*x+c))/d+1/15*(20*a*b*B+5*b^2*(2*A+3*C)+2*a^2*(4*A+5*C))*tan(d*x+c)/d+1/8*(6*A*a*b+3*B*a^2+4*B*b^2+8*C*a*b)*sec(d*x+c)*tan(d*x+c)/d+1/15*(2*A*b^2+10*a*b*B+a^2*(4*A+5*C))*sec(d*x+c)^2*tan(d*x+c)/d+1/20*a*(2*A*b+5*B*a)*sec(d*x+c)^3*tan(d*x+c)/d+1/5*A*(a+b*cos(d*x+c))^2*sec(d*x+c)^4*tan(d*x+c)/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,5,1/16*(8*a^3*B+18*a*b^2*B+6*a^2*b*(4*A+3*C)+b^3*(6*A+5*C))*x+1/15*(30*a^2*b*B+8*b^3*B+5*a^3*(3*A+2*C)+6*a*b^2*(5*A+4*C))*sin(d*x+c)/d+1/16*(8*a^3*B+18*a*b^2*B+6*a^2*b*(4*A+3*C)+b^3*(6*A+5*C))*cos(d*x+c)*sin(d*x+c)/d+1/15*(12*a^2*b*B+4*b^3*B+a^3*C+3*a*b^2*(5*A+4*C))*cos(d*x+c)^2*sin(d*x+c)/d+1/120*b*(30*A*b^2+42*B*a*b+6*C*a^2+25*C*b^2)*cos(d*x+c)^3*sin(d*x+c)/d+1/10*(2*B*b+C*a)*cos(d*x+c)^2*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+1/6*C*cos(d*x+c)^2*(a+b*cos(d*x+c))^3*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,4,1/8*(12*a^2*b*B+3*b^3*B+4*a^3*(2*A+C)+3*a*b^2*(4*A+3*C))*x+1/30*(15*a^3*b*B+60*a*b^3*B-3*a^4*C+4*b^4*(5*A+4*C)+4*a^2*b^2*(20*A+13*C))*sin(d*x+c)/b/d+1/120*(30*a^2*b*B+45*b^3*B-6*a^3*C+a*b^2*(100*A+71*C))*cos(d*x+c)*sin(d*x+c)/d+1/60*(4*b^2*(5*A+4*C)+3*a*(5*B*b-C*a))*(a+b*cos(d*x+c))^2*sin(d*x+c)/b/d+1/20*(5*B*b-C*a)*(a+b*cos(d*x+c))^3*sin(d*x+c)/b/d+1/5*C*(a+b*cos(d*x+c))^4*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,6,1/8*(8*a^3*B+12*a*b^2*B+12*a^2*b*(2*A+C)+b^3*(4*A+3*C))*x+a^3*A*arctanh(sin(d*x+c))/d+1/6*(16*a^2*b*B+4*b^3*B+3*a^3*C+6*a*b^2*(3*A+2*C))*sin(d*x+c)/d+1/24*b*(12*A*b^2+20*B*a*b+6*C*a^2+9*C*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/12*(4*B*b+3*C*a)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+1/4*C*(a+b*cos(d*x+c))^3*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,6,1/2*(6*a^2*b*B+b^3*B+2*a^3*C+3*a*b^2*(2*A+C))*x+a^2*(3*A*b+B*a)*arctanh(sin(d*x+c))/d+1/3*b*(9*a*b*B-a^2*(6*A-8*C)+b^2*(3*A+2*C))*sin(d*x+c)/d-1/6*b^2*(6*A*a-3*B*b-5*C*a)*cos(d*x+c)*sin(d*x+c)/d-1/3*b*(3*A-C)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+A*(a+b*cos(d*x+c))^3*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,6,1/2*b*(2*A*b^2+6*B*a*b+6*C*a^2+C*b^2)*x+1/2*a*(6*A*b^2+6*a*b*B+a^2*(A+2*C))*arctanh(sin(d*x+c))/d-1/2*b*(9*A*a*b+4*B*a^2-2*B*b^2-6*C*a*b)*sin(d*x+c)/d-1/2*b^2*(4*A*b+2*B*a-C*b)*cos(d*x+c)*sin(d*x+c)/d+1/2*(3*A*b+2*B*a)*(a+b*cos(d*x+c))^2*tan(d*x+c)/d+1/2*A*(a+b*cos(d*x+c))^3*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,6,b^2*(B*b+3*C*a)*x+1/2*(2*A*b^3+a^3*B+6*a*b^2*B+3*a^2*b*(A+2*C))*arctanh(sin(d*x+c))/d-1/6*b^2*(5*A*b+3*B*a-6*C*b)*sin(d*x+c)/d+1/3*a*(3*A*b^2+6*a*b*B+a^2*(2*A+3*C))*tan(d*x+c)/d+1/2*(A*b+B*a)*(a+b*cos(d*x+c))^2*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(a+b*cos(d*x+c))^3*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,6,b^3*C*x+1/8*(12*a^2*b*B+8*b^3*B+12*a*b^2*(A+2*C)+a^3*(3*A+4*C))*arctanh(sin(d*x+c))/d+1/6*(3*A*b^3+4*a^3*B+16*a*b^2*B+6*a^2*b*(2*A+3*C))*tan(d*x+c)/d+1/24*a*(6*A*b^2+20*a*b*B+3*a^2*(3*A+4*C))*sec(d*x+c)*tan(d*x+c)/d+1/12*(3*A*b+4*B*a)*(a+b*cos(d*x+c))^2*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a+b*cos(d*x+c))^3*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,8,1/8*(3*a^3*B+12*a*b^2*B+4*b^3*(A+2*C)+3*a^2*b*(3*A+4*C))*arctanh(sin(d*x+c))/d+1/15*(30*a^2*b*B+15*b^3*B+15*a*b^2*(2*A+3*C)+2*a^3*(4*A+5*C))*tan(d*x+c)/d+1/40*(6*A*b^3+15*a^3*B+50*a*b^2*B+15*a^2*b*(3*A+4*C))*sec(d*x+c)*tan(d*x+c)/d+1/30*a*(3*A*b^2+15*a*b*B+2*a^2*(4*A+5*C))*sec(d*x+c)^2*tan(d*x+c)/d+1/20*(3*A*b+5*B*a)*(a+b*cos(d*x+c))^2*sec(d*x+c)^3*tan(d*x+c)/d+1/5*A*(a+b*cos(d*x+c))^3*sec(d*x+c)^4*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x,9,1/16*(18*a^2*b*B+8*b^3*B+6*a*b^2*(3*A+4*C)+a^3*(5*A+6*C))*arctanh(sin(d*x+c))/d+1/15*(8*a^3*B+30*a*b^2*B+5*b^3*(2*A+3*C)+6*a^2*b*(4*A+5*C))*tan(d*x+c)/d+1/16*(18*a^2*b*B+8*b^3*B+6*a*b^2*(3*A+4*C)+a^3*(5*A+6*C))*sec(d*x+c)*tan(d*x+c)/d+1/15*(A*b^3+4*a^3*B+12*a*b^2*B+3*a^2*b*(4*A+5*C))*sec(d*x+c)^2*tan(d*x+c)/d+1/120*a*(6*A*b^2+42*a*b*B+5*a^2*(5*A+6*C))*sec(d*x+c)^3*tan(d*x+c)/d+1/10*(A*b+2*B*a)*(a+b*cos(d*x+c))^2*sec(d*x+c)^4*tan(d*x+c)/d+1/6*A*(a+b*cos(d*x+c))^3*sec(d*x+c)^5*tan(d*x+c)/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,6,1/16*(8*a^4*B+36*a^2*b^2*B+5*b^4*B+8*a^3*b*(4*A+3*C)+4*a*b^3*(6*A+5*C))*x+1/105*(280*a^3*b*B+224*a*b^3*B+35*a^4*(3*A+2*C)+84*a^2*b^2*(5*A+4*C)+8*b^4*(7*A+6*C))*sin(d*x+c)/d+1/16*(8*a^4*B+36*a^2*b^2*B+5*b^4*B+8*a^3*b*(4*A+3*C)+4*a*b^3*(6*A+5*C))*cos(d*x+c)*sin(d*x+c)/d+1/105*(91*a^3*b*B+112*a*b^3*B+4*a^4*C+4*b^4*(7*A+6*C)+3*a^2*b^2*(63*A+50*C))*cos(d*x+c)^2*sin(d*x+c)/d+1/840*b*(336*a^2*b*B+175*b^3*B+24*a^3*C+4*a*b^2*(126*A+103*C))*cos(d*x+c)^3*sin(d*x+c)/d+1/70*(14*A*b^2+21*B*a*b+4*C*a^2+12*C*b^2)*cos(d*x+c)^2*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+1/42*(7*B*b+4*C*a)*cos(d*x+c)^2*(a+b*cos(d*x+c))^3*sin(d*x+c)/d+1/7*C*cos(d*x+c)^2*(a+b*cos(d*x+c))^4*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,5,1/16*(32*a^3*b*B+24*a*b^3*B+8*a^4*(2*A+C)+12*a^2*b^2*(4*A+3*C)+b^4*(6*A+5*C))*x+1/60*(24*a^4*b*B+224*a^2*b^3*B+32*b^5*B-4*a^5*C+32*a*b^4*(5*A+4*C)+a^3*b^2*(190*A+121*C))*sin(d*x+c)/b/d+1/240*(48*a^3*b*B+232*a*b^3*B-8*a^4*C+15*b^4*(6*A+5*C)+2*a^2*b^2*(130*A+89*C))*cos(d*x+c)*sin(d*x+c)/d+1/120*(24*a^2*b*B+32*b^3*B-4*a^3*C+a*b^2*(70*A+53*C))*(a+b*cos(d*x+c))^2*sin(d*x+c)/b/d+1/120*(5*b^2*(6*A+5*C)+4*a*(6*B*b-C*a))*(a+b*cos(d*x+c))^3*sin(d*x+c)/b/d+1/30*(6*B*b-C*a)*(a+b*cos(d*x+c))^4*sin(d*x+c)/b/d+1/6*C*(a+b*cos(d*x+c))^5*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,7,1/8*(8*a^4*B+24*a^2*b^2*B+3*b^4*B+16*a^3*b*(2*A+C)+4*a*b^3*(4*A+3*C))*x+a^4*A*arctanh(sin(d*x+c))/d+1/30*(95*a^3*b*B+80*a*b^3*B+12*a^4*C+4*b^4*(5*A+4*C)+2*a^2*b^2*(85*A+56*C))*sin(d*x+c)/d+1/120*b*(130*a^2*b*B+45*b^3*B+24*a^3*C+4*a*b^2*(40*A+29*C))*cos(d*x+c)*sin(d*x+c)/d+1/60*(20*A*b^2+35*B*a*b+12*C*a^2+16*C*b^2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+1/20*(5*B*b+4*C*a)*(a+b*cos(d*x+c))^3*sin(d*x+c)/d+1/5*C*(a+b*cos(d*x+c))^4*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,7,1/8*(32*a^3*b*B+16*a*b^3*B+8*a^4*C+24*a^2*b^2*(2*A+C)+b^4*(4*A+3*C))*x+a^3*(4*A*b+B*a)*arctanh(sin(d*x+c))/d+1/6*b*(34*a^2*b*B+4*b^3*B-a^3*(12*A-19*C)+8*a*b^2*(3*A+2*C))*sin(d*x+c)/d+1/24*b^2*(32*a*b*B-a^2*(24*A-26*C)+3*b^2*(4*A+3*C))*cos(d*x+c)*sin(d*x+c)/d-1/12*b*(12*A*a-4*B*b-7*C*a)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d-1/4*b*(4*A-C)*(a+b*cos(d*x+c))^3*sin(d*x+c)/d+A*(a+b*cos(d*x+c))^4*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,7,1/2*b*(12*a^2*b*B+b^3*B+8*a^3*C+4*a*b^2*(2*A+C))*x+1/2*a^2*(12*A*b^2+8*a*b*B+a^2*(A+2*C))*arctanh(sin(d*x+c))/d-1/6*b*(12*a^3*B-24*a*b^2*B+a^2*b*(39*A-34*C)-2*b^3*(3*A+2*C))*sin(d*x+c)/d-1/6*b^2*(6*a^2*B-3*b^2*B+2*a*b*(9*A-4*C))*cos(d*x+c)*sin(d*x+c)/d-1/6*b*(15*A*b+6*B*a-2*C*b)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+(2*A*b+B*a)*(a+b*cos(d*x+c))^3*tan(d*x+c)/d+1/2*A*(a+b*cos(d*x+c))^4*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,7,1/2*b^2*(2*A*b^2+8*B*a*b+12*C*a^2+C*b^2)*x+1/2*a*(8*A*b^3+a^3*B+12*a*b^2*B+4*a^2*b*(A+2*C))*arctanh(sin(d*x+c))/d-1/6*b*(39*a^2*b*B-6*b^3*B+4*a*b^2*(11*A-6*C)+4*a^3*(2*A+3*C))*sin(d*x+c)/d-1/6*b^2*(18*a*b*B+3*b^2*(6*A-C)+a^2*(4*A+6*C))*cos(d*x+c)*sin(d*x+c)/d+1/6*(12*A*b^2+15*a*b*B+a^2*(4*A+6*C))*(a+b*cos(d*x+c))^2*tan(d*x+c)/d+1/6*(4*A*b+3*B*a)*(a+b*cos(d*x+c))^3*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,7,b^3*(B*b+4*C*a)*x+1/8*(8*A*b^4+16*a^3*b*B+32*a*b^3*B+24*a^2*b^2*(A+2*C)+a^4*(3*A+4*C))*arctanh(sin(d*x+c))/d-1/24*b^2*(32*a*b*B+2*b^2*(13*A-12*C)+3*a^2*(3*A+4*C))*sin(d*x+c)/d+1/12*a*(12*A*b^3+8*a^3*B+36*a*b^2*B+a^2*b*(23*A+36*C))*tan(d*x+c)/d+1/8*(4*A*b^2+8*a*b*B+a^2*(3*A+4*C))*(a+b*cos(d*x+c))^2*sec(d*x+c)*tan(d*x+c)/d+1/3*(A*b+B*a)*(a+b*cos(d*x+c))^3*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,7,b^4*C*x+1/8*(3*a^4*B+24*a^2*b^2*B+8*b^4*B+16*a*b^3*(A+2*C)+4*a^3*b*(3*A+4*C))*arctanh(sin(d*x+c))/d+1/30*(12*A*b^4+80*a^3*b*B+95*a*b^3*B+4*a^4*(4*A+5*C)+2*a^2*b^2*(56*A+85*C))*tan(d*x+c)/d+1/120*a*(24*A*b^3+45*a^3*B+130*a*b^2*B+4*a^2*b*(29*A+40*C))*sec(d*x+c)*tan(d*x+c)/d+1/60*(12*A*b^2+35*a*b*B+4*a^2*(4*A+5*C))*(a+b*cos(d*x+c))^2*sec(d*x+c)^2*tan(d*x+c)/d+1/20*(4*A*b+5*B*a)*(a+b*cos(d*x+c))^3*sec(d*x+c)^3*tan(d*x+c)/d+1/5*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^4*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^7,x,9,1/16*(24*a^3*b*B+32*a*b^3*B+8*b^4*(A+2*C)+12*a^2*b^2*(3*A+4*C)+a^4*(5*A+6*C))*arctanh(sin(d*x+c))/d+1/15*(8*a^4*B+60*a^2*b^2*B+15*b^4*B+20*a*b^3*(2*A+3*C)+8*a^3*b*(4*A+5*C))*tan(d*x+c)/d+1/240*(24*A*b^4+360*a^3*b*B+336*a*b^3*B+15*a^4*(5*A+6*C)+10*a^2*b^2*(49*A+66*C))*sec(d*x+c)*tan(d*x+c)/d+1/60*a*(4*A*b^3+16*a^3*B+36*a*b^2*B+a^2*b*(39*A+50*C))*sec(d*x+c)^2*tan(d*x+c)/d+1/120*(12*A*b^2+48*a*b*B+5*a^2*(5*A+6*C))*(a+b*cos(d*x+c))^2*sec(d*x+c)^3*tan(d*x+c)/d+1/15*(2*A*b+3*B*a)*(a+b*cos(d*x+c))^3*sec(d*x+c)^4*tan(d*x+c)/d+1/6*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^5*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^8,x,10,1/16*(5*a^4*B+36*a^2*b^2*B+8*b^4*B+8*a*b^3*(3*A+4*C)+4*a^3*b*(5*A+6*C))*arctanh(sin(d*x+c))/d+1/105*(224*a^3*b*B+280*a*b^3*B+35*b^4*(2*A+3*C)+84*a^2*b^2*(4*A+5*C)+8*a^4*(6*A+7*C))*tan(d*x+c)/d+1/16*(5*a^4*B+36*a^2*b^2*B+8*b^4*B+8*a*b^3*(3*A+4*C)+4*a^3*b*(5*A+6*C))*sec(d*x+c)*tan(d*x+c)/d+1/105*(4*A*b^4+112*a^3*b*B+91*a*b^3*B+4*a^4*(6*A+7*C)+3*a^2*b^2*(50*A+63*C))*sec(d*x+c)^2*tan(d*x+c)/d+1/840*a*(24*A*b^3+175*a^3*B+336*a*b^2*B+a^2*(412*A*b+504*C*b))*sec(d*x+c)^3*tan(d*x+c)/d+1/70*(4*A*b^2+21*a*b*B+2*a^2*(6*A+7*C))*(a+b*cos(d*x+c))^2*sec(d*x+c)^4*tan(d*x+c)/d+1/42*(4*A*b+7*B*a)*(a+b*cos(d*x+c))^3*sec(d*x+c)^5*tan(d*x+c)/d+1/7*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^6*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x,5,1/8*(8*B*a^4*b+24*B*a^2*b^3+3*B*b^5-8*C*a^5-8*C*a^3*b^2+9*C*a*b^4)*x+1/30*b*(95*B*a^3*b+80*B*a*b^3-83*C*a^4+32*C*a^2*b^2+16*C*b^4)*sin(d*x+c)/d+1/120*b^2*(130*B*a^2*b+45*B*b^3-106*C*a^3+71*C*a*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/60*b*(35*B*a*b-23*C*a^2+16*C*b^2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+1/20*b*(5*B*b-C*a)*(a+b*cos(d*x+c))^3*sin(d*x+c)/d+1/5*b*C*(a+b*cos(d*x+c))^4*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x,4,1/8*(8*B*a^3*b+12*B*a*b^3-8*C*a^4+3*C*b^4)*x+1/6*b*(16*B*a^2*b+4*B*b^3-13*C*a^3+8*C*a*b^2)*sin(d*x+c)/d+1/24*b^2*(20*B*a*b-14*C*a^2+9*C*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/12*b*(4*B*b-C*a)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+1/4*b*C*(a+b*cos(d*x+c))^3*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x,3,1/2*(2*B*a^2*b+B*b^3-2*C*a^3+C*a*b^2)*x+2/3*b*(3*B*a*b-2*C*a^2+C*b^2)*sin(d*x+c)/d+1/6*b^2*(3*B*b-C*a)*cos(d*x+c)*sin(d*x+c)/d+1/3*b*C*(a+b*cos(d*x+c))^2*sin(d*x+c)/d,1],
[cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,7,-1/8*(8*a^3*b*B+4*a*b^3*B-8*a^4*C-4*a^2*b^2*(2*A+C)-b^4*(4*A+3*C))*x/b^5-2*a^3*(A*b^2-a*(B*b-C*a))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^5/sqrt(a+b)/d+1/3*(3*a^2*b*B+2*b^3*B-3*a^3*C-a*b^2*(3*A+2*C))*sin(d*x+c)/b^4/d+1/8*(4*A*b^2-4*B*a*b+4*C*a^2+3*C*b^2)*cos(d*x+c)*sin(d*x+c)/b^3/d+1/3*(B*b-C*a)*cos(d*x+c)^2*sin(d*x+c)/b^2/d+1/4*C*cos(d*x+c)^3*sin(d*x+c)/b/d,1],
[cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,6,1/2*(2*a^2*b*B+b^3*B-2*a^3*C-a*b^2*(2*A+C))*x/b^4+2*a^2*(A*b^2-a*(B*b-C*a))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^4/sqrt(a+b)/d+1/3*(3*A*b^2-3*B*a*b+3*C*a^2+2*C*b^2)*sin(d*x+c)/b^3/d+1/2*(B*b-C*a)*cos(d*x+c)*sin(d*x+c)/b^2/d+1/3*C*cos(d*x+c)^2*sin(d*x+c)/b/d,1],
[cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,5,1/2*(b^2*(2*A+C)-2*a*(B*b-C*a))*x/b^3-2*a*(A*b^2-a*(B*b-C*a))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^3/sqrt(a+b)/d+(B*b-C*a)*sin(d*x+c)/b^2/d+1/2*C*cos(d*x+c)*sin(d*x+c)/b/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,4,(B*b-C*a)*x/b^2+2*(A*b^2-a*(B*b-C*a))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^2/sqrt(a+b)/d+C*sin(d*x+c)/b/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c)),x,4,C*x/b-2*(A*b^2-a*(B*b-C*a))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a/sqrt(a-b)/b/sqrt(a+b)/d+A*arctanh(sin(d*x+c))/a/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c)),x,5,2*(A*b^2-a*(B*b-C*a))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^2/sqrt(a-b)/sqrt(a+b)/d-(A*b-B*a)*arctanh(sin(d*x+c))/a^2/d+A*tan(d*x+c)/a/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c)),x,6,-2*b*(A*b^2-a*(B*b-C*a))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^3/sqrt(a-b)/sqrt(a+b)/d+1/2*(2*A*b^2-2*a*b*B+a^2*(A+2*C))*arctanh(sin(d*x+c))/a^3/d-(A*b-B*a)*tan(d*x+c)/a^2/d+1/2*A*sec(d*x+c)*tan(d*x+c)/a/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c)),x,7,2*b^2*(A*b^2-a*(B*b-C*a))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^4/sqrt(a-b)/sqrt(a+b)/d-1/2*(2*A*b^3-a^3*B-2*a*b^2*B+a^2*b*(A+2*C))*arctanh(sin(d*x+c))/a^4/d+1/3*(3*A*b^2-3*a*b*B+a^2*(2*A+3*C))*tan(d*x+c)/a^3/d-1/2*(A*b-B*a)*sec(d*x+c)*tan(d*x+c)/a^2/d+1/3*A*sec(d*x+c)^2*tan(d*x+c)/a/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5/(a+b*cos(d*x+c)),x,8,-2*b^3*(A*b^2-a*(B*b-C*a))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^5/sqrt(a-b)/sqrt(a+b)/d+1/8*(8*A*b^4-4*a^3*b*B-8*a*b^3*B+4*a^2*b^2*(A+2*C)+a^4*(3*A+4*C))*arctanh(sin(d*x+c))/a^5/d-1/3*(3*A*b^3-2*a^3*B-3*a*b^2*B+a^2*b*(2*A+3*C))*tan(d*x+c)/a^4/d+1/8*(4*A*b^2-4*a*b*B+a^2*(3*A+4*C))*sec(d*x+c)*tan(d*x+c)/a^3/d-1/3*(A*b-B*a)*sec(d*x+c)^2*tan(d*x+c)/a^2/d+1/4*A*sec(d*x+c)^3*tan(d*x+c)/a/d,1],
[cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,7,1/2*(6*a^2*b*B+b^3*B-8*a^3*C-2*a*b^2*(2*A+C))*x/b^5+2*a^2*(2*A*a^2*b^2-3*A*b^4-3*B*a^3*b+4*B*a*b^3+4*C*a^4-5*C*a^2*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/b^5/(a+b)^(3/2)/d-1/3*(9*a^3*b*B-6*a*b^3*B-a^2*b^2*(6*A-7*C)-12*a^4*C+b^4*(3*A+2*C))*sin(d*x+c)/b^4/(a^2-b^2)/d+1/2*(3*a^2*b*B-b^3*B-2*a*b^2*(A-C)-4*a^3*C)*cos(d*x+c)*sin(d*x+c)/b^3/(a^2-b^2)/d+1/3*(3*A*b^2-3*B*a*b+4*C*a^2-C*b^2)*cos(d*x+c)^2*sin(d*x+c)/b^2/(a^2-b^2)/d-(A*b^2-a*(B*b-C*a))*cos(d*x+c)^3*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,6,1/2*(2*A*b^2-4*B*a*b+6*C*a^2+C*b^2)*x/b^4-2*a*(A*a^2*b^2-2*A*b^4-2*B*a^3*b+3*B*a*b^3+3*C*a^4-4*C*a^2*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/b^4/(a+b)^(3/2)/d+(2*a^2*b*B-b^3*B-a*b^2*(A-2*C)-3*a^3*C)*sin(d*x+c)/b^3/(a^2-b^2)/d+1/2*(2*A*b^2-2*B*a*b+3*C*a^2-C*b^2)*cos(d*x+c)*sin(d*x+c)/b^2/(a^2-b^2)/d-(A*b^2-a*(B*b-C*a))*cos(d*x+c)^2*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,5,(B*b-2*C*a)*x/b^3-2*(A*b^4+B*a^3*b-2*B*a*b^3-2*C*a^4+3*C*a^2*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/b^3/(a+b)^(3/2)/d+C*sin(d*x+c)/b^2/d+a*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b^2/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,4,C*x/b^2+2*(A*a*b^2-B*b^3-C*a^3+2*C*a*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/b^2/(a+b)^(3/2)/d-(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^2,x,5,-2*(2*A*a^2*b-A*b^3-B*a^3+C*a^2*b)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^2/(a-b)^(3/2)/(a+b)^(3/2)/d+A*arctanh(sin(d*x+c))/a^2/d+(A*b^2-a*(B*b-C*a))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x,6,2*(3*A*a^2*b^2-2*A*b^4-2*B*a^3*b+B*a*b^3+C*a^4)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^3/(a-b)^(3/2)/(a+b)^(3/2)/d-(2*A*b-B*a)*arctanh(sin(d*x+c))/a^3/d-(2*A*b^2-a*b*B-a^2*(A-C))*tan(d*x+c)/a^2/(a^2-b^2)/d+(A*b^2-a*(B*b-C*a))*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x,7,-2*b*(4*A*a^2*b^2-3*A*b^4-3*B*a^3*b+2*B*a*b^3+2*C*a^4-C*a^2*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^4/(a-b)^(3/2)/(a+b)^(3/2)/d+1/2*(6*A*b^2-4*a*b*B+a^2*(A+2*C))*arctanh(sin(d*x+c))/a^4/d+(3*A*b^3+a^3*B-2*a*b^2*B-a^2*b*(2*A-C))*tan(d*x+c)/a^3/(a^2-b^2)/d-1/2*(3*A*b^2-2*a*b*B-a^2*(A-2*C))*sec(d*x+c)*tan(d*x+c)/a^2/(a^2-b^2)/d+(A*b^2-a*(B*b-C*a))*sec(d*x+c)*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/(a+b*cos(d*x+c))^2,x,8,2*b^2*(5*A*a^2*b^2-4*A*b^4-4*B*a^3*b+3*B*a*b^3+3*C*a^4-2*C*a^2*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^5/(a-b)^(3/2)/(a+b)^(3/2)/d-1/2*(8*A*b^3-a^3*B-6*a*b^2*B+2*a^2*b*(A+2*C))*arctanh(sin(d*x+c))/a^5/d-1/3*(12*A*b^4+6*a^3*b*B-9*a*b^3*B-a^2*b^2*(7*A-6*C)-a^4*(2*A+3*C))*tan(d*x+c)/a^4/(a^2-b^2)/d+1/2*(4*A*b^3+a^3*B-3*a*b^2*B-2*a^2*b*(A-C))*sec(d*x+c)*tan(d*x+c)/a^3/(a^2-b^2)/d-1/3*(4*A*b^2-3*a*b*B-a^2*(A-3*C))*sec(d*x+c)^2*tan(d*x+c)/a^2/(a^2-b^2)/d+(A*b^2-a*(B*b-C*a))*sec(d*x+c)^2*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,7,1/2*(2*A*b^2-6*B*a*b+12*C*a^2+C*b^2)*x/b^5-a*(6*A*b^6-6*a^5*b*B+15*a^3*b^3*B-12*a*b^5*B+a^4*b^2*(2*A-29*C)-5*a^2*b^4*(A-4*C)+12*a^6*C)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(5/2)/b^5/(a+b)^(5/2)/d+1/2*(6*a^4*b*B-11*a^2*b^3*B+2*b^5*B-a^3*b^2*(2*A-21*C)+a*b^4*(5*A-6*C)-12*a^5*C)*sin(d*x+c)/b^4/(a^2-b^2)^2/d-1/2*(3*a^3*b*B-6*a*b^3*B-a^2*b^2*(A-10*C)+b^4*(4*A-C)-6*a^4*C)*cos(d*x+c)*sin(d*x+c)/b^3/(a^2-b^2)^2/d-1/2*(A*b^2-a*(B*b-C*a))*cos(d*x+c)^3*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/2*(3*A*b^4+a*(2*B*a^2*b-5*B*b^3-4*C*a^3+7*C*a*b^2))*cos(d*x+c)^2*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,6,(B*b-3*C*a)*x/b^4+(2*A*b^6-2*a^5*b*B+5*a^3*b^3*B-6*a*b^5*B+6*a^6*C-15*a^4*b^2*C+a^2*b^4*(A+12*C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(5/2)/b^4/(a+b)^(5/2)/d+1/2*(A*b^2-B*a*b+3*C*a^2-2*C*b^2)*sin(d*x+c)/b^3/(a^2-b^2)/d-1/2*(A*b^2-a*(B*b-C*a))*cos(d*x+c)^2*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/2*a*(2*A*b^4+a^3*b*B-4*a*b^3*B-3*a^4*C+a^2*b^2*(A+6*C))*sin(d*x+c)/b^3/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,5,C*x/b^3+(a^2*b^3*B+2*b^5*B-2*a^5*C+5*a^3*b^2*C-3*a*b^4*(A+2*C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(5/2)/b^3/(a+b)^(5/2)/d+1/2*a*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b^2/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/2*(2*A*b^4+a^3*b*B-4*a*b^3*B-3*a^4*C+a^2*b^2*(A+6*C))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,5,-(3*a*b*B-a^2*(2*A+C)-b^2*(A+2*C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(5/2)/(a+b)^(5/2)/d-1/2*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/2*(a^2*b*B+2*b^3*B+a^3*C-a*b^2*(3*A+4*C))*sin(d*x+c)/b/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^3,x,6,(5*a^2*A*b^3-2*A*b^5+2*a^5*B+a^3*b^2*B-3*a^4*b*(2*A+C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^3/(a-b)^(5/2)/(a+b)^(5/2)/d+A*arctanh(sin(d*x+c))/a^3/d+1/2*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/2*(2*A*b^4+3*a^3*b*B-a^4*C-a^2*b^2*(5*A+2*C))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^3,x,7,-(15*a^2*A*b^4-6*A*b^6+6*a^5*b*B-5*a^3*b^3*B+2*a*b^5*B-2*a^6*C-a^4*b^2*(12*A+C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^4/(a-b)^(5/2)/(a+b)^(5/2)/d-(3*A*b-B*a)*arctanh(sin(d*x+c))/a^4/d-1/2*(11*a^2*A*b^2-6*A*b^4-5*a^3*b*B+2*a*b^3*B-a^4*(2*A-3*C))*tan(d*x+c)/a^3/(a^2-b^2)^2/d+1/2*(A*b^2-a*(B*b-C*a))*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/2*(3*A*b^4+4*a^3*b*B-a*b^3*B-2*a^4*C-a^2*b^2*(6*A+C))*tan(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^3,x,8,-b*(12*A*b^6-12*a^5*b*B+15*a^3*b^3*B-6*a*b^5*B-a^2*b^4*(29*A-2*C)+5*a^4*b^2*(4*A-C)+6*a^6*C)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^5/(a-b)^(5/2)/(a+b)^(5/2)/d+1/2*(12*A*b^2-6*a*b*B+a^2*(A+2*C))*arctanh(sin(d*x+c))/a^5/d-1/2*(12*A*b^5-2*a^5*B+11*a^3*b^2*B-6*a*b^4*B+a^4*b*(6*A-5*C)-a^2*b^3*(21*A-2*C))*tan(d*x+c)/a^4/(a^2-b^2)^2/d+1/2*(6*A*b^4+6*a^3*b*B-3*a*b^3*B+a^4*(A-4*C)-a^2*b^2*(10*A-C))*sec(d*x+c)*tan(d*x+c)/a^3/(a^2-b^2)^2/d+1/2*(A*b^2-a*(B*b-C*a))*sec(d*x+c)*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/2*(7*A*a^2*b^2-4*A*b^4-5*B*a^3*b+2*B*a*b^3+3*C*a^4)*sec(d*x+c)*tan(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x,8,1/2*(2*A*b^2-8*B*a*b+20*C*a^2+C*b^2)*x/b^6+a*(8*A*b^8+8*a^7*b*B-28*a^5*b^3*B+35*a^3*b^5*B-20*a*b^7*B-a^6*b^2*(2*A-69*C)+7*a^4*b^4*(A-12*C)-8*a^2*b^6*(A-5*C)-20*a^8*C)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^6/sqrt(a+b)/(a^2-b^2)^3/d+1/6*(24*a^6*b*B-68*a^4*b^3*B+65*a^2*b^5*B-6*b^7*B-a^5*b^2*(6*A-167*C)+a^3*b^4*(17*A-146*C)-2*a*b^6*(13*A-12*C)-60*a^7*C)*sin(d*x+c)/b^5/(a^2-b^2)^3/d-1/2*(4*a^5*b*B-11*a^3*b^3*B+12*a*b^5*B-a^4*b^2*(A-27*C)+a^2*b^4*(2*A-23*C)-b^6*(6*A-C)-10*a^6*C)*cos(d*x+c)*sin(d*x+c)/b^4/(a^2-b^2)^3/d-1/3*(A*b^2-a*(B*b-C*a))*cos(d*x+c)^4*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^3+1/6*(4*A*b^4+2*a^3*b*B-7*a*b^3*B-5*a^4*C+a^2*b^2*(A+10*C))*cos(d*x+c)^3*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2-1/6*(12*A*b^6-8*a^5*b*B+20*a^3*b^3*B-27*a*b^5*B+a^4*b^2*(2*A-53*C)+20*a^6*C+a^2*b^4*(A+48*C))*cos(d*x+c)^2*sin(d*x+c)/b^3/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x,7,(B*b-4*C*a)*x/b^5-(2*A*b^8+2*a^7*b*B-7*a^5*b^3*B+8*a^3*b^5*B-8*a*b^7*B-8*a^8*C+28*a^6*b^2*C-35*a^4*b^4*C+a^2*b^6*(3*A+20*C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(7/2)/b^5/(a+b)^(7/2)/d-1/6*(5*A*b^4+3*B*a^3*b-8*B*a*b^3-12*C*a^4+23*C*a^2*b^2-6*C*b^4)*sin(d*x+c)/b^4/(a^2-b^2)^2/d-1/3*(A*b^2-a*(B*b-C*a))*cos(d*x+c)^3*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^3+1/6*(3*A*b^4+a^3*b*B-6*a*b^3*B-4*a^4*C+a^2*b^2*(2*A+9*C))*cos(d*x+c)^2*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2+1/2*a*(2*A*b^6-a^5*b*B+2*a^3*b^3*B-6*a*b^5*B+4*a^6*C-11*a^4*b^2*C+3*a^2*b^4*(A+4*C))*sin(d*x+c)/b^4/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x,6,C*x/b^4-(3*a^2*b^5*B+2*b^7*B-a^3*b^4*(A-8*C)+2*a^7*C-7*a^5*b^2*C-4*a*b^6*(A+2*C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(7/2)/b^4/(a+b)^(7/2)/d-1/3*(A*b^2-a*(B*b-C*a))*cos(d*x+c)^2*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^3-1/6*a*(2*A*b^4-5*a*b^3*B-3*a^4*C+a^2*b^2*(3*A+8*C))*sin(d*x+c)/b^3/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2-1/6*(4*A*b^6+a^3*b^3*B-16*a*b^5*B+9*a^6*C+2*a^2*b^4*(7*A+17*C)-a^4*b^2*(3*A+28*C))*sin(d*x+c)/b^3/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x,6,(a^3*B+4*a*b^2*B-b^3*(A+2*C)-a^2*b*(4*A+3*C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(7/2)/(a+b)^(7/2)/d+1/3*a*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b^2/(a^2-b^2)/d/(a+b*cos(d*x+c))^3+1/6*(3*A*b^4+a^3*b*B-6*a*b^3*B-4*a^4*C+a^2*b^2*(2*A+9*C))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2+1/6*(a^4*b*B-10*a^2*b^3*B-6*b^5*B+a^3*b^2*(2*A-5*C)+2*a^5*C+a*b^4*(13*A+18*C))*sin(d*x+c)/b^2/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x,6,-(4*a^2*b*B+b^3*B-a^3*(2*A+C)-a*b^2*(3*A+4*C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(7/2)/(a+b)^(7/2)/d-1/3*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^3+1/6*(2*a^2*b*B+3*b^3*B+a^3*C-a*b^2*(5*A+6*C))*sin(d*x+c)/b/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2+1/6*(2*a^3*b*B+13*a*b^3*B+a^4*C-2*b^4*(2*A+3*C)-a^2*b^2*(11*A+10*C))*sin(d*x+c)/b/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^4,x,7,-(7*a^2*A*b^5-2*A*b^7-2*a^7*B-3*a^5*b^2*B-a^4*b^3*(8*A-C)+4*a^6*b*(2*A+C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^4/(a-b)^(7/2)/(a+b)^(7/2)/d+A*arctanh(sin(d*x+c))/a^4/d+1/3*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^3-1/6*(3*A*b^4+5*a^3*b*B-2*a^4*C-a^2*b^2*(8*A+3*C))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2-1/6*(17*a^2*A*b^4-6*A*b^6+11*a^5*b*B+4*a^3*b^3*B-2*a^6*C-13*a^4*b^2*(2*A+C))*sin(d*x+c)/a^3/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^4,x,8,-(35*a^4*A*b^4-28*a^2*A*b^6+8*A*b^8+8*a^7*b*B-8*a^5*b^3*B+7*a^3*b^5*B-2*a*b^7*B-2*a^8*C-a^6*b^2*(20*A+3*C))*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^5/(a-b)^(7/2)/(a+b)^(7/2)/d-(4*A*b-B*a)*arctanh(sin(d*x+c))/a^5/d+1/6*(68*a^2*A*b^4-24*A*b^6+26*a^5*b*B-17*a^3*b^3*B+6*a*b^5*B+a^6*(6*A-11*C)-a^4*b^2*(65*A+4*C))*tan(d*x+c)/a^4/(a^2-b^2)^3/d+1/3*(A*b^2-a*(B*b-C*a))*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^3-1/6*(4*A*b^4+6*a^3*b*B-a*b^3*B-3*a^4*C-a^2*b^2*(9*A+2*C))*tan(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2-1/2*(11*a^2*A*b^4-4*A*b^6+6*a^5*b*B-2*a^3*b^3*B+a*b^5*B-2*a^6*C-3*a^4*b^2*(4*A+C))*tan(d*x+c)/a^3/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^4,x,9,b*(20*A*b^8+20*a^7*b*B-35*a^5*b^3*B+28*a^3*b^5*B-8*a*b^7*B-a^2*b^6*(69*A-2*C)-8*a^6*b^2*(5*A-C)+7*a^4*b^4*(12*A-C)-8*a^8*C)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^6/sqrt(a-b)/sqrt(a+b)/(a^2-b^2)^3/d+1/2*(20*A*b^2-8*a*b*B+a^2*(A+2*C))*arctanh(sin(d*x+c))/a^6/d+1/6*(60*A*b^7+6*a^7*B-65*a^5*b^2*B+68*a^3*b^4*B-24*a*b^6*B+a^4*b^3*(146*A-17*C)-a^2*b^5*(167*A-6*C)-a^6*(24*A*b-26*C*b))*tan(d*x+c)/a^5/(a^2-b^2)^3/d-1/2*(10*A*b^6-12*a^5*b*B+11*a^3*b^3*B-4*a*b^5*B-a^6*(A-6*C)+a^4*b^2*(23*A-2*C)-a^2*b^4*(27*A-C))*sec(d*x+c)*tan(d*x+c)/a^4/(a^2-b^2)^3/d+1/3*(A*b^2-a*(B*b-C*a))*sec(d*x+c)*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^3-1/6*(5*A*b^4+7*a^3*b*B-2*a*b^3*B-4*a^4*C-a^2*b^2*(10*A+C))*sec(d*x+c)*tan(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2+1/6*(20*A*b^6-27*a^5*b*B+20*a^3*b^3*B-8*a*b^5*B-a^2*b^4*(53*A-2*C)+12*a^6*C+a^4*b^2*(48*A+C))*sec(d*x+c)*tan(d*x+c)/a^3/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,3,(B*b-C*a)*x+b*C*sin(d*x+c)/d,1],
[(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,4,C*x+2*(B*b-2*C*a)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/sqrt(a+b)/d,1],
[(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,5,2*(B*a*b-C*a^2-C*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(3/2)/(a+b)^(3/2)/d-b*(B*b-2*C*a)*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^4,x,6,(2*B*a^2*b+B*b^3-2*C*a^3-4*C*a*b^2)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(5/2)/(a+b)^(5/2)/d-1/2*b*(B*b-2*C*a)*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/2*b*(3*B*a*b-4*C*a^2-2*C*b^2)*sin(d*x+c)/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^5,x,7,(2*B*a^3*b+3*B*a*b^3-2*C*a^4-7*C*a^2*b^2-C*b^4)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/(a-b)^(7/2)/(a+b)^(7/2)/d-1/3*b*(B*b-2*C*a)*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c))^3-1/6*b*(5*B*a*b-7*C*a^2-3*C*b^2)*sin(d*x+c)/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2-1/6*b*(11*B*a^2*b+4*B*b^3-13*C*a^3-17*C*a*b^2)*sin(d*x+c)/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^2*sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,9,2/315*(24*a^3*b*B+57*a*b^3*B-16*a^4*C-6*a^2*b^2*(7*A+4*C)+21*b^4*(9*A+7*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^4/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/315*(a^2-b^2)*(24*a^2*b*B+75*b^3*B-16*a^3*C-6*a*b^2*(7*A+6*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^4/d/sqrt(a+b*cos(d*x+c))+2/315*(24*a^2*b*B+75*b^3*B-16*a^3*C-6*a*b^2*(7*A+6*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/d+2/315*(63*A*b^2-36*B*a*b+24*C*a^2+49*C*b^2)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^3/d+2/21*(3*B*b-2*C*a)*cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^2/d+2/9*C*cos(d*x+c)^2*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d,1],
[cos(d*x+c)*sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,8,-2/105*(14*a^2*b*B-63*b^3*B-8*a^3*C-a*b^2*(35*A+19*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^3/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/105*(a^2-b^2)*(35*A*b^2-14*B*a*b+8*C*a^2+25*C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^3/d/sqrt(a+b*cos(d*x+c))+2/105*(35*A*b^2-14*B*a*b+8*C*a^2+25*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d+2/35*(7*B*b-4*C*a)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^2/d+2/7*C*cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d,1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,7,2/15*(3*b^2*(5*A+3*C)+a*(5*B*b-2*C*a))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/15*(a^2-b^2)*(5*B*b-2*C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/d/sqrt(a+b*cos(d*x+c))+2/15*(5*B*b-2*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+2/5*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d,1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,9,2/3*(3*B*b+C*a)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/3*(3*A*b^2-(a^2-b^2)*C)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b/d/sqrt(a+b*cos(d*x+c))+2*a*A*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+2/3*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,9,-(A-2*C)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+(A*a+2*B*b)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+(A*b+2*B*a)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+A*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,10,-1/4*(A*b+4*B*a)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/4*(3*A*b+4*B*a+8*C*b)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-1/4*(A*b^2-4*a*b*B-4*a^2*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+1/4*(A*b+4*B*a)*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a/d+1/2*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,11,1/24*(3*A*b^2-6*a*b*B-8*a^2*(2*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-1/24*(A*b^2-18*a*b*B-8*a^2*(2*A+3*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+1/8*(A*b^3+8*a^3*B-2*a*b^2*B+4*a^2*b*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^2/d/sqrt(a+b*cos(d*x+c))-1/24*(3*A*b^2-6*a*b*B-8*a^2*(2*A+3*C))*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a^2/d+1/12*(A*b+6*B*a)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/a/d+1/3*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d,1],
[cos(d*x+c)^2*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,10,2/3465*(88*a^4*b*B+363*a^2*b^3*B+1617*b^5*B-48*a^5*C-18*a^3*b^2*(11*A+6*C)+6*a*b^4*(451*A+348*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^4/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/3465*(a^2-b^2)*(88*a^3*b*B+429*a*b^3*B-48*a^4*C-18*a^2*b^2*(11*A+8*C)+75*b^4*(11*A+9*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^4/d/sqrt(a+b*cos(d*x+c))+2/3465*(88*a^3*b*B+429*a*b^3*B-48*a^4*C-18*a^2*b^2*(11*A+8*C)+75*b^4*(11*A+9*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/d+2/3465*(88*a^2*b*B+539*b^3*B-48*a^3*C-6*a*b^2*(33*A+34*C))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^3/d+2/693*(99*A*b^2-44*B*a*b+24*C*a^2+81*C*b^2)*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b^3/d+2/99*(11*B*b-6*C*a)*cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b^2/d+2/11*C*cos(d*x+c)^2*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,9,-2/315*(18*a^3*b*B-246*a*b^3*B-8*a^4*C-21*b^4*(9*A+7*C)-3*a^2*b^2*(21*A+11*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^3/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/315*(a^2-b^2)*(18*a^2*b*B-75*b^3*B-8*a^3*C-3*a*b^2*(21*A+13*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^3/d/sqrt(a+b*cos(d*x+c))-2/315*(18*a^2*b*B-75*b^3*B-8*a^3*C-3*a*b^2*(21*A+13*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d+2/315*(63*A*b^2-18*B*a*b+8*C*a^2+49*C*b^2)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^2/d+2/63*(9*B*b-4*C*a)*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b^2/d+2/9*C*cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,8,2/105*(21*a^2*b*B+63*b^3*B-6*a^3*C+2*a*b^2*(70*A+41*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/105*(a^2-b^2)*(35*A*b^2+21*B*a*b-6*C*a^2+25*C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/d/sqrt(a+b*cos(d*x+c))+2/105*(35*A*b^2+21*B*a*b-6*C*a^2+25*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+2/35*(7*B*b-2*C*a)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d+2/7*C*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,10,2/15*(15*A*b^2+20*B*a*b+3*C*a^2+9*C*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/15*(5*a^2*b*B-5*b^3*B+3*a^3*C-3*a*b^2*(5*A+C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b/d/sqrt(a+b*cos(d*x+c))+2*a^2*A*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+2/15*(5*B*b+3*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+2/5*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,10,-1/3*(3*A*a-6*B*b-8*C*a)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/3*(6*a*b*B+a^2*(3*A-2*C)+2*b^2*(3*A+C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+a*(3*A*b+2*B*a)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-1/3*b*(3*A-2*C)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+A*(a+b*cos(d*x+c))^(3/2)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,10,-1/4*(5*A*b+4*B*a-8*C*b)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/4*(4*a^2*B+8*b^2*B+a*b*(7*A+8*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+1/4*(3*A*b^2+12*a*b*B+4*a^2*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+1/4*(3*A*b+4*B*a)*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/d+1/2*A*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,11,-1/24*(3*A*b^2+30*a*b*B+8*a^2*(2*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/24*(42*a*b*B+8*a^2*(2*A+3*C)+b^2*(17*A+48*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-1/8*(A*b^3-8*a^3*B-6*a*b^2*B-12*a^2*b*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+1/24*(3*A*b^2+30*a*b*B+8*a^2*(2*A+3*C))*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a/d+1/4*(A*b+2*B*a)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,12,1/192*(9*A*b^3-128*a^3*B-24*a*b^2*B-12*a^2*b*(13*A+20*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-1/192*(3*A*b^3-128*a^3*B-136*a*b^2*B-12*a^2*b*(19*A+28*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+1/64*(3*A*b^4+96*a^3*b*B-8*a*b^3*B+24*a^2*b^2*(A+2*C)+16*a^4*(3*A+4*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^2/d/sqrt(a+b*cos(d*x+c))-1/192*(9*A*b^3-128*a^3*B-24*a*b^2*B-12*a^2*b*(13*A+20*C))*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a^2/d+1/96*(3*A*b^2+56*a*b*B+12*a^2*(3*A+4*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/a/d+1/24*(3*A*b+8*B*a)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^3*tan(d*x+c)/d,1],
[cos(d*x+c)^2*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,11,2/45045*(520*a^5*b*B+3315*a^3*b^3*B+48165*a*b^5*B-240*a^6*C+1617*b^6*(13*A+11*C)-10*a^4*b^2*(143*A+76*C)+3*a^2*b^4*(13299*A+10223*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^4/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/45045*(a^2-b^2)*(520*a^4*b*B+3705*a^2*b^3*B+8775*b^5*B-240*a^5*C-10*a^3*b^2*(143*A+94*C)+6*a*b^4*(2717*A+2174*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^4/d/sqrt(a+b*cos(d*x+c))+2/45045*(520*a^4*b*B+3705*a^2*b^3*B+8775*b^5*B-240*a^5*C-10*a^3*b^2*(143*A+94*C)+6*a*b^4*(2717*A+2174*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/d+2/45045*(520*a^3*b*B+4355*a*b^3*B-240*a^4*C+539*b^4*(13*A+11*C)-10*a^2*b^2*(143*A+124*C))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^3/d+2/9009*(104*a^2*b*B+1053*b^3*B-48*a^3*C-2*a*b^2*(143*A+166*C))*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b^3/d+2/1287*(143*A*b^2-52*B*a*b+24*C*a^2+121*C*b^2)*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b^3/d+2/143*(13*B*b-6*C*a)*cos(d*x+c)*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b^2/d+2/13*C*cos(d*x+c)^2*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,10,-2/3465*(110*a^4*b*B-3069*a^2*b^3*B-1617*b^5*B-40*a^5*C-15*a^3*b^2*(33*A+17*C)-15*a*b^4*(319*A+247*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^3/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/3465*(a^2-b^2)*(110*a^3*b*B-1254*a*b^3*B-40*a^4*C-75*b^4*(11*A+9*C)-15*a^2*b^2*(33*A+19*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^3/d/sqrt(a+b*cos(d*x+c))-2/3465*(110*a^3*b*B-1254*a*b^3*B-40*a^4*C-75*b^4*(11*A+9*C)-15*a^2*b^2*(33*A+19*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d-2/3465*(110*a^2*b*B-539*b^3*B-40*a^3*C-5*a*b^2*(99*A+67*C))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^2/d+2/693*(99*A*b^2-22*B*a*b+8*C*a^2+81*C*b^2)*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b^2/d+2/99*(11*B*b-4*C*a)*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b^2/d+2/11*C*cos(d*x+c)*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,9,2/315*(45*a^3*b*B+435*a*b^3*B-10*a^4*C+21*b^4*(9*A+7*C)+3*a^2*b^2*(161*A+93*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/315*(a^2-b^2)*(45*a^2*b*B+75*b^3*B-10*a^3*C+6*a*b^2*(28*A+19*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/d/sqrt(a+b*cos(d*x+c))+2/315*(45*a^2*b*B+75*b^3*B-10*a^3*C+6*a*b^2*(28*A+19*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+2/315*(63*A*b^2+45*B*a*b-10*C*a^2+49*C*b^2)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d+2/63*(9*B*b-2*C*a)*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d+2/9*C*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c),x,11,2/105*(161*a^2*b*B+63*b^3*B+15*a^3*C+5*a*b^2*(49*A+29*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/105*(56*a^3*b*B-56*a*b^3*B-10*a^2*b^2*(7*A-C)+15*a^4*C-5*b^4*(7*A+5*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b/d/sqrt(a+b*cos(d*x+c))+2*a^3*A*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+2/105*(35*A*b^2+56*B*a*b+15*C*a^2+25*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+2/35*(7*B*b+5*C*a)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/7*C*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2,x,11,1/15*(70*a*b*B-a^2*(15*A-46*C)+6*b^2*(5*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/15*(20*a^2*b*B+10*b^3*B+a^3*(15*A-16*C)+4*a*b^2*(15*A+4*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+a^2*(5*A*b+2*B*a)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-1/15*b*(15*A*a-10*B*b-16*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d-1/5*b*(5*A-2*C)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d+A*(a+b*cos(d*x+c))^(5/2)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3,x,11,-1/12*(12*a^2*B-24*b^2*B+a*b*(27*A-56*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/12*(12*a^3*B+48*a*b^2*B+8*b^3*(3*A+C)+a^2*b*(33*A+16*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+1/4*a*(15*A*b^2+20*a*b*B+4*a^2*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-1/12*b*(21*A*b+12*B*a-8*C*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+1/4*(5*A*b+4*B*a)*(a+b*cos(d*x+c))^(3/2)*tan(d*x+c)/d+1/2*A*(a+b*cos(d*x+c))^(5/2)*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4,x,11,-1/24*(54*a*b*B+3*b^2*(11*A-16*C)+8*a^2*(2*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/24*(66*a^2*b*B+48*b^3*B+8*a^3*(2*A+3*C)+a*b^2*(59*A+96*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+1/8*(5*A*b^3+8*a^3*B+30*a*b^2*B+20*a^2*b*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+1/24*(15*A*b^2+42*a*b*B+8*a^2*(2*A+3*C))*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/d+1/12*(5*A*b+6*B*a)*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^5,x,12,-1/192*(15*A*b^3+128*a^3*B+264*a*b^2*B+4*a^2*b*(71*A+108*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/192*(128*a^3*B+472*a*b^2*B+4*a^2*b*(89*A+132*C)+b^3*(133*A+384*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-1/64*(5*A*b^4-160*a^3*b*B-40*a*b^3*B-120*a^2*b^2*(A+2*C)-16*a^4*(3*A+4*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+1/192*(15*A*b^3+128*a^3*B+264*a*b^2*B+4*a^2*b*(71*A+108*C))*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a/d+1/32*(5*A*b^2+24*a*b*B+4*a^2*(3*A+4*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/24*(5*A*b+8*B*a)*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^6,x,13,1/1920*(45*A*b^4-2840*a^3*b*B-150*a*b^3*B-256*a^4*(4*A+5*C)-12*a^2*b^2*(141*A+220*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-1/1920*(15*A*b^4-3560*a^3*b*B-1330*a*b^3*B-256*a^4*(4*A+5*C)-4*a^2*b^2*(809*A+1180*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+1/128*(3*A*b^5+96*a^5*B+240*a^3*b^2*B-10*a*b^4*B+40*a^2*b^3*(A+2*C)+80*a^4*b*(3*A+4*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^2/d/sqrt(a+b*cos(d*x+c))-1/1920*(45*A*b^4-2840*a^3*b*B-150*a*b^3*B-256*a^4*(4*A+5*C)-12*a^2*b^2*(141*A+220*C))*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a^2/d+1/960*(15*A*b^3+360*a^3*B+590*a*b^2*B+4*a^2*b*(193*A+260*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/a/d+1/240*(15*A*b^2+110*a*b*B+16*a^2*(4*A+5*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d+1/8*(A*b+2*B*a)*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^3*tan(d*x+c)/d+1/5*A*(a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^4*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x,9,2/105*(161*B*a^2*b+63*B*b^3-146*C*a^3+82*C*a*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/105*(a^2-b^2)*(56*B*a*b-41*C*a^2+25*C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+2/105*b*(56*B*a*b-41*C*a^2+25*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+2/35*b*(7*B*b-2*C*a)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/7*b*C*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2),x,8,2/15*(20*B*a*b-17*C*a^2+9*C*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/15*(a^2-b^2)*(5*B*b-2*C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+2/15*b*(5*B*b-2*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+2/5*b*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c)),x,8,2/105*(56*a^2*b*B+63*b^3*B-48*a^3*C-2*a*b^2*(35*A+22*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^4/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/105*(56*a^3*b*B+49*a*b^3*B-48*a^4*C-5*b^4*(7*A+5*C)-2*a^2*b^2*(35*A+16*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^4/d/sqrt(a+b*cos(d*x+c))+2/105*(35*A*b^2-28*B*a*b+24*C*a^2+25*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/d+2/35*(7*B*b-6*C*a)*cos(d*x+c)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d+2/7*C*cos(d*x+c)^2*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d,1],
[cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c)),x,7,2/15*(15*A*b^2-10*B*a*b+8*C*a^2+9*C*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^3/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/15*(10*a^2*b*B+5*b^3*B-8*a^3*C-a*b^2*(15*A+7*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^3/d/sqrt(a+b*cos(d*x+c))+2/15*(5*B*b-4*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d+2/5*C*cos(d*x+c)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c)),x,6,2/3*(3*B*b-2*C*a)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/3*(3*A*b^2-3*B*a*b+2*C*a^2+C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/d/sqrt(a+b*cos(d*x+c))+2/3*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/sqrt(a+b*cos(d*x+c)),x,8,2*C*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b/d/sqrt((a+b*cos(d*x+c))/(a+b))+2*(B*b-C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b/d/sqrt(a+b*cos(d*x+c))+2*A*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/sqrt(a+b*cos(d*x+c)),x,9,-A*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a/d/sqrt((a+b*cos(d*x+c))/(a+b))+(A+2*C)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-(A*b-2*B*a)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+A*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/sqrt(a+b*cos(d*x+c)),x,10,1/4*(3*A*b-4*B*a)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-1/4*(A*b-4*B*a)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+1/4*(3*A*b^2-4*a*b*B+4*a^2*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^2/d/sqrt(a+b*cos(d*x+c))-1/4*(3*A*b-4*B*a)*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a^2/d+1/2*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/a/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^4/sqrt(a+b*cos(d*x+c)),x,11,-1/24*(15*A*b^2-18*a*b*B+8*a^2*(2*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^3/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/24*(5*A*b^2-6*a*b*B+8*a^2*(2*A+3*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a^2/d/sqrt(a+b*cos(d*x+c))-1/8*(5*A*b^3-8*a^3*B-6*a*b^2*B+4*a^2*b*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^3/d/sqrt(a+b*cos(d*x+c))+1/24*(15*A*b^2-18*a*b*B+8*a^2*(2*A+3*C))*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a^3/d-1/12*(5*A*b-6*B*a)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/a^2/d+1/3*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/a/d,1],
[cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x,8,-2/15*(40*a^3*b*B-25*a*b^3*B-6*a^2*b^2*(5*A-4*C)-48*a^4*C+3*b^4*(5*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^4/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/15*(40*a^2*b*B+5*b^3*B-48*a^3*C-6*a*b^2*(5*A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^4/d/sqrt(a+b*cos(d*x+c))-2*(A*b^2-a*(B*b-C*a))*cos(d*x+c)^2*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+2/15*(20*a^2*b*B-5*b^3*B-3*a*b^2*(5*A-3*C)-24*a^3*C)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)/d+2/5*(5*A*b^2-5*B*a*b+6*C*a^2-C*b^2)*cos(d*x+c)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)/d,1],
[cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x,7,2/3*(6*a^2*b*B-3*b^3*B-a*b^2*(3*A-5*C)-8*a^3*C)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^3/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/3*(3*A*b^2-6*B*a*b+8*C*a^2+C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^3/d/sqrt(a+b*cos(d*x+c))+2*a*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b^2/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+2/3*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x,6,2*(A*b^2-B*a*b+2*C*a^2-C*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))+2*(B*b-2*C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/d/sqrt(a+b*cos(d*x+c))-2*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x,9,-2*(A*b^2-a*(B*b-C*a))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a/b/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))+2*C*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b/d/sqrt(a+b*cos(d*x+c))+2*A*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))+2*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x,10,(3*A*b^2-2*a*b*B-a^2*(A-2*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^2/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))+A*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a/d/sqrt(a+b*cos(d*x+c))-(3*A*b-2*B*a)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^2/d/sqrt(a+b*cos(d*x+c))-b*(3*A*b^2-2*a*b*B-a^2*(A-2*C))*sin(d*x+c)/a^2/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+A*tan(d*x+c)/a/d/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x,11,-1/4*(15*A*b^3+4*a^3*B-12*a*b^2*B-a^2*(7*A*b-8*C*b))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^3/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))-1/4*(5*A*b-4*B*a)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a^2/d/sqrt(a+b*cos(d*x+c))+1/4*(15*A*b^2-12*a*b*B+4*a^2*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^3/d/sqrt(a+b*cos(d*x+c))+1/4*b*(15*A*b^3+4*a^3*B-12*a*b^2*B-a^2*(7*A*b-8*C*b))*sin(d*x+c)/a^3/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-1/4*(5*A*b-4*B*a)*tan(d*x+c)/a^2/d/sqrt(a+b*cos(d*x+c))+1/2*A*sec(d*x+c)*tan(d*x+c)/a/d/sqrt(a+b*cos(d*x+c)),1],
[cos(d*x+c)^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,9,-2/15*(80*a^5*b*B-140*a^3*b^3*B+40*a*b^5*B-4*a^4*b^2*(10*A-53*C)+5*a^2*b^4*(15*A-11*C)-128*a^6*C-3*b^6*(5*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^5/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/15*(80*a^4*b*B-80*a^2*b^3*B-5*b^5*B-4*a^3*b^2*(10*A-29*C)-128*a^5*C+a*b^4*(45*A+17*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^5/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-2/3*(A*b^2-a*(B*b-C*a))*cos(d*x+c)^3*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+2/3*(6*A*b^4+5*a^3*b*B-9*a*b^3*B-2*a^2*b^2*(A-6*C)-8*a^4*C)*cos(d*x+c)^2*sin(d*x+c)/b^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c))+2/15*(40*a^4*b*B-65*a^2*b^3*B+5*b^5*B-2*a^3*b^2*(10*A-49*C)+2*a*b^4*(20*A-7*C)-64*a^5*C)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^4/(a^2-b^2)^2/d-2/15*(30*a^3*b*B-50*a*b^3*B-a^2*b^2*(15*A-71*C)+b^4*(35*A-3*C)-48*a^4*C)*cos(d*x+c)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)^2/d,1],
[cos(d*x+c)^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,8,2/3*(8*a^4*b*B-15*a^2*b^3*B+3*b^5*B-2*a^3*b^2*(A-14*C)+2*a*b^4*(3*A-4*C)-16*a^5*C)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^4/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/3*(8*a^3*b*B-9*a*b^3*B-2*a^2*b^2*(A-8*C)-16*a^4*C+b^4*(3*A+C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^4/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-2/3*(A*b^2-a*(B*b-C*a))*cos(d*x+c)^2*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)-2/3*a*(4*A*b^4+a*(3*B*a^2*b-7*B*b^3-6*C*a^3+10*C*a*b^2))*sin(d*x+c)/b^3/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c))+2/3*(A*b^2-B*a*b+2*C*a^2-C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)/d,1],
[cos(d*x+c)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,7,-2/3*(2*a^3*b*B-6*a*b^3*B+3*b^4*(A-C)-8*a^4*C+a^2*b^2*(A+15*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^3/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/3*(2*a^2*b*B-3*b^3*B-8*a^3*C+a*b^2*(A+9*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^3/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+2/3*a*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b^2/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+2/3*(3*A*b^4+2*a^3*b*B-6*a*b^3*B-5*a^4*C+a^2*b^2*(A+9*C))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,7,-2/3*(a^2*b*B+3*b^3*B+2*a^3*C-2*a*b^2*(2*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/3*(A*b^2-B*a*b-2*C*a^2+3*C*b^2)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-2/3*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+2/3*(a^2*b*B+3*b^3*B+2*a^3*C-2*a*b^2*(2*A+3*C))*sin(d*x+c)/b/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x,10,2/3*(3*A*b^4+4*a^3*b*B-a^4*C-a^2*b^2*(7*A+3*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^2/b/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/3*(A*b^2-a*(B*b-C*a))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+2*A*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^2/d/sqrt(a+b*cos(d*x+c))+2/3*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)-2/3*(3*A*b^4+4*a^3*b*B-a^4*C-a^2*b^2*(7*A+3*C))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x,11,1/3*(26*a^2*A*b^2-15*A*b^4-14*a^3*b*B+6*a*b^3*B-a^4*(3*A-8*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^3/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-1/3*(5*A*b^2-2*a*b*B-a^2*(3*A-2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a^2/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-(5*A*b-2*B*a)*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^3/d/sqrt(a+b*cos(d*x+c))-1/3*b*(5*A*b^2-2*a*b*B-a^2*(3*A-2*C))*sin(d*x+c)/a^2/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)-1/3*b*(26*a^2*A*b^2-15*A*b^4-14*a^3*b*B+6*a*b^3*B-a^4*(3*A-8*C))*sin(d*x+c)/a^3/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c))+A*tan(d*x+c)/a/d/(a+b*cos(d*x+c))^(3/2),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^3/(a+b*cos(d*x+c))^(5/2),x,12,1/12*(105*A*b^5-12*a^5*B+104*a^3*b^2*B-60*a*b^4*B+a^4*b*(33*A-56*C)-2*a^2*b^3*(85*A-12*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/a^4/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/12*(35*A*b^3+12*a^3*B-20*a*b^2*B-a^2*(27*A*b-8*C*b))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/a^3/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+1/4*(35*A*b^2-20*a*b*B+4*a^2*(A+2*C))*sqrt((a+b*cos(d*x+c))/(a+b))*EllipticPi(sin(1/2*d*x+1/2*c),2,sqrt(2*b/(a+b)))/a^4/d/sqrt(a+b*cos(d*x+c))+1/12*b*(35*A*b^3+12*a^3*B-20*a*b^2*B-a^2*(27*A*b-8*C*b))*sin(d*x+c)/a^3/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)-1/12*b*(105*A*b^5-12*a^5*B+104*a^3*b^2*B-60*a*b^4*B+a^4*b*(33*A-56*C)-2*a^2*b^3*(85*A-12*C))*sin(d*x+c)/a^4/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c))-1/4*(7*A*b-4*B*a)*tan(d*x+c)/a^2/d/(a+b*cos(d*x+c))^(3/2)+1/2*A*sec(d*x+c)*tan(d*x+c)/a/d/(a+b*cos(d*x+c))^(3/2),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(7/2),x,8,-2/15*(3*a^3*b*B+29*a*b^3*B+2*a^4*C-3*b^4*(3*A+5*C)-a^2*b^2*(23*A+19*C))*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/b^2/(a^2-b^2)^3/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/15*(3*a^2*b*B+5*b^3*B+2*a^3*C-2*a*b^2*(4*A+5*C))*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/b^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c))-2/5*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(5/2)+2/15*(3*a^2*b*B+5*b^3*B+2*a^3*C-2*a*b^2*(4*A+5*C))*sin(d*x+c)/b/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^(3/2)+2/15*(3*a^3*b*B+29*a*b^3*B+2*a^4*C-3*b^4*(3*A+5*C)-a^2*b^2*(23*A+19*C))*sin(d*x+c)/b/(a^2-b^2)^3/d/sqrt(a+b*cos(d*x+c)),1],
[(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c)),x,7,2/3*(3*B*b-2*C*a)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/3*(a^2-b^2)*C*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))+2/3*b*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x,6,2*C*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+2*(B*b-2*C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c)),1],
[(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,7,2*(B*b-2*C*a)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/(a^2-b^2)/d/sqrt((a+b*cos(d*x+c))/(a+b))+2*C*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/d/sqrt(a+b*cos(d*x+c))-2*b*(B*b-2*C*a)*sin(d*x+c)/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c)),1],
[(a*b*B-a^2*C+b^2*B*cos(d*x+c)+b^2*C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(7/2),x,8,2/3*(4*B*a*b-5*C*a^2-3*C*b^2)*sqrt(a+b*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2*b/(a+b)))/(a^2-b^2)^2/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/3*(B*b-2*C*a)*sqrt((a+b*cos(d*x+c))/(a+b))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2*b/(a+b)))/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-2/3*b*(B*b-2*C*a)*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)-2/3*b*(4*B*a*b-5*C*a^2-3*C*b^2)*sin(d*x+c)/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,7,2/15*(9*A*b+9*B*a+7*C*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(7*A*a+5*B*b+5*C*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*(7*A*a+5*B*b+5*C*a)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*(9*A*b+9*B*a+7*C*b)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*(B*b+C*a)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/9*b*C*cos(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,6,2/5*(5*A*a+3*B*b+3*C*a)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(7*A*b+7*B*a+5*C*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*(7*A*b+7*B*a+5*C*b)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*(B*b+C*a)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*b*C*cos(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,5,2/5*(5*A*b+5*B*a+3*C*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(b*B+a*(3*A+C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*(B*b+C*a)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*b*C*cos(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,5,2*(b*B-a*(A-C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(3*A*b+3*B*a+C*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2*a*A*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*b*C*sqrt(cos(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,5,-2*(A*b+B*a-C*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(3*b*B+a*(A+3*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*a*A*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2*(A*b+B*a)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,6,-2/5*(3*A*a+5*B*b+5*C*a)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(A*b+B*a+3*C*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/5*a*A*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/3*(A*b+B*a)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*(3*A*a+5*B*b+5*C*a)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,7,-2/5*(3*A*b+3*B*a+5*C*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(5*A*a+7*B*b+7*C*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/7*a*A*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/5*(A*b+B*a)*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/21*(5*A*a+7*B*b+7*C*a)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*(3*A*b+3*B*a+5*C*b)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,8,2/15*(18*A*a*b+9*B*a^2+7*B*b^2+14*C*a*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/231*(110*a*b*B+11*a^2*(7*A+5*C)+5*b^2*(11*A+9*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/231*(110*a*b*B+11*a^2*(7*A+5*C)+5*b^2*(11*A+9*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*(18*A*a*b+9*B*a^2+7*B*b^2+14*C*a*b)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/77*(11*A*b^2+22*B*a*b+4*C*a^2+9*C*b^2)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/99*b*(11*B*b+4*C*a)*cos(d*x+c)^(7/2)*sin(d*x+c)/d+2/11*C*cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,7,2/15*(18*a*b*B+3*a^2*(5*A+3*C)+b^2*(9*A+7*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(14*A*a*b+7*B*a^2+5*B*b^2+10*C*a*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*(14*A*a*b+7*B*a^2+5*B*b^2+10*C*a*b)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*(9*A*b^2+18*B*a*b+4*C*a^2+7*C*b^2)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/63*b*(9*B*b+4*C*a)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/9*C*cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,6,2/5*(10*A*a*b+5*B*a^2+3*B*b^2+6*C*a*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(14*a*b*B+7*a^2*(3*A+C)+b^2*(7*A+5*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*(7*A*b^2+14*B*a*b+4*C*a^2+5*C*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/35*b*(7*B*b+4*C*a)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,6,2/5*(10*a*b*B-5*a^2*(A-C)+b^2*(5*A+3*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(3*a^2*B+b^2*B+2*a*b*(3*A+C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-2/3*b*(6*A*a-B*b-2*C*a)*sqrt(cos(d*x+c))*sin(d*x+c)/d-2/5*b^2*(5*A-C)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2*A*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,6,-2*(a^2*B-b^2*B+2*a*b*(A-C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(6*a*b*B+b^2*(3*A+C)+a^2*(A+3*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*a*(4*A*b+3*B*a)*sin(d*x+c)/d/sqrt(cos(d*x+c))-2/3*b^2*(A-C)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/3*A*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,6,-2/5*(10*a*b*B+5*b^2*(A-C)+a^2*(3*A+5*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(a^2*B+3*b^2*B+2*a*b*(A+3*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/15*a*(4*A*b+5*B*a)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*(4*A*b^2+10*a*b*B+a^2*(3*A+5*C))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/5*A*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,7,-2/5*(6*A*a*b+3*B*a^2+5*B*b^2+10*C*a*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(14*a*b*B+7*b^2*(A+3*C)+a^2*(5*A+7*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/35*a*(4*A*b+7*B*a)*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/21*(4*A*b^2+14*a*b*B+a^2*(5*A+7*C))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*(6*A*a*b+3*B*a^2+5*B*b^2+10*C*a*b)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/7*A*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,8,-2/15*(18*a*b*B+3*b^2*(3*A+5*C)+a^2*(7*A+9*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(10*A*a*b+5*B*a^2+7*B*b^2+14*C*a*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/63*a*(4*A*b+9*B*a)*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/45*(4*A*b^2+18*a*b*B+a^2*(7*A+9*C))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/21*(10*A*a*b+5*B*a^2+7*B*b^2+14*C*a*b)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/15*(18*a*b*B+3*b^2*(3*A+5*C)+a^2*(7*A+9*C))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/9*A*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(9/2),1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,8,2/15*(27*a^2*b*B+7*b^3*B+3*a^3*(5*A+3*C)+3*a*b^2*(9*A+7*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/231*(77*a^3*B+165*a*b^2*B+33*a^2*b*(7*A+5*C)+5*b^3*(11*A+9*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/231*(77*a^3*B+165*a*b^2*B+33*a^2*b*(7*A+5*C)+5*b^3*(11*A+9*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/495*(242*a^2*b*B+77*b^3*B+24*a^3*C+33*a*b^2*(9*A+7*C))*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/693*b*(99*A*b^2+143*B*a*b+24*C*a^2+81*C*b^2)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/99*(11*B*b+6*C*a)*cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+2/11*C*cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^3*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,7,2/15*(15*a^3*B+27*a*b^2*B+9*a^2*b*(5*A+3*C)+b^3*(9*A+7*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(21*a^2*b*B+5*b^3*B+7*a^3*(3*A+C)+3*a*b^2*(7*A+5*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/63*(54*a^2*b*B+15*b^3*B+8*a^3*C+9*a*b^2*(7*A+5*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/315*b*(63*A*b^2+99*B*a*b+24*C*a^2+49*C*b^2)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/21*(3*B*b+2*C*a)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+2/9*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^3*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,7,2/5*(15*a^2*b*B+3*b^3*B-5*a^3*(A-C)+3*a*b^2*(5*A+3*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(21*a^3*B+21*a*b^2*B+21*a^2*b*(3*A+C)+b^3*(7*A+5*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*b*(21*a*b*B-6*a^2*(7*A-3*C)+b^2*(7*A+5*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d-2/35*b^2*(35*A*a-7*B*b-11*C*a)*cos(d*x+c)^(3/2)*sin(d*x+c)/d-2/7*b*(7*A-C)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+2*A*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,7,-2/5*(5*a^3*B-15*a*b^2*B+15*a^2*b*(A-C)-b^3*(5*A+3*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(9*a^2*b*B+b^3*B+3*a*b^2*(3*A+C)+a^3*(A+3*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-2/3*b*(6*a^2*B-b^2*B+3*a*b*(5*A-C))*sqrt(cos(d*x+c))*sin(d*x+c)/d-2/15*b^2*(35*A*b+15*B*a-3*C*b)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2*(2*A*b+B*a)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*A*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,7,-2/5*(15*a^2*b*B-5*b^3*B+15*a*b^2*(A-C)+a^3*(3*A+5*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(a^3*B+9*a*b^2*B+b^3*(3*A+C)+3*a^2*b*(A+3*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/15*a*(24*A*b^2+35*a*b*B+3*a^2*(3*A+5*C))*sin(d*x+c)/d/sqrt(cos(d*x+c))-2/15*b^2*(9*A*b+5*B*a-5*C*b)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/15*(6*A*b+5*B*a)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*A*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,7,-2/5*(3*a^3*B+15*a*b^2*B+5*b^3*(A-C)+3*a^2*b*(3*A+5*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(21*a^2*b*B+21*b^3*B+21*a*b^2*(A+3*C)+a^3*(5*A+7*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/105*a*(24*A*b^2+63*a*b*B+5*a^2*(5*A+7*C))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/35*(24*A*b^3+21*a^3*B+98*a*b^2*B+21*a^2*b*(3*A+5*C))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/35*(6*A*b+7*B*a)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/7*A*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,8,-2/15*(27*a^2*b*B+15*b^3*B+9*a*b^2*(3*A+5*C)+a^3*(7*A+9*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(5*a^3*B+21*a*b^2*B+7*b^3*(A+3*C)+3*a^2*b*(5*A+7*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/315*a*(24*A*b^2+99*a*b*B+7*a^2*(7*A+9*C))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/63*(8*A*b^3+15*a^3*B+54*a*b^2*B+9*a^2*b*(5*A+7*C))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/15*(27*a^2*b*B+15*b^3*B+9*a*b^2*(3*A+5*C)+a^3*(7*A+9*C))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/21*(2*A*b+3*B*a)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/9*A*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(9/2),1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,9,2/195*(468*a^3*b*B+364*a*b^3*B+39*a^4*(5*A+3*C)+78*a^2*b^2*(9*A+7*C)+7*b^4*(13*A+11*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/231*(77*a^4*B+330*a^2*b^2*B+45*b^4*B+44*a^3*b*(7*A+5*C)+20*a*b^3*(11*A+9*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/231*(77*a^4*B+330*a^2*b^2*B+45*b^4*B+44*a^3*b*(7*A+5*C)+20*a*b^3*(11*A+9*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/6435*(3458*a^3*b*B+4004*a*b^3*B+192*a^4*C+77*b^4*(13*A+11*C)+11*a^2*b^2*(637*A+491*C))*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/9009*b*(2171*a^2*b*B+1053*b^3*B+192*a^3*C+2*a*b^2*(1573*A+1259*C))*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/1287*(143*A*b^2+221*B*a*b+48*C*a^2+121*C*b^2)*cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+2/143*(13*B*b+8*C*a)*cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^3*sin(d*x+c)/d+2/13*C*cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^4*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,8,2/15*(15*a^4*B+54*a^2*b^2*B+7*b^4*B+12*a^3*b*(5*A+3*C)+4*a*b^3*(9*A+7*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/231*(308*a^3*b*B+220*a*b^3*B+77*a^4*(3*A+C)+66*a^2*b^2*(7*A+5*C)+5*b^4*(11*A+9*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/693*(682*a^3*b*B+660*a*b^3*B+64*a^4*C+15*b^4*(11*A+9*C)+9*a^2*b^2*(143*A+101*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/3465*b*(1353*a^2*b*B+539*b^3*B+192*a^3*C+2*a*b^2*(891*A+673*C))*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/231*(33*A*b^2+55*B*a*b+16*C*a^2+27*C*b^2)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+2/99*(11*B*b+8*C*a)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^3*sin(d*x+c)/d+2/11*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^4*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,8,2/15*(60*a^3*b*B+36*a*b^3*B-15*a^4*(A-C)+18*a^2*b^2*(5*A+3*C)+b^4*(9*A+7*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(21*a^4*B+42*a^2*b^2*B+5*b^4*B+28*a^3*b*(3*A+C)+4*a*b^3*(7*A+5*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/63*b*(117*a^2*b*B+15*b^3*B-a^3*(126*A-62*C)+12*a*b^2*(7*A+5*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/315*b^2*(162*a*b*B-a^2*(315*A-123*C)+7*b^2*(9*A+7*C))*cos(d*x+c)^(3/2)*sin(d*x+c)/d-2/21*b*(21*A*a-3*B*b-5*C*a)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d-2/9*b*(9*A-C)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^3*sin(d*x+c)/d+2*A*(a+b*cos(d*x+c))^4*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,8,-2/5*(5*a^4*B-30*a^2*b^2*B-3*b^4*B+20*a^3*b*(A-C)-4*a*b^3*(5*A+3*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(84*a^3*b*B+28*a*b^3*B+42*a^2*b^2*(3*A+C)+7*a^4*(A+3*C)+b^4*(7*A+5*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-2/21*b*(42*a^3*B-28*a*b^2*B+3*a^2*b*(49*A-13*C)-b^3*(7*A+5*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d-2/105*b^2*(350*A*a*b+105*B*a^2-21*B*b^2-54*C*a*b)*cos(d*x+c)^(3/2)*sin(d*x+c)/d-2/7*b*(21*A*b+7*B*a-C*b)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+2/3*(8*A*b+3*B*a)*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*A*(a+b*cos(d*x+c))^4*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,8,-2/5*(20*a^3*b*B-20*a*b^3*B+30*a^2*b^2*(A-C)-b^4*(5*A+3*C)+a^4*(3*A+5*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(a^4*B+18*a^2*b^2*B+b^4*B+4*a*b^3*(3*A+C)+4*a^3*b*(A+3*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-2/15*b*(105*a^2*b*B-5*b^3*B+4*a*b^2*(33*A-5*C)+6*a^3*(3*A+5*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d-2/15*b^2*(50*a*b*B+b^2*(59*A-3*C)+3*a^2*(3*A+5*C))*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*(16*A*b^2+15*a*b*B+a^2*(3*A+5*C))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/15*(8*A*b+5*B*a)*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*A*(a+b*cos(d*x+c))^4*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,8,-2/5*(3*a^4*B+30*a^2*b^2*B-5*b^4*B+20*a*b^3*(A-C)+4*a^3*b*(3*A+5*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(28*a^3*b*B+84*a*b^3*B+7*b^4*(3*A+C)+42*a^2*b^2*(A+3*C)+a^4*(5*A+7*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/105*a*(192*A*b^3+63*a^3*B+413*a*b^2*B+a^2*(202*A*b+350*C*b))*sin(d*x+c)/d/sqrt(cos(d*x+c))-2/105*b^2*(98*a*b*B+b^2*(87*A-35*C)+5*a^2*(5*A+7*C))*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/105*(48*A*b^2+77*a*b*B+5*a^2*(5*A+7*C))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/35*(8*A*b+7*B*a)*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/7*A*(a+b*cos(d*x+c))^4*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,8,-2/15*(36*a^3*b*B+60*a*b^3*B+15*b^4*(A-C)+18*a^2*b^2*(3*A+5*C)+a^4*(7*A+9*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(5*a^4*B+42*a^2*b^2*B+21*b^4*B+28*a*b^3*(A+3*C)+4*a^3*b*(5*A+7*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/315*a*(64*A*b^3+75*a^3*B+261*a*b^2*B+a^2*(202*A*b+294*C*b))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/315*(192*A*b^4+756*a^3*b*B+1098*a*b^3*B+21*a^4*(7*A+9*C)+7*a^2*b^2*(155*A+261*C))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/315*(48*A*b^2+117*a*b*B+7*a^2*(7*A+9*C))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/63*(8*A*b+9*B*a)*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/9*A*(a+b*cos(d*x+c))^4*sin(d*x+c)/d/cos(d*x+c)^(9/2),1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(13/2),x,9,-2/15*(7*a^4*B+54*a^2*b^2*B+15*b^4*B+12*a*b^3*(3*A+5*C)+4*a^3*b*(7*A+9*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/231*(220*a^3*b*B+308*a*b^3*B+77*b^4*(A+3*C)+66*a^2*b^2*(5*A+7*C)+5*a^4*(9*A+11*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3465*a*(192*A*b^3+539*a^3*B+1353*a*b^2*B+2*a^2*b*(673*A+891*C))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/693*(64*A*b^4+660*a^3*b*B+682*a*b^3*B+15*a^4*(9*A+11*C)+9*a^2*b^2*(101*A+143*C))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/15*(7*a^4*B+54*a^2*b^2*B+15*b^4*B+12*a*b^3*(3*A+5*C)+4*a^3*b*(7*A+9*C))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/231*(16*A*b^2+55*a*b*B+3*a^2*(9*A+11*C))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/99*(8*A*b+11*B*a)*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/cos(d*x+c)^(9/2)+2/11*A*(a+b*cos(d*x+c))^4*sin(d*x+c)/d/cos(d*x+c)^(11/2),1],
[cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,8,2/5*(5*a^2*b*B+3*b^3*B-5*a^3*C-a*b^2*(5*A+3*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^4/d-2/21*(21*a^3*b*B+7*a*b^3*B-21*a^4*C-7*a^2*b^2*(3*A+C)-b^4*(7*A+5*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^5/d-2*a^3*(A*b^2-a*(B*b-C*a))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b^5/(a+b)/d+2/21*(7*A*b^2-7*B*a*b+7*C*a^2+5*C*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/b^3/d+2/5*(B*b-C*a)*cos(d*x+c)^(3/2)*sin(d*x+c)/b^2/d+2/7*C*cos(d*x+c)^(5/2)*sin(d*x+c)/b/d,1],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,7,2/5*(5*A*b^2-5*B*a*b+5*C*a^2+3*C*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^3/d+2/3*(3*a^2*b*B+b^3*B-3*a^3*C-a*b^2*(3*A+C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^4/d+2*a^2*(A*b^2-a*(B*b-C*a))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b^4/(a+b)/d+2/3*(B*b-C*a)*sqrt(cos(d*x+c))*sin(d*x+c)/b^2/d+2/5*C*cos(d*x+c)^(3/2)*sin(d*x+c)/b/d,1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,6,2*(B*b-C*a)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^2/d+2/3*(b^2*(3*A+C)-3*a*(B*b-C*a))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^3/d-2*a*(A*b^2-a*(B*b-C*a))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b^3/(a+b)/d+2/3*C*sqrt(cos(d*x+c))*sin(d*x+c)/b/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+b*cos(d*x+c)),x,5,2*C*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b/d+2*(B*b-C*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^2/d+2*(A*b^2-a*(B*b-C*a))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b^2/(a+b)/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x,6,-2*A*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d+2*C*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b/d-2*(A*b^2-a*(B*b-C*a))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a/b/(a+b)/d+2*A*sin(d*x+c)/a/d/sqrt(cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x,7,2*(A*b-B*a)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d+2/3*A*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d+2*(A*b^2-a*(B*b-C*a))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^2/(a+b)/d+2/3*A*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)-2*(A*b-B*a)*sin(d*x+c)/a^2/d/sqrt(cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x,8,-2/5*(5*A*b^2-5*a*b*B+a^2*(3*A+5*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d-2/3*(A*b-B*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d-2*b*(A*b^2-a*(B*b-C*a))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^3/(a+b)/d+2/5*A*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)-2/3*(A*b-B*a)*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2)+2/5*(5*A*b^2-5*a*b*B+a^2*(3*A+5*C))*sin(d*x+c)/a^3/d/sqrt(cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/(a+b*cos(d*x+c)),x,9,2/5*(5*A*b^3-3*a^3*B-5*a*b^2*B+a^2*b*(3*A+5*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^4/d+2/21*(7*A*b^2-7*a*b*B+a^2*(5*A+7*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d+2*b^2*(A*b^2-a*(B*b-C*a))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^4/(a+b)/d+2/7*A*sin(d*x+c)/a/d/cos(d*x+c)^(7/2)-2/5*(A*b-B*a)*sin(d*x+c)/a^2/d/cos(d*x+c)^(5/2)+2/21*(7*A*b^2-7*a*b*B+a^2*(5*A+7*C))*sin(d*x+c)/a^3/d/cos(d*x+c)^(3/2)-2/5*(5*A*b^3-3*a^3*B-5*a*b^2*B+a^2*b*(3*A+5*C))*sin(d*x+c)/a^4/d/sqrt(cos(d*x+c)),1],
[cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,8,-1/5*(25*a^3*b*B-20*a*b^3*B-3*a^2*b^2*(5*A-8*C)-35*a^4*C+2*b^4*(5*A+3*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^4/(a^2-b^2)/d+1/3*(15*a^4*b*B-16*a^2*b^3*B-2*b^5*B-a^3*b^2*(9*A-20*C)-21*a^5*C+4*a*b^4*(3*A+C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^5/(a^2-b^2)/d-a^2*(5*A*b^4+5*a^3*b*B-7*a*b^3*B-3*a^2*b^2*(A-3*C)-7*a^4*C)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a-b)/b^5/(a+b)^2/d+1/3*(5*a^2*b*B-2*b^3*B-a*b^2*(3*A-4*C)-7*a^3*C)*sqrt(cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)/d+1/5*(5*A*b^2-5*B*a*b+7*C*a^2-2*C*b^2)*cos(d*x+c)^(3/2)*sin(d*x+c)/b^2/(a^2-b^2)/d-(A*b^2-a*(B*b-C*a))*cos(d*x+c)^(5/2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,7,(3*a^2*b*B-2*b^3*B-a*b^2*(A-4*C)-5*a^3*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^3/(a^2-b^2)/d-1/3*(9*a^3*b*B-12*a*b^3*B-a^2*b^2*(3*A-16*C)-15*a^4*C+2*b^4*(3*A+C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^4/(a^2-b^2)/d+a*(3*A*b^4+3*a^3*b*B-5*a*b^3*B-a^2*b^2*(A-7*C)-5*a^4*C)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a-b)/b^4/(a+b)^2/d+1/3*(3*A*b^2-3*B*a*b+5*C*a^2-2*C*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)/d-(A*b^2-a*(B*b-C*a))*cos(d*x+c)^(3/2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,6,(A*b^2-B*a*b+3*C*a^2-2*C*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^2/(a^2-b^2)/d+(a^2*b*B-2*b^3*B-3*a^3*C+a*b^2*(A+4*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^3/(a^2-b^2)/d-(A*b^4+a^3*b*B-3*a*b^3*B-3*a^4*C+a^2*b^2*(A+5*C))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a-b)/b^3/(a+b)^2/d-(A*b^2-a*(B*b-C*a))*sqrt(cos(d*x+c))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^2,x,6,-(A*b^2-a*(B*b-C*a))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/b/(a^2-b^2)/d-(A*b^2-B*a*b-C*a^2+2*C*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^2/(a^2-b^2)/d-(A*b^4+a^3*b*B+a*b^3*B+a^4*C-3*a^2*b^2*(A+C))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a/(a-b)/b^2/(a+b)^2/d+(A*b^2-a*(B*b-C*a))*sqrt(cos(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x,7,(3*A*b^2-a*b*B-a^2*(2*A-C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/(a^2-b^2)/d+(A*b^2-a*(B*b-C*a))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/b/(a^2-b^2)/d+(3*A*b^4+3*a^3*b*B-a*b^3*B-a^4*C-a^2*b^2*(5*A+C))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^2/(a-b)/b/(a+b)^2/d-(3*A*b^2-a*b*B-a^2*(2*A-C))*sin(d*x+c)/a^2/(a^2-b^2)/d/sqrt(cos(d*x+c))+(A*b^2-a*(B*b-C*a))*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(cos(d*x+c))/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x,8,-(5*A*b^3+2*a^3*B-3*a*b^2*B-a^2*b*(4*A-C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/(a^2-b^2)/d-1/3*(5*A*b^2-3*a*b*B-a^2*(2*A-3*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/(a^2-b^2)/d-(5*A*b^4+5*a^3*b*B-3*a*b^3*B-a^2*b^2*(7*A-C)-3*a^4*C)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^3/(a-b)/(a+b)^2/d-1/3*(5*A*b^2-3*a*b*B-a^2*(2*A-3*C))*sin(d*x+c)/a^2/(a^2-b^2)/d/cos(d*x+c)^(3/2)+(5*A*b^3+2*a^3*B-3*a*b^2*B-a^2*b*(4*A-C))*sin(d*x+c)/a^3/(a^2-b^2)/d/sqrt(cos(d*x+c))+(A*b^2-a*(B*b-C*a))*sin(d*x+c)/a/(a^2-b^2)/d/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^(7/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,9,-1/20*(175*a^5*b*B-325*a^3*b^3*B+120*a*b^5*B+a^2*b^4*(145*A-192*C)-3*a^4*b^2*(25*A-187*C)-315*a^6*C-8*b^6*(5*A+3*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^5/(a^2-b^2)^2/d+1/12*(105*a^6*b*B-223*a^4*b^3*B+128*a^2*b^5*B+8*b^7*B+3*a^3*b^4*(33*A-64*C)-9*a^5*b^2*(5*A-43*C)-189*a^7*C-24*a*b^6*(3*A+C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^6/(a^2-b^2)^2/d+1/4*a^2*(35*A*b^6-35*a^5*b*B+86*a^3*b^3*B-63*a*b^5*B-a^2*b^4*(38*A-99*C)+15*a^4*b^2*(A-10*C)+63*a^6*C)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a-b)^2/b^6/(a+b)^3/d+1/12*(35*a^4*b*B-61*a^2*b^3*B+8*b^5*B+3*a*b^4*(11*A-8*C)-15*a^3*b^2*(A-7*C)-63*a^5*C)*sqrt(cos(d*x+c))*sin(d*x+c)/b^4/(a^2-b^2)^2/d-1/20*(35*a^3*b*B-65*a*b^3*B-a^2*b^2*(15*A-101*C)+b^4*(45*A-8*C)-63*a^4*C)*cos(d*x+c)^(3/2)*sin(d*x+c)/b^3/(a^2-b^2)^2/d-1/2*(A*b^2-a*(B*b-C*a))*cos(d*x+c)^(7/2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/4*(7*A*b^4+5*a^3*b*B-11*a*b^3*B-a^2*b^2*(A-15*C)-9*a^4*C)*cos(d*x+c)^(5/2)*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,8,1/4*(15*a^4*b*B-29*a^2*b^3*B+8*b^5*B-a^3*b^2*(3*A-65*C)+3*a*b^4*(3*A-8*C)-35*a^5*C)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^4/(a^2-b^2)^2/d-1/12*(45*a^5*b*B-99*a^3*b^3*B+72*a*b^5*B-a^4*b^2*(9*A-223*C)+a^2*b^4*(15*A-128*C)-105*a^6*C-8*b^6*(3*A+C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^5/(a^2-b^2)^2/d-1/4*a*(15*A*b^6-15*a^5*b*B+38*a^3*b^3*B-35*a*b^5*B+a^4*b^2*(3*A-86*C)-3*a^2*b^4*(2*A-21*C)+35*a^6*C)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a-b)^2/b^5/(a+b)^3/d-1/12*(15*a^3*b*B-33*a*b^3*B-a^2*b^2*(3*A-61*C)+b^4*(21*A-8*C)-35*a^4*C)*sqrt(cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)^2/d-1/2*(A*b^2-a*(B*b-C*a))*cos(d*x+c)^(5/2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/4*(5*A*b^4+3*a^3*b*B-9*a*b^3*B-7*a^4*C+a^2*b^2*(A+13*C))*cos(d*x+c)^(3/2)*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,7,-1/4*(3*a^3*b*B-9*a*b^3*B+b^4*(5*A-8*C)-15*a^4*C+a^2*b^2*(A+29*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^3/(a^2-b^2)^2/d+1/4*(3*a^4*b*B-5*a^2*b^3*B+8*b^5*B-15*a^5*C-a*b^4*(7*A+24*C)+a^3*b^2*(A+33*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^4/(a^2-b^2)^2/d+1/4*(3*A*b^6-3*a^5*b*B+6*a^3*b^3*B-15*a*b^5*B+15*a^6*C+5*a^2*b^4*(2*A+7*C)-a^4*b^2*(A+38*C))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a-b)^2/b^4/(a+b)^3/d-1/2*(A*b^2-a*(B*b-C*a))*cos(d*x+c)^(3/2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/4*(3*A*b^4+a^3*b*B-7*a*b^3*B-5*a^4*C+a^2*b^2*(3*A+11*C))*sqrt(cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3,x,7,1/4*(A*b^4-a^3*b*B-5*a*b^3*B-3*a^4*C+a^2*b^2*(5*A+9*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/b^2/(a^2-b^2)^2/d+1/4*(a^3*b*B-7*a*b^3*B+a^2*b^2*(3*A-5*C)+3*a^4*C+b^4*(3*A+8*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^3/(a^2-b^2)^2/d+1/4*(A*b^6-a^5*b*B+10*a^3*b^3*B+3*a*b^5*B-3*a^4*b^2*(A-2*C)-3*a^6*C-5*a^2*b^4*(2*A+3*C))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a/(a-b)^2/b^3/(a+b)^3/d-1/2*(A*b^2-a*(B*b-C*a))*sqrt(cos(d*x+c))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/4*(A*b^4-a^3*b*B-5*a*b^3*B-3*a^4*C+a^2*b^2*(5*A+9*C))*sqrt(cos(d*x+c))*sin(d*x+c)/a/b/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^3,x,7,1/4*(3*A*b^4+5*a^3*b*B+a*b^3*B-a^4*C-a^2*b^2*(9*A+5*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/b/(a^2-b^2)^2/d+1/4*(A*b^4+3*a^3*b*B+3*a*b^3*B+a^4*C-7*a^2*b^2*(A+C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/b^2/(a^2-b^2)^2/d+1/4*(3*A*b^6-3*a^5*b*B-10*a^3*b^3*B+a*b^5*B-3*a^2*b^4*(2*A-C)-a^6*C+5*a^4*b^2*(3*A+2*C))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^2/(a-b)^2/b^2/(a+b)^3/d+1/2*(A*b^2-a*(B*b-C*a))*sqrt(cos(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/4*(3*A*b^4+5*a^3*b*B+a*b^3*B-a^4*C-a^2*b^2*(9*A+5*C))*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x,8,-1/4*(15*A*b^4+9*a^3*b*B-3*a*b^3*B+a^4*(8*A-5*C)-a^2*b^2*(29*A+C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/(a^2-b^2)^2/d-1/4*(5*A*b^4+7*a^3*b*B-a*b^3*B-3*a^4*C-a^2*b^2*(11*A+3*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/b/(a^2-b^2)^2/d-1/4*(15*A*b^6-15*a^5*b*B+6*a^3*b^3*B-3*a*b^5*B+3*a^6*C-a^2*b^4*(38*A+C)+5*a^4*b^2*(7*A+2*C))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^3/(a-b)^2/b/(a+b)^3/d+1/4*(15*A*b^4+9*a^3*b*B-3*a*b^3*B+a^4*(8*A-5*C)-a^2*b^2*(29*A+C))*sin(d*x+c)/a^3/(a^2-b^2)^2/d/sqrt(cos(d*x+c))+1/2*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^2-1/4*(5*A*b^4+7*a^3*b*B-a*b^3*B-3*a^4*C-a^2*b^2*(11*A+3*C))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/sqrt(cos(d*x+c))/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x,9,1/4*(35*A*b^5-8*a^5*B+29*a^3*b^2*B-15*a*b^4*B+3*a^4*b*(8*A-3*C)-a^2*b^3*(65*A-3*C))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^4/(a^2-b^2)^2/d+1/12*(35*A*b^4+33*a^3*b*B-15*a*b^3*B+a^4*(8*A-21*C)-a^2*b^2*(61*A-3*C))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/(a^2-b^2)^2/d+1/4*(35*A*b^6-35*a^5*b*B+38*a^3*b^3*B-15*a*b^5*B-a^2*b^4*(86*A-3*C)+3*a^4*b^2*(21*A-2*C)+15*a^6*C)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a^4/(a-b)^2/(a+b)^3/d+1/12*(35*A*b^4+33*a^3*b*B-15*a*b^3*B+a^4*(8*A-21*C)-a^2*b^2*(61*A-3*C))*sin(d*x+c)/a^3/(a^2-b^2)^2/d/cos(d*x+c)^(3/2)-1/4*(35*A*b^5-8*a^5*B+29*a^3*b^2*B-15*a*b^4*B+3*a^4*b*(8*A-3*C)-a^2*b^3*(65*A-3*C))*sin(d*x+c)/a^4/(a^2-b^2)^2/d/sqrt(cos(d*x+c))+1/2*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/a/(a^2-b^2)/d/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2-1/4*(7*A*b^4+9*a^3*b*B-3*a*b^3*B-5*a^4*C-a^2*b^2*(13*A+C))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,8,-1/24*(a-b)*sqrt(a+b)*(8*b^2*(3*A+2*C)+3*a*(2*B*b-C*a))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/d+1/24*sqrt(a+b)*(24*A*b^2+(a+2*b)*(6*B*b-3*C*a+8*C*b))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+1/8*sqrt(a+b)*(2*a^2*b*B-8*b^3*B-a^3*C-4*a*b^2*(2*A+C))*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d+1/24*(8*b^2*(3*A+2*C)+3*a*(2*B*b-C*a))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d/sqrt(cos(d*x+c))+1/4*(2*B*b-C*a)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+1/3*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d,1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,7,-1/4*(a-b)*sqrt(a+b)*(4*B*b+C*a)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d+1/4*sqrt(a+b)*(8*A*b+a*C+2*b*(2*B+C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d-1/4*sqrt(a+b)*(8*A*b^2+4*B*a*b-C*a^2+4*C*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+1/4*(4*B*b+C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(cos(d*x+c))+1/2*C*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,7,(a-b)*sqrt(a+b)*(2*A-C)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d+sqrt(a+b)*(2*A*b-a*(2*A-2*B-C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-sqrt(a+b)*(2*B*b+C*a)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d+2*A*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))-(2*A-C)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,6,2/3*(a-b)*sqrt(a+b)*(A*b+3*B*a)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d-2/3*sqrt(a+b)*(b*(A-3*B)-a*(A-3*B+3*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-2*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d+2/3*A*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,5,-2/15*(a-b)*sqrt(a+b)*(2*A*b^2-5*a*b*B-3*a^2*(3*A+5*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d-2/15*(a-b)*sqrt(a+b)*(2*A*b+a*(9*A-5*B+15*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d+2/5*A*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/15*(A*b+5*B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(3/2),1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,6,2/105*(a-b)*sqrt(a+b)*(8*A*b^3+63*a^3*B-14*a*b^2*B+a^2*b*(19*A+35*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d+2/105*(a-b)*sqrt(a+b)*(8*A*b^2+2*a*b*(3*A-7*B)+a^2*(25*A-63*B+35*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d+2/7*A*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/35*(A*b+7*B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)-2/105*(4*A*b^2-7*a*b*B-5*a^2*(5*A+7*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2),1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,9,-1/192*(a-b)*sqrt(a+b)*(24*a^2*b*B+128*b^3*B-9*a^3*C+12*a*b^2*(20*A+13*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/d-1/192*sqrt(a+b)*(9*a^3*C-6*a^2*b*(4*B+C)-8*b^3*(12*A+16*B+9*C)-4*a*b^2*(60*A+28*B+39*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+1/64*sqrt(a+b)*(8*a^3*b*B-96*a*b^3*B-3*a^4*C-24*a^2*b^2*(2*A+C)-16*b^4*(4*A+3*C))*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d+1/192*(24*a^2*b*B+128*b^3*B-9*a^3*C+12*a*b^2*(20*A+13*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d/sqrt(cos(d*x+c))+1/32*(4*b^2*(4*A+3*C)+a*(8*B*b-3*C*a))*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+1/24*(8*B*b-3*C*a)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d+1/4*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,8,-1/24*(a-b)*sqrt(a+b)*(24*A*b^2+30*B*a*b+3*C*a^2+16*C*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d+1/24*sqrt(a+b)*(3*a^2*C+4*b^2*(6*A+3*B+4*C)+2*a*b*(24*A+15*B+7*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d-1/8*sqrt(a+b)*(6*a^2*b*B+8*b^3*B-a^3*C+12*a*b^2*(2*A+C))*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+1/24*(24*A*b^2+30*B*a*b+3*C*a^2+16*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(cos(d*x+c))+1/4*(2*B*b+C*a)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+1/3*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,8,1/4*(a-b)*sqrt(a+b)*(8*A*a-4*B*b-5*C*a)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-1/4*sqrt(a+b)*(a*(8*A-8*B-5*C)-2*b*(8*A+2*B+C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d-1/4*sqrt(a+b)*(8*A*b^2+12*B*a*b+3*C*a^2+4*C*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d-1/4*(8*A*a-4*B*b-5*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))-1/2*b*(4*A-C)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+2*A*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,8,1/3*(a-b)*sqrt(a+b)*(8*A*b+6*B*a-3*C*b)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d+1/3*sqrt(a+b)*(6*A*b^2+2*a^2*(A-3*B+3*C)-a*b*(8*A-12*B-3*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-sqrt(a+b)*(2*B*b+3*C*a)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d+2*(A*b+B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))-1/3*(8*A*b+6*B*a-3*C*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*A*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,7,2/15*(a-b)*sqrt(a+b)*(3*A*b^2+20*a*b*B+3*a^2*(3*A+5*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d-2/15*sqrt(a+b)*(3*b^2*(A-5*B)-2*a*b*(6*A-10*B+15*C)+a^2*(9*A-5*B+15*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-2*b*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d+2/15*(3*A*b+5*B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*A*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,6,-2/105*(a-b)*sqrt(a+b)*(6*A*b^3-63*a^3*B-21*a*b^2*B-2*a^2*b*(41*A+70*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d-2/105*(a-b)*sqrt(a+b)*(6*A*b^2-a^2*(25*A-63*B+35*C)+3*a*b*(19*A-7*B+35*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d+2/35*(3*A*b+7*B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/105*(3*A*b^2+42*a*b*B+5*a^2*(5*A+7*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)+2/7*A*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,7,2/315*(a-b)*sqrt(a+b)*(8*A*b^4+246*a^3*b*B-18*a*b^3*B+21*a^4*(7*A+9*C)+3*a^2*b^2*(11*A+21*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d+2/315*(a-b)*sqrt(a+b)*(8*A*b^3+6*a*b^2*(A-3*B)+3*a^2*b*(13*A-57*B+21*C)-3*a^3*(49*A-25*B+63*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d+2/21*(A*b+3*B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/315*(3*A*b^2+72*a*b*B+7*a^2*(7*A+9*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)-2/315*(4*A*b^3-75*a^3*B-9*a*b^2*B-2*a^2*b*(44*A+63*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2)+2/9*A*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(9/2),1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,10,-1/1920*(a-b)*sqrt(a+b)*(150*a^3*b*B+2840*a*b^3*B-45*a^4*C+256*b^4*(5*A+4*C)+12*a^2*b^2*(220*A+141*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/d-1/1920*sqrt(a+b)*(45*a^4*C-30*a^3*b*(5*B+C)-16*b^4*(80*A+45*B+64*C)-8*a*b^3*(260*A+355*B+193*C)-4*a^2*b^2*(660*A+295*B+423*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+1/128*sqrt(a+b)*(10*a^4*b*B-240*a^2*b^3*B-96*b^5*B-3*a^5*C-40*a^3*b^2*(2*A+C)-80*a*b^4*(4*A+3*C))*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d+1/1920*(150*a^3*b*B+2840*a*b^3*B-45*a^4*C+256*b^4*(5*A+4*C)+12*a^2*b^2*(220*A+141*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d/sqrt(cos(d*x+c))+1/320*(50*a^2*b*B+120*b^3*B-15*a^3*C+4*a*b^2*(60*A+43*C))*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+1/240*(80*A*b^2+50*B*a*b-15*C*a^2+64*C*b^2)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d+1/40*(10*B*b-3*C*a)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d+1/5*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c)),x,9,-1/192*(a-b)*sqrt(a+b)*(264*a^2*b*B+128*b^3*B+15*a^3*C+4*a*b^2*(108*A+71*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d+1/192*sqrt(a+b)*(15*a^3*C+8*b^3*(12*A+16*B+9*C)+2*a^2*b*(192*A+132*B+59*C)+4*a*b^2*(108*A+52*B+71*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d-1/64*sqrt(a+b)*(40*a^3*b*B+160*a*b^3*B-5*a^4*C+120*a^2*b^2*(2*A+C)+16*b^4*(4*A+3*C))*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+1/192*(264*a^2*b*B+128*b^3*B+15*a^3*C+4*a*b^2*(108*A+71*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(cos(d*x+c))+1/32*(16*A*b^2+24*B*a*b+5*C*a^2+12*C*b^2)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+1/24*(8*B*b+5*C*a)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d+1/4*C*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2),x,9,-1/24*(a-b)*sqrt(a+b)*(54*a*b*B-a^2*(48*A-33*C)+8*b^2*(3*A+2*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-1/24*sqrt(a+b)*(a^2*(48*A-48*B-33*C)-4*b^2*(6*A+3*B+4*C)-2*a*b*(72*A+27*B+13*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d-1/8*sqrt(a+b)*(30*a^2*b*B+8*b^3*B+5*a^3*C+20*a*b^2*(2*A+C))*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d+1/24*(54*a*b*B-a^2*(48*A-33*C)+8*b^2*(3*A+2*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))-1/4*b*(8*A*a-2*B*b-3*C*a)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d-1/3*b*(6*A-C)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2*A*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2),x,9,1/12*(a-b)*sqrt(a+b)*(24*a^2*B-12*b^2*B+a*b*(56*A-27*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-1/12*sqrt(a+b)*(a*b*(56*A-72*B-27*C)-6*b^2*(12*A+2*B+C)-8*a^2*(A-3*B+3*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d-1/4*sqrt(a+b)*(8*A*b^2+20*B*a*b+15*C*a^2+4*C*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d-1/12*(24*a^2*B-12*b^2*B+a*b*(56*A-27*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))-1/2*b*(8*A*b+4*B*a-C*b)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+2/3*(5*A*b+3*B*a)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*A*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2),x,9,1/15*(a-b)*sqrt(a+b)*(70*a*b*B+b^2*(46*A-15*C)+6*a^2*(3*A+5*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d+1/15*sqrt(a+b)*(30*A*b^3-2*a^3*(9*A-5*B+15*C)+2*a^2*b*(17*A-35*B+45*C)-a*b^2*(46*A-90*B-15*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-b*sqrt(a+b)*(2*B*b+5*C*a)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d+2/5*(5*A*b^2+10*a*b*B+a^2*(3*A+5*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))-1/15*(70*a*b*B+b^2*(46*A-15*C)+6*a^2*(3*A+5*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*(A*b+B*a)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*A*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2),x,8,2/105*(a-b)*sqrt(a+b)*(15*A*b^3+63*a^3*B+161*a*b^2*B+5*a^2*b*(29*A+49*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d-2/105*sqrt(a+b)*(15*b^3*(A-7*B)-a^3*(25*A-63*B+35*C)+a^2*b*(145*A-119*B+245*C)-a*b^2*(135*A-161*B+315*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-2*b^2*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d+2/105*(15*A*b^2+56*a*b*B+5*a^2*(5*A+7*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/35*(5*A*b+7*B*a)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/7*A*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(7/2),1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(11/2),x,7,-2/315*(a-b)*sqrt(a+b)*(10*A*b^4-435*a^3*b*B-45*a*b^3*B-21*a^4*(7*A+9*C)-3*a^2*b^2*(93*A+161*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d-2/315*(a-b)*sqrt(a+b)*(10*A*b^3+15*a*b^2*(11*A-3*B+21*C)-6*a^2*b*(19*A-60*B+28*C)+3*a^3*(49*A-25*B+63*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d+2/315*(15*A*b^2+90*a*b*B+7*a^2*(7*A+9*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/315*(5*A*b^3+75*a^3*B+135*a*b^2*B+a^2*b*(163*A+231*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)+2/63*(5*A*b+9*B*a)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/9*A*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d/cos(d*x+c)^(9/2),1],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c)),x,8,-1/24*(a-b)*sqrt(a+b)*(24*A*b^2-18*B*a*b+15*C*a^2+16*C*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^3/d+1/24*sqrt(a+b)*(24*A*b^2-18*B*a*b+12*B*b^2+15*C*a^2-10*C*a*b+16*C*b^2)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d-1/8*sqrt(a+b)*(6*a^2*b*B+8*b^3*B-5*a^3*C-4*a*b^2*(2*A+C))*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^4/d+1/24*(24*A*b^2-18*B*a*b+15*C*a^2+16*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/d/sqrt(cos(d*x+c))+1/12*(6*B*b-5*C*a)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d+1/3*C*cos(d*x+c)^(3/2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d,1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c)),x,7,-1/4*(a-b)*sqrt(a+b)*(4*B*b-3*C*a)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/d-1/4*sqrt(a+b)*(3*a*C-2*b*(2*B+C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d-1/4*sqrt(a+b)*(8*A*b^2-4*B*a*b+3*C*a^2+4*C*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d+1/4*(4*B*b-3*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d/sqrt(cos(d*x+c))+1/2*C*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),x,6,-(a-b)*sqrt(a+b)*C*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d+sqrt(a+b)*(2*A*b+C*a)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d-sqrt(a+b)*(2*B*b-C*a)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/sqrt(a+b*cos(d*x+c)),x,5,2*A*(a-b)*sqrt(a+b)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d-2*sqrt(a+b)*(A-B)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d-2*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/sqrt(a+b*cos(d*x+c)),x,4,-2/3*(a-b)*sqrt(a+b)*(2*A*b-3*B*a)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d+2/3*sqrt(a+b)*(2*A*b+a*(A-3*B+3*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d+2/3*A*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(3/2),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/sqrt(a+b*cos(d*x+c)),x,5,2/15*(a-b)*sqrt(a+b)*(8*A*b^2-10*a*b*B+3*a^2*(3*A+5*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d-2/15*sqrt(a+b)*(8*A*b^2-2*a*b*(A+5*B)+a^2*(9*A-5*B+15*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d+2/5*A*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)-2/15*(4*A*b-5*B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(9/2)/sqrt(a+b*cos(d*x+c)),x,6,-2/105*(a-b)*sqrt(a+b)*(48*A*b^3-63*a^3*B-56*a*b^2*B+a^2*(44*A*b+70*C*b))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^5/d+2/105*sqrt(a+b)*(48*A*b^3-4*a*b^2*(3*A+14*B)+a^3*(25*A-63*B+35*C)+2*a^2*b*(22*A+7*B+35*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d+2/7*A*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(7/2)-2/35*(6*A*b-7*B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^2/d/cos(d*x+c)^(5/2)+2/105*(24*A*b^2-28*a*b*B+5*a^2*(5*A+7*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^3/d/cos(d*x+c)^(3/2),1],
[sqrt(cos(d*x+c))*(a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c)),x,8,-1/4*(a-b)*sqrt(a+b)*(4*A*b+B*a)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d+1/4*sqrt(a+b)*(4*A*b+(a+2*b)*B)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d-1/4*sqrt(a+b)*(4*A*a*b-B*a^2+4*B*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d+1/4*(4*A*b+B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(cos(d*x+c))+1/2*B*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c)+2*b*cos(d*x+c)^2)/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),x,4,-2*(a-b)*sqrt(a+b)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d+4*sqrt(a+b)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d+2*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x,8,-1/4*(12*a^2*b*B-4*b^3*B-a*b^2*(8*A-7*C)-15*a^3*C)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^3/sqrt(a+b)/d-1/4*(8*A*b^2-a*b*(12*B-5*C)+15*a^2*C-2*b^2*(2*B+C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/sqrt(a+b)/d-1/4*sqrt(a+b)*(8*A*b^2-12*B*a*b+15*C*a^2+4*C*b^2)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^4/d-2*(A*b^2-a*(B*b-C*a))*cos(d*x+c)^(3/2)*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+1/4*(12*a^2*b*B-4*b^3*B-a*b^2*(8*A-7*C)-15*a^3*C)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)/d/sqrt(cos(d*x+c))+1/2*(4*A*b^2-4*B*a*b+5*C*a^2-C*b^2)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)/d,1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2),x,7,-(2*A*b^2-2*B*a*b+3*C*a^2-C*b^2)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/sqrt(a+b)/d+(2*A*b^2-a*(b*(2*B-C)-3*a*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/sqrt(a+b)/d-sqrt(a+b)*(2*B*b-3*C*a)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d-2*(A*b^2-a*(B*b-C*a))*sqrt(cos(d*x+c))*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+(2*A*b^2-2*B*a*b+3*C*a^2-C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)/d/sqrt(cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x,6,2*(A*b^2-a*(B*b-C*a))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/b/sqrt(a+b)/d+2*(A*b+B*b-C*a)*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/sqrt(a+b)/d-2*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d-2*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x,4,-2*(2*A*b^2-a*b*B-a^2*(A-C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/sqrt(a+b)/d-2*(2*A*b+a*(A-B-C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/sqrt(a+b)/d+2*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x,5,2/3*(8*A*b^3+3*a^3*B-6*a*b^2*B-a^2*(5*A*b-3*C*b))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/sqrt(a+b)/d+2/3*(8*A*b^2+6*a*b*(A-B)+a^2*(A-3*B+3*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/sqrt(a+b)/d+2*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/a/(a^2-b^2)/d/cos(d*x+c)^(3/2)/sqrt(a+b*cos(d*x+c))-2/3*(4*A*b^2-3*a*b*B-a^2*(A-3*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^2/(a^2-b^2)/d/cos(d*x+c)^(3/2),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x,6,-2/15*(48*A*b^4+25*a^3*b*B-40*a*b^3*B-6*a^2*b^2*(4*A-5*C)-3*a^4*(3*A+5*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^5/sqrt(a+b)/d-2/15*(48*A*b^3+4*a*b^2*(9*A-10*B)+6*a^2*b*(2*A-5*B+5*C)+a^3*(9*A-5*B+15*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/sqrt(a+b)/d+2*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/a/(a^2-b^2)/d/cos(d*x+c)^(5/2)/sqrt(a+b*cos(d*x+c))-2/5*(6*A*b^2-5*a*b*B-a^2*(A-5*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^2/(a^2-b^2)/d/cos(d*x+c)^(5/2)+2/15*(24*A*b^3+5*a^3*B-20*a*b^2*B-a^2*(9*A*b-15*C*b))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^3/(a^2-b^2)/d/cos(d*x+c)^(3/2),1],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,8,1/3*(8*A*b^4+6*B*a^3*b-14*B*a*b^3-15*C*a^4+26*C*a^2*b^2-3*C*b^4)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/(a-b)/b^3/(a+b)^(3/2)/d-1/3*(6*A*b^4-a*b^3*(2*A+12*B-3*C)+a^3*b*(6*B-5*C)-15*a^4*C+a^2*b^2*(2*B+21*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^3/sqrt(a+b)/(a^2-b^2)/d-sqrt(a+b)*(2*B*b-5*C*a)*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^4/d-2/3*(A*b^2-a*(B*b-C*a))*cos(d*x+c)^(3/2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+2/3*(3*A*b^4+2*a^3*b*B-6*a*b^3*B-5*a^4*C+a^2*b^2*(A+9*C))*sqrt(cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c))-1/3*(8*A*b^4+6*B*a^3*b-14*B*a*b^3-15*C*a^4+26*C*a^2*b^2-3*C*b^4)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)^2/d/sqrt(cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2),x,7,-2/3*(A*b^4-4*a*b^3*B-3*a^4*C+a^2*b^2*(3*A+7*C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/b^2/sqrt(a+b)/(a^2-b^2)/d-2/3*(b^3*(A+3*B)+3*a^3*C+a^2*b*C-a*b^2*(3*A+B+6*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/sqrt(a+b)/(a^2-b^2)/d-2*sqrt(a+b)*C*cot(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d-2/3*(A*b^2-a*(B*b-C*a))*sqrt(cos(d*x+c))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+2/3*(A*b^4-4*a*b^3*B-3*a^4*C+a^2*b^2*(3*A+7*C))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x,5,2/3*(6*A*a^2*b-2*A*b^3-3*B*a^3-B*a*b^2+4*C*a^2*b)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/(a-b)/(a+b)^(3/2)/d-2/3*(2*A*b^2-a^2*(3*A+3*B+C)+a*b*(3*A+B+3*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/sqrt(a+b)/(a^2-b^2)/d+2/3*(A*b^2-a*(B*b-C*a))*sqrt(cos(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+2/3*(2*A*b^3+3*a^3*B+a*b^2*B-2*a^2*b*(3*A+2*C))*sin(d*x+c)/a/(a^2-b^2)^2/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x,5,2/3*(8*A*b^4+6*a^3*b*B-2*a*b^3*B+3*a^4*(A-C)-a^2*b^2*(15*A+C))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/sqrt(a+b)/(a^2-b^2)/d+2/3*(8*A*b^3+2*a*b^2*(3*A-B)-3*a^3*(A-B-C)-a^2*b*(9*A+3*B+C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/sqrt(a+b)/(a^2-b^2)/d+2/3*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^(3/2)-2/3*(4*A*b^4+5*a^3*b*B-a*b^3*B-2*a^4*C-2*a^2*b^2*(4*A+C))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x,6,-2/3*(16*A*b^5-3*a^5*B+15*a^3*b^2*B-8*a*b^4*B-2*a^2*b^3*(14*A-C)+a^4*(8*A*b-6*C*b))*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^5/sqrt(a+b)/(a^2-b^2)/d-2/3*(16*A*b^4+4*a*b^3*(3*A-2*B)-3*a^3*b*(3*A-3*B-C)-2*a^2*b^2*(8*A+3*B-C)-a^4*(A-3*B+3*C))*cot(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/sqrt(a+b)/(a^2-b^2)/d+2/3*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/a/(a^2-b^2)/d/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2)+2/3*(10*A*a^2*b^2-6*A*b^4-7*B*a^3*b+3*B*a*b^3+4*C*a^4)*sin(d*x+c)/a^2/(a^2-b^2)^2/d/cos(d*x+c)^(3/2)/sqrt(a+b*cos(d*x+c))+2/3*(8*A*b^4+8*a^3*b*B-4*a*b^3*B+a^4*(A-5*C)-a^2*b^2*(13*A-C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a^3/(a^2-b^2)^2/d/cos(d*x+c)^(3/2),1],
[cos(d*x+c)^m*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,6,(2*a^2*C+b^2*C*(3+m)+A*b^2*(4+m)+2*a*b*B*(4+m))*cos(d*x+c)^(1+m)*sin(d*x+c)/d/(2+m)/(4+m)+b*(2*a*C+b*B*(4+m))*cos(d*x+c)^(2+m)*sin(d*x+c)/d/(3+m)/(4+m)+C*cos(d*x+c)^(1+m)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/(4+m)-(2*a*b*B*(m^2+5*m+4)+a^2*(4+m)*(C*(1+m)+A*(2+m))+b^2*(1+m)*(C*(3+m)+A*(4+m)))*cos(d*x+c)^(1+m)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],cos(d*x+c)^2)*sin(d*x+c)/d/(1+m)/(2+m)/(4+m)/sqrt(sin(d*x+c)^2)-(b^2*B*(2+m)+a^2*B*(3+m)+2*a*b*(C*(2+m)+A*(3+m)))*cos(d*x+c)^(2+m)*hypergeom([1/2, 1+1/2*m],[2+1/2*m],cos(d*x+c)^2)*sin(d*x+c)/d/(2+m)/(3+m)/sqrt(sin(d*x+c)^2),1],
[cos(d*x+c)^m*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2),x,5,(B*b+C*a)*cos(d*x+c)^(1+m)*sin(d*x+c)/d/(2+m)+b*C*cos(d*x+c)^(2+m)*sin(d*x+c)/d/(3+m)-((B*b+C*a)*(1+m)+a*A*(2+m))*cos(d*x+c)^(1+m)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],cos(d*x+c)^2)*sin(d*x+c)/d/(1+m)/(2+m)/sqrt(sin(d*x+c)^2)-(b*C*(2+m)+A*b*(3+m)+a*B*(3+m))*cos(d*x+c)^(2+m)*hypergeom([1/2, 1+1/2*m],[2+1/2*m],cos(d*x+c)^2)*sin(d*x+c)/d/(2+m)/(3+m)/sqrt(sin(d*x+c)^2),1],
[cos(d*x+c)^m*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c)),x,10,a*(A*b^2-a*(B*b-C*a))*AppellF1(1/2,1/2-1/2*m,1,3/2,sin(d*x+c)^2,-b^2*sin(d*x+c)^2/(a^2-b^2))*cos(d*x+c)^(-1+m)*(cos(d*x+c)^2)^(1/2-1/2*m)*sin(d*x+c)/b^2/(a^2-b^2)/d-(A*b^2-a*(B*b-C*a))*AppellF1(1/2,-1/2*m,1,3/2,sin(d*x+c)^2,-b^2*sin(d*x+c)^2/(a^2-b^2))*cos(d*x+c)^m*sin(d*x+c)/b/(a^2-b^2)/d/((cos(d*x+c)^2)^(1/2*m))-(B*b-C*a)*cos(d*x+c)^(1+m)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],cos(d*x+c)^2)*sin(d*x+c)/b^2/d/(1+m)/sqrt(sin(d*x+c)^2)-C*cos(d*x+c)^(2+m)*hypergeom([1/2, 1+1/2*m],[2+1/2*m],cos(d*x+c)^2)*sin(d*x+c)/b/d/(2+m)/sqrt(sin(d*x+c)^2),1],
[cos(d*x+c)^m*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2,x,11,(A*b^4*m+a^3*b*B*m-a*b^3*B*(1+m)-a^4*C*(1+m)+a^2*b^2*(A-A*m+C*(2+m)))*AppellF1(1/2,1/2-1/2*m,1,3/2,sin(d*x+c)^2,-b^2*sin(d*x+c)^2/(a^2-b^2))*cos(d*x+c)^(-1+m)*(cos(d*x+c)^2)^(1/2-1/2*m)*sin(d*x+c)/b^2/(a^2-b^2)^2/d-(A*b^4*m+a^3*b*B*m-a*b^3*B*(1+m)-a^4*C*(1+m)+a^2*b^2*(A-A*m+C*(2+m)))*AppellF1(1/2,-1/2*m,1,3/2,sin(d*x+c)^2,-b^2*sin(d*x+c)^2/(a^2-b^2))*cos(d*x+c)^m*sin(d*x+c)/a/b/(a^2-b^2)^2/d/((cos(d*x+c)^2)^(1/2*m))+(A*b^2-a*(B*b-C*a))*cos(d*x+c)^(1+m)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))+(a*b*B*m-a^2*C*(1+m)+b^2*(-A*m+C))*cos(d*x+c)^(1+m)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],cos(d*x+c)^2)*sin(d*x+c)/b^2/(a^2-b^2)/d/(1+m)/sqrt(sin(d*x+c)^2)+(A*b^2-a*(B*b-C*a))*(1+m)*cos(d*x+c)^(2+m)*hypergeom([1/2, 1+1/2*m],[2+1/2*m],cos(d*x+c)^2)*sin(d*x+c)/a/b/(a^2-b^2)/d/(2+m)/sqrt(sin(d*x+c)^2),1],
[(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,8,-2/5*a*(3*A+5*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*a*(5*A+7*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*a*(3*A+5*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/21*a*(5*A+7*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*a*A*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*a*A*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,7,-2/5*a*(3*A+5*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*a*(A+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*a*(3*A+5*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*a*A*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*a*A*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,6,-2*a*(A-C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*a*(A+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2*a*A*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*a*A*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,6,-2*a*(A-C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*a*(3*A+C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/3*a*C*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*a*A*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,6,2/5*a*(5*A+3*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*a*(3*A+C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*a*C*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/3*a*C*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,7,2/5*a*(5*A+3*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*a*(7*A+5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/7*a*C*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/5*a*C*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/21*a*(7*A+5*C)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,8,2/15*a*(9*A+7*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*a*(7*A+5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/9*a*C*sin(d*x+c)/d/sec(d*x+c)^(7/2)+2/7*a*C*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/45*a*(9*A+7*C)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/21*a*(7*A+5*C)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,10,-16/15*a^2*(2*A+3*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/21*a^2*(5*A+7*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+16/15*a^2*(2*A+3*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+4/21*a^2*(5*A+7*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/105*a^2*(19*A+21*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d+8/63*A*(a^2+a^2*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/9*A*(a+a*cos(d*x+c))^2*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,9,-4/5*a^2*(3*A+5*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+8/21*a^2*(3*A+7*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+4/5*a^2*(3*A+5*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/105*a^2*(33*A+35*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+8/35*A*(a^2+a^2*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*A*(a+a*cos(d*x+c))^2*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,8,-16/5*a^2*A*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/3*a^2*(A+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/15*a^2*(17*A+15*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+8/15*A*(a^2+a^2*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*(a+a*cos(d*x+c))^2*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,8,-4*a^2*(A-C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+8/3*a^2*(A+C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/3*a^2*(5*A-C)*sin(d*x+c)/d/sqrt(sec(d*x+c))+8/3*A*(a^2+a^2*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*(a+a*cos(d*x+c))^2*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,8,16/5*a^2*C*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/3*a^2*(3*A+C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/15*a^2*(15*A-7*C)*sin(d*x+c)/d/sqrt(sec(d*x+c))-2/5*(5*A-C)*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*A*(a+a*cos(d*x+c))^2*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,8,4/5*a^2*(5*A+3*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+8/21*a^2*(7*A+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/105*a^2*(35*A+33*C)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/7*C*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(sec(d*x+c))+8/35*C*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,9,16/15*a^2*(3*A+2*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/21*a^2*(7*A+5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/105*a^2*(21*A+19*C)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/9*C*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(3/2)+8/63*C*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+4/21*a^2*(7*A+5*C)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,10,4/15*a^2*(9*A+7*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+8/231*a^2*(33*A+25*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/693*a^2*(99*A+89*C)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/11*C*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(5/2)+8/99*C*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(5/2)+4/45*a^2*(9*A+7*C)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+8/231*a^2*(33*A+25*C)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x,11,-4/5*a^3*(5*A+7*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/231*a^3*(105*A+143*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+4/5*a^3*(5*A+7*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+4/231*a^3*(105*A+143*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+8/385*a^3*(35*A+44*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/231*(35*A+33*C)*(a^3+a^3*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/d+4/33*A*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^(9/2)*sin(d*x+c)/a/d+2/11*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^(11/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,10,-4/15*a^3*(17*A+27*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/21*a^3*(11*A+21*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+4/15*a^3*(17*A+27*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+8/105*a^3*(16*A+21*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/315*(73*A+63*C)*(a^3+a^3*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+4/21*A*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^(7/2)*sin(d*x+c)/a/d+2/9*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,9,-4/5*a^3*(7*A+5*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/21*a^3*(13*A+35*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+8/105*a^3*(53*A+70*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/15*(7*A+5*C)*(a^3+a^3*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+12/35*A*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d+2/7*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,9,-4/5*a^3*(9*A-5*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/3*a^3*(3*A+5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-4/15*a^3*(21*A+5*C)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/5*(11*A+5*C)*(a^3+a^3*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+4/5*A*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d+2/5*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,9,-4/5*a^3*(5*A-9*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/3*a^3*(5*A+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-8/15*a^3*(10*A-3*C)*sin(d*x+c)/d/sqrt(sec(d*x+c))-2/15*(35*A-3*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+4*A*(a^2+a^2*cos(d*x+c))^2*sqrt(sec(d*x+c))*sin(d*x+c)/a/d+2/3*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,9,4/5*a^3*(5*A+7*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/21*a^3*(35*A+13*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-4/105*a^3*(35*A-41*C)*sin(d*x+c)/d/sqrt(sec(d*x+c))-2/7*(7*A-C)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d/sqrt(sec(d*x+c))-2/35*(35*A-11*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*A*(a+a*cos(d*x+c))^3*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,9,4/15*a^3*(27*A+17*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/21*a^3*(21*A+11*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+8/105*a^3*(21*A+16*C)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/9*C*(a+a*cos(d*x+c))^3*sin(d*x+c)/d/sqrt(sec(d*x+c))+4/21*C*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d/sqrt(sec(d*x+c))+2/315*(63*A+73*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,10,4/5*a^3*(7*A+5*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/231*a^3*(143*A+105*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+8/385*a^3*(44*A+35*C)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/11*C*(a+a*cos(d*x+c))^3*sin(d*x+c)/d/sec(d*x+c)^(3/2)+4/33*C*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d/sec(d*x+c)^(3/2)+2/231*(33*A+35*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+4/231*a^3*(143*A+105*C)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,11,4/195*a^3*(221*A+175*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/231*a^3*(121*A+95*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+40/9009*a^3*(143*A+118*C)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/13*C*(a+a*cos(d*x+c))^3*sin(d*x+c)/d/sec(d*x+c)^(5/2)+12/143*C*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d/sec(d*x+c)^(5/2)+2/1287*(143*A+145*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(5/2)+4/585*a^3*(221*A+175*C)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+4/231*a^3*(121*A+95*C)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c)),x,8,-3/5*(7*A+5*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/d-1/3*(5*A+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d+3/5*(7*A+5*C)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d-1/3*(5*A+3*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d+1/5*(7*A+5*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d-(A+C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x,7,(3*A+C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/d+1/3*(5*A+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d-(3*A+C)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d+1/3*(5*A+3*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d-(A+C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x,6,-(3*A+C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/d-(A-C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d+(3*A+C)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d-(A+C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+a*cos(d*x+c)),x,5,(A+3*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/d+(A-C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d-(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),x,6,-(A+3*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/d+1/3*(3*A+5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d-(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/3*(3*A+5*C)*sin(d*x+c)/a/d/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(3/2),x,7,3/5*(5*A+7*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/d-1/3*(3*A+5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d-(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))/sec(d*x+c)^(5/2)+1/5*(5*A+7*C)*sin(d*x+c)/a/d/sec(d*x+c)^(3/2)-1/3*(3*A+5*C)*sin(d*x+c)/a/d/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(5/2),x,8,-3/5*(5*A+7*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/d+5/21*(7*A+9*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d-(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))/sec(d*x+c)^(7/2)+1/7*(7*A+9*C)*sin(d*x+c)/a/d/sec(d*x+c)^(5/2)-1/5*(5*A+7*C)*sin(d*x+c)/a/d/sec(d*x+c)^(3/2)+5/21*(7*A+9*C)*sin(d*x+c)/a/d/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x,8,(7*A+C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^2/d+2/3*(5*A+C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/d-(7*A+C)*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d+2/3*(5*A+C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d-1/3*(7*A+C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A+C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x,7,-4*A*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^2/d-1/3*(5*A-C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/d+4*A*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d-1/3*(5*A-C)*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A+C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+a*cos(d*x+c))^2,x,6,(A-C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^2/d+2/3*(A+C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/d-(A-C)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))/sqrt(sec(d*x+c))-1/3*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sqrt(sec(d*x+c)),x,6,4*C*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^2/d+1/3*(A-5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/d-1/3*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2)+1/3*(A-5*C)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2),x,7,-(A+7*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^2/d+2/3*(A+5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/d-1/3*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2/sec(d*x+c)^(5/2)-1/3*(A+7*C)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))/sec(d*x+c)^(3/2)+2/3*(A+5*C)*sin(d*x+c)/a^2/d/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(5/2),x,8,4/5*(5*A+14*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^2/d-5/3*(A+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/d-1/3*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2/sec(d*x+c)^(7/2)-(A+3*C)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))/sec(d*x+c)^(5/2)+4/15*(5*A+14*C)*sin(d*x+c)/a^2/d/sec(d*x+c)^(3/2)-5/3*(A+3*C)*sin(d*x+c)/a^2/d/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x,9,1/10*(119*A+9*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/d+1/2*(11*A+C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^3/d-1/10*(119*A+9*C)*sqrt(sec(d*x+c))*sin(d*x+c)/a^3/d+1/2*(11*A+C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^3/d-1/5*(A+C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-2/3*A*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/30*(119*A+9*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x,8,-1/10*(49*A-C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/d-1/6*(13*A-C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^3/d+1/10*(49*A-C)*sqrt(sec(d*x+c))*sin(d*x+c)/a^3/d-1/5*(A+C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-2/15*(4*A-C)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/6*(13*A-C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+a*cos(d*x+c))^3,x,7,1/10*(9*A-C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/d+1/6*(3*A+C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^3/d-1/5*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3/sqrt(sec(d*x+c))-2/15*(3*A-2*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2/sqrt(sec(d*x+c))-1/10*(9*A-C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sqrt(sec(d*x+c)),x,7,1/10*(A-9*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/d+1/6*(A+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^3/d-1/5*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3/sec(d*x+c)^(3/2)+2/15*(2*A-3*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2/sqrt(sec(d*x+c))-1/10*(A-9*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(3/2),x,7,-1/10*(A-49*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/d+1/6*(A-13*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^3/d-1/5*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3/sec(d*x+c)^(5/2)+2/15*(A-4*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2)+1/6*(A-13*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(5/2),x,8,-1/10*(9*A+119*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/d+1/2*(A+11*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^3/d-1/5*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3/sec(d*x+c)^(7/2)-2/3*C*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2/sec(d*x+c)^(5/2)-1/30*(9*A+119*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c))/sec(d*x+c)^(3/2)+1/2*(A+11*C)*sin(d*x+c)/a^3/d/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(7/2),x,9,7/10*(7*A+33*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/d-1/6*(13*A+63*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^3/d-1/5*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3/sec(d*x+c)^(9/2)-2/15*(A+6*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2/sec(d*x+c)^(7/2)-1/10*(13*A+63*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c))/sec(d*x+c)^(5/2)+7/30*(7*A+33*C)*sin(d*x+c)/a^3/d/sec(d*x+c)^(3/2)-1/6*(13*A+63*C)*sin(d*x+c)/a^3/d/sqrt(sec(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,6,16/315*a*(16*A+21*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+8/315*a*(16*A+21*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*a*(16*A+21*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/63*a*A*sec(d*x+c)^(7/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/9*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,5,4/105*a*(24*A+35*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*a*(24*A+35*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/35*a*A*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/7*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,4,2/15*a*(8*A+15*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*a*A*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/5*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,5,2*sqrt(a)*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+2/3*a*A*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/3*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,5,sqrt(a)*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d-a*(2*A-C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))+2*A*sqrt(a+a*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,5,1/4*sqrt(a)*(8*A+3*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+1/4*a*C*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))+1/2*C*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,6,1/8*sqrt(a)*(8*A+5*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+1/12*a*C*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/3*C*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+1/8*a*(8*A+5*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,7,1/64*sqrt(a)*(48*A+35*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+1/24*a*C*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(5/2)+1/4*C*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(5/2)+1/96*a*(48*A+35*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/64*a*(48*A+35*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x,7,16/1155*a^2*(112*A+143*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+8/1155*a^2*(112*A+143*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/385*a^2*(112*A+143*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/231*a^2*(28*A+33*C)*sec(d*x+c)^(7/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/33*a*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(9/2)*sin(d*x+c)/d+2/11*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(11/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,6,4/315*a^2*(136*A+189*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/315*a^2*(136*A+189*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/315*a^2*(52*A+63*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/21*a*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/9*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,5,2/105*a^2*(104*A+175*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*a^2*(4*A+5*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+6/35*a*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,6,2*a^(3/2)*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+2/5*a^2*(4*A+5*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/5*a*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,6,3*a^(3/2)*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d-1/3*a^2*(8*A-3*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))+2*a*A*sqrt(a+a*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,6,1/4*a^(3/2)*(8*A+7*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d-1/4*a^2*(8*A-5*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))-1/2*a*(4*A-C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*A*(a+a*cos(d*x+c))^(3/2)*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,6,1/8*a^(3/2)*(24*A+11*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+1/24*a^2*(24*A+19*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))+1/4*a*C*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/3*C*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,7,1/64*a^(3/2)*(112*A+75*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+1/32*a^2*(16*A+13*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/8*a*C*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+1/4*C*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+1/64*a^2*(112*A+75*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,8,1/128*a^(3/2)*(176*A+133*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+1/240*a^2*(80*A+67*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(5/2)+3/40*a*C*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(5/2)+1/5*C*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+1/192*a^2*(176*A+133*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/128*a^2*(176*A+133*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(15/2),x,8,16/45045*a^3*(8368*A+10439*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+8/45045*a^3*(8368*A+10439*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15015*a^3*(8368*A+10439*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/9009*a^3*(2224*A+2717*C)*sec(d*x+c)^(7/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/1287*a^2*(136*A+143*C)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(9/2)*sin(d*x+c)/d+10/143*a*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(11/2)*sin(d*x+c)/d+2/13*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(13/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x,7,4/693*a^3*(568*A+759*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/693*a^3*(568*A+759*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/693*a^3*(232*A+297*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/231*a^2*(32*A+33*C)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/d+10/99*a*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(9/2)*sin(d*x+c)/d+2/11*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(11/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,6,2/315*a^3*(584*A+903*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*a^3*(8*A+11*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/315*a^2*(64*A+63*C)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+10/63*a*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/9*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,7,2*a^(5/2)*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+2/21*a^3*(32*A+49*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/21*a^2*(8*A+7*C)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*a*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,7,5*a^(5/2)*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d-1/15*a^3*(64*A+15*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))+2/5*a^2*(8*A+5*C)*sqrt(a+a*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*a*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,7,1/4*a^(5/2)*(8*A+19*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d-1/12*a^3*(56*A-27*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))-1/2*a^2*(8*A-C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+10/3*a*A*(a+a*cos(d*x+c))^(3/2)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,7,5/8*a^(5/2)*(8*A+5*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d-1/24*a^3*(24*A-49*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))-1/4*a^2*(8*A-3*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))-1/3*a*(6*A-C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*A*(a+a*cos(d*x+c))^(5/2)*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,7,1/64*a^(5/2)*(304*A+163*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+1/192*a^3*(432*A+299*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))+1/32*a^2*(16*A+17*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+5/24*a*C*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/4*C*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,8,1/128*a^(5/2)*(400*A+283*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+1/960*a^3*(1040*A+787*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/240*a^2*(80*A+79*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+1/8*a*C*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+1/5*C*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+1/128*a^3*(400*A+283*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,9,1/512*a^(5/2)*(1304*A+1015*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+1/192*a^3*(136*A+109*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(5/2)+1/96*a^2*(24*A+23*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(5/2)+1/12*a*C*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+1/6*C*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+1/768*a^3*(1304*A+1015*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/512*a^3*(1304*A+1015*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)/sqrt(a+a*cos(d*x+c)),x,9,-sqrt(2)*(A+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d+2/315*(257*A+273*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-2/315*(29*A+21*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*(19*A+21*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-2/63*A*sec(d*x+c)^(7/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/9*A*sec(d*x+c)^(9/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/sqrt(a+a*cos(d*x+c)),x,8,sqrt(2)*(A+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d-2/105*(43*A+35*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*(31*A+35*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-2/35*A*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/7*A*sec(d*x+c)^(7/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/sqrt(a+a*cos(d*x+c)),x,7,-sqrt(2)*(A+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d+2/15*(13*A+15*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-2/15*A*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/5*A*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c)),x,6,sqrt(2)*(A+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d-2/3*A*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/3*A*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c)),x,7,2*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d-sqrt(2)*(A+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d+2*A*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/sqrt(a+a*cos(d*x+c)),x,7,-C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d+sqrt(2)*(A+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d+C*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),x,8,1/4*(8*A+7*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d-sqrt(2)*(A+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d+1/2*C*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)-1/4*C*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2),x,9,-1/8*(8*A+9*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d+sqrt(2)*(A+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d+1/3*C*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(5/2)-1/12*C*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/8*(8*A+7*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(3/2),x,9,1/2*(19*A+11*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(3/2)/d-1/210*(1201*A+665*C)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))+1/210*(397*A+245*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/70*(67*A+35*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/2*(A+C)*sec(d*x+c)^(7/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/14*(11*A+7*C)*sec(d*x+c)^(7/2)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x,8,-1/2*(15*A+7*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(3/2)/d+1/10*(49*A+25*C)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/10*(13*A+5*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/2*(A+C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/10*(9*A+5*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x,7,1/2*(11*A+3*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(3/2)/d-1/6*(19*A+3*C)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/2*(A+C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/6*(7*A+3*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x,6,-1/2*(7*A-C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(3/2)/d-1/2*(A+C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/2*(5*A+C)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+a*cos(d*x+c))^(3/2),x,7,2*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/a^(3/2)/d+1/2*(3*A-5*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(3/2)/d-1/2*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c)),x,8,-3*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/a^(3/2)/d+1/2*(A+9*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(3/2)/d-1/2*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2)+1/2*(A+3*C)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x,9,1/4*(8*A+19*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/a^(3/2)/d-1/2*(5*A+13*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(3/2)/d-1/2*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(5/2)+1/2*(A+2*C)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)-1/4*(2*A+7*C)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(5/2),x,9,-1/16*(283*A+75*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(5/2)/d+1/240*(2671*A+735*C)*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))-1/240*(787*A+195*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))-1/4*(A+C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(21*A+5*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+1/80*(157*A+45*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x,8,1/16*(163*A+19*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(5/2)/d-1/48*(299*A+27*C)*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))-1/4*(A+C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(17*A+C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+5/48*(19*A+3*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x,7,-5/16*(15*A-C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(5/2)/d-1/4*(A+C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(13*A-3*C)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+1/16*(49*A+C)*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+a*cos(d*x+c))^(5/2),x,6,1/16*(19*A+3*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(5/2)/d-1/4*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)/sqrt(sec(d*x+c))-1/16*(9*A-7*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sqrt(sec(d*x+c)),x,8,2*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/a^(5/2)/d+1/16*(5*A-43*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(5/2)/d-1/4*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2)+1/16*(5*A-11*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x,9,-5*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/a^(5/2)/d+1/16*(3*A+115*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(5/2)/d-1/4*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2)+1/16*(A-15*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2)+1/16*(3*A+35*C)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x,10,1/4*(8*A+39*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/a^(5/2)/d-1/16*(43*A+219*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(5/2)/d-1/4*(A+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(7/2)-1/16*(3*A+19*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(5/2)+1/16*(7*A+31*C)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)-1/16*(11*A+63*C)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,8,-6/5*B*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*C*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+6/5*B*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*C*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*B*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,7,-2*C*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*B*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2*C*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*B*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,6,-2*B*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2*C*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2*B*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,5,2*C*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2*B*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d,1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,6,2*B*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*C*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/3*C*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,7,6/5*C*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*B*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*C*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/3*B*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,8,6/5*B*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+10/21*C*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/7*C*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/5*B*sin(d*x+c)/d/sec(d*x+c)^(3/2)+10/21*C*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,7,-2/5*(3*A+5*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*B*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*(3*A+5*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*B*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,6,-2*B*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*(A+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2*B*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,5,-2*(A-C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2*B*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2*A*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,5,2*B*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*(3*A+C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/3*C*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,6,2/5*(5*A+3*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*B*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*C*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/3*B*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,7,6/5*B*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(7*A+5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/7*C*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/5*B*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/21*(7*A+5*C)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,8,-2/5*a*(3*A+3*B+5*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*a*(5*A+7*B+7*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*a*(3*A+3*B+5*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/21*a*(5*A+7*B+7*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*a*(A+B)*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*a*A*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,7,-2/5*a*(3*A+5*B+5*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*a*(A+B+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*a*(3*A+5*B+5*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*a*(A+B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*a*A*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,6,-2*a*(A+B-C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*a*(A+3*B+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2*a*(A+B)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*a*A*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,6,-2*a*(A-B-C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*a*(3*A+3*B+C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/3*a*C*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*a*A*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,6,2/5*a*(5*A+5*B+3*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*a*(3*A+B+C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*a*C*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/3*a*(B+C)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,7,2/5*a*(5*A+3*B+3*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*a*(7*A+7*B+5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/7*a*C*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/5*a*(B+C)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/21*a*(7*A+7*B+5*C)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,8,2/15*a*(9*A+9*B+7*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*a*(7*A+5*B+5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/9*a*C*sin(d*x+c)/d/sec(d*x+c)^(7/2)+2/7*a*(B+C)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/45*a*(9*A+9*B+7*C)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/21*a*(7*A+5*B+5*C)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,10,-4/15*a^2*(8*A+9*B+12*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/21*a^2*(5*A+6*B+7*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+4/15*a^2*(8*A+9*B+12*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+4/21*a^2*(5*A+6*B+7*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/105*a^2*(19*A+27*B+21*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/63*(4*A+9*B)*(a^2+a^2*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/9*A*(a+a*cos(d*x+c))^2*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,9,-4/5*a^2*(3*A+4*B+5*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/21*a^2*(6*A+7*B+14*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+4/5*a^2*(3*A+4*B+5*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/105*a^2*(33*A+49*B+35*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/35*(4*A+7*B)*(a^2+a^2*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*A*(a+a*cos(d*x+c))^2*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,8,-4/5*a^2*(4*A+5*B)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/3*a^2*(A+2*B+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/15*a^2*(17*A+25*B+15*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/15*(4*A+5*B)*(a^2+a^2*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*(a+a*cos(d*x+c))^2*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,8,-4*a^2*(A-C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/3*a^2*(2*A+3*B+2*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/3*a^2*(5*A+3*B-C)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/3*(4*A+3*B)*(a^2+a^2*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*(a+a*cos(d*x+c))^2*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,8,4/5*a^2*(5*B+4*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/3*a^2*(3*A+2*B+C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/15*a^2*(15*A-5*B-7*C)*sin(d*x+c)/d/sqrt(sec(d*x+c))-2/5*(5*A-C)*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*A*(a+a*cos(d*x+c))^2*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,8,4/5*a^2*(5*A+4*B+3*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/21*a^2*(14*A+7*B+6*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/105*a^2*(35*A+49*B+33*C)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/7*C*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/35*(7*B+4*C)*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,9,4/15*a^2*(12*A+9*B+8*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/21*a^2*(7*A+6*B+5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/105*a^2*(21*A+27*B+19*C)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/9*C*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/63*(9*B+4*C)*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+4/21*a^2*(7*A+6*B+5*C)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,10,4/15*a^2*(9*A+8*B+7*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/231*a^2*(66*A+55*B+50*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/693*a^2*(99*A+121*B+89*C)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/11*C*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/99*(11*B+4*C)*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(5/2)+4/45*a^2*(9*A+8*B+7*C)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+4/231*a^2*(66*A+55*B+50*C)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x,11,-4/15*a^3*(15*A+17*B+21*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/231*a^3*(105*A+121*B+143*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+4/15*a^3*(15*A+17*B+21*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+4/231*a^3*(105*A+121*B+143*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+4/1155*a^3*(210*A+253*B+264*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/693*(105*A+143*B+99*C)*(a^3+a^3*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/99*(6*A+11*B)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^(9/2)*sin(d*x+c)/a/d+2/11*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^(11/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,10,-4/15*a^3*(17*A+21*B+27*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/21*a^3*(11*A+13*B+21*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+4/15*a^3*(17*A+21*B+27*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+4/105*a^3*(32*A+41*B+42*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/315*(73*A+99*B+63*C)*(a^3+a^3*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/21*(2*A+3*B)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^(7/2)*sin(d*x+c)/a/d+2/9*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,9,-4/5*a^3*(7*A+9*B+5*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/21*a^3*(13*A+21*B+35*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+4/105*a^3*(106*A+147*B+140*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/15*(7*A+9*B+5*C)*(a^3+a^3*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/35*(6*A+7*B)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d+2/7*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,9,-4/5*a^3*(9*A+5*B-5*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/3*a^3*(3*A+5*B+5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-4/15*a^3*(21*A+20*B+5*C)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/15*(33*A+35*B+15*C)*(a^3+a^3*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/15*(6*A+5*B)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d+2/5*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,9,-4/5*a^3*(5*A-5*B-9*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/3*a^3*(5*A+5*B+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-4/15*a^3*(20*A+5*B-6*C)*sin(d*x+c)/d/sqrt(sec(d*x+c))-2/15*(35*A+15*B-3*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*(2*A+B)*(a^2+a^2*cos(d*x+c))^2*sqrt(sec(d*x+c))*sin(d*x+c)/a/d+2/3*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,9,4/5*a^3*(5*A+9*B+7*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/21*a^3*(35*A+21*B+13*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-4/105*a^3*(35*A-42*B-41*C)*sin(d*x+c)/d/sqrt(sec(d*x+c))-2/7*(7*A-C)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d/sqrt(sec(d*x+c))-2/35*(35*A-7*B-11*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*A*(a+a*cos(d*x+c))^3*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,9,4/15*a^3*(27*A+21*B+17*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/21*a^3*(21*A+13*B+11*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+4/105*a^3*(42*A+41*B+32*C)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/9*C*(a+a*cos(d*x+c))^3*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/21*(3*B+2*C)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d/sqrt(sec(d*x+c))+2/315*(63*A+99*B+73*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,10,4/15*a^3*(21*A+17*B+15*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/231*a^3*(143*A+121*B+105*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+4/1155*a^3*(264*A+253*B+210*C)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/11*C*(a+a*cos(d*x+c))^3*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/99*(11*B+6*C)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d/sec(d*x+c)^(3/2)+2/693*(99*A+143*B+105*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+4/231*a^3*(143*A+121*B+105*C)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,11,4/195*a^3*(221*A+195*B+175*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/231*a^3*(121*A+105*B+95*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+20/9009*a^3*(286*A+273*B+236*C)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/13*C*(a+a*cos(d*x+c))^3*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/143*(13*B+6*C)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/a/d/sec(d*x+c)^(5/2)+2/1287*(143*A+195*B+145*C)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(5/2)+4/585*a^3*(221*A+195*B+175*C)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+4/231*a^3*(121*A+105*B+95*C)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c)),x,8,-3/5*(7*A-5*B+5*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/d-1/3*(5*A-5*B+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d+3/5*(7*A-5*B+5*C)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d-1/3*(5*A-5*B+3*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d+1/5*(7*A-5*B+5*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d-(A-B+C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x,7,(3*A-3*B+C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/d+1/3*(5*A-3*B+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d-(3*A-3*B+C)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d+1/3*(5*A-3*B+3*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d-(A-B+C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x,6,-(3*A-B+C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/d-(A-B-C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d+(3*A-B+C)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d-(A-B+C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+a*cos(d*x+c)),x,5,(A-B+3*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/d+(A+B-C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d-(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),x,6,-(A-3*B+3*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/d+1/3*(3*A-3*B+5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d-(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/3*(3*A-3*B+5*C)*sin(d*x+c)/a/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(3/2),x,7,3/5*(5*A-5*B+7*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/d-1/3*(3*A-5*B+5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d-(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))/sec(d*x+c)^(5/2)+1/5*(5*A-5*B+7*C)*sin(d*x+c)/a/d/sec(d*x+c)^(3/2)-1/3*(3*A-5*B+5*C)*sin(d*x+c)/a/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))/sec(d*x+c)^(5/2),x,8,-3/5*(5*A-7*B+7*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/d+5/21*(7*A-7*B+9*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d-(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))/sec(d*x+c)^(7/2)+1/7*(7*A-7*B+9*C)*sin(d*x+c)/a/d/sec(d*x+c)^(5/2)-1/5*(5*A-7*B+7*C)*sin(d*x+c)/a/d/sec(d*x+c)^(3/2)+5/21*(7*A-7*B+9*C)*sin(d*x+c)/a/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x,8,(7*A-4*B+C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^2/d+1/3*(10*A-5*B+2*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/d-(7*A-4*B+C)*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d+1/3*(10*A-5*B+2*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d-1/3*(7*A-4*B+C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A-B+C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x,7,-(4*A-B)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^2/d-1/3*(5*A-2*B-C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/d+(4*A-B)*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d-1/3*(5*A-2*B-C)*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A-B+C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+a*cos(d*x+c))^2,x,6,(A-C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^2/d+1/3*(2*A+B+2*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/d-(A-C)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))/sqrt(sec(d*x+c))-1/3*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sqrt(sec(d*x+c)),x,6,-(B-4*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^2/d+1/3*(A+2*B-5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/d-1/3*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2)+1/3*(A+2*B-5*C)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2),x,7,-(A-4*B+7*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^2/d+1/3*(2*A-5*B+10*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/d-1/3*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2/sec(d*x+c)^(5/2)-1/3*(A-4*B+7*C)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))/sec(d*x+c)^(3/2)+1/3*(2*A-5*B+10*C)*sin(d*x+c)/a^2/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^2/sec(d*x+c)^(5/2),x,8,1/5*(20*A-35*B+56*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^2/d-5/3*(A-2*B+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/d-1/3*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2/sec(d*x+c)^(7/2)-(A-2*B+3*C)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))/sec(d*x+c)^(5/2)+1/15*(20*A-35*B+56*C)*sin(d*x+c)/a^2/d/sec(d*x+c)^(3/2)-5/3*(A-2*B+3*C)*sin(d*x+c)/a^2/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x,9,1/10*(119*A-49*B+9*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/d+1/6*(33*A-13*B+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^3/d-1/10*(119*A-49*B+9*C)*sqrt(sec(d*x+c))*sin(d*x+c)/a^3/d+1/6*(33*A-13*B+3*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^3/d-1/5*(A-B+C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-1/3*(2*A-B)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/30*(119*A-49*B+9*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x,8,-1/10*(49*A-9*B-C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/d-1/6*(13*A-3*B-C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^3/d+1/10*(49*A-9*B-C)*sqrt(sec(d*x+c))*sin(d*x+c)/a^3/d-1/5*(A-B+C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(8*A-3*B-2*C)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/6*(13*A-3*B-C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+a*cos(d*x+c))^3,x,7,1/10*(9*A+B-C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/d+1/6*(3*A+B+C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^3/d-1/5*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3/sqrt(sec(d*x+c))-1/15*(6*A-B-4*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2/sqrt(sec(d*x+c))-1/10*(9*A+B-C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sqrt(sec(d*x+c)),x,7,1/10*(A-B-9*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/d+1/6*(A+B+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^3/d-1/5*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3/sec(d*x+c)^(3/2)+1/15*(4*A+B-6*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2/sqrt(sec(d*x+c))-1/10*(A-B-9*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(3/2),x,7,-1/10*(A+9*B-49*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/d+1/6*(A+3*B-13*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^3/d-1/5*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3/sec(d*x+c)^(5/2)+1/15*(2*A+3*B-8*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2)+1/6*(A+3*B-13*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(5/2),x,8,-1/10*(9*A-49*B+119*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/d+1/6*(3*A-13*B+33*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^3/d-1/5*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3/sec(d*x+c)^(7/2)+1/3*(B-2*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2/sec(d*x+c)^(5/2)-1/30*(9*A-49*B+119*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c))/sec(d*x+c)^(3/2)+1/6*(3*A-13*B+33*C)*sin(d*x+c)/a^3/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^3/sec(d*x+c)^(7/2),x,9,7/10*(7*A-17*B+33*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/d-1/6*(13*A-33*B+63*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^3/d-1/5*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3/sec(d*x+c)^(9/2)-1/15*(2*A-7*B+12*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2/sec(d*x+c)^(7/2)-1/10*(13*A-33*B+63*C)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c))/sec(d*x+c)^(5/2)+7/30*(7*A-17*B+33*C)*sin(d*x+c)/a^3/d/sec(d*x+c)^(3/2)-1/6*(13*A-33*B+63*C)*sin(d*x+c)/a^3/d/sqrt(sec(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,6,16/315*a*(16*A+18*B+21*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+8/315*a*(16*A+18*B+21*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*a*(16*A+18*B+21*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/63*a*(A+9*B)*sec(d*x+c)^(7/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/9*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,5,4/105*a*(24*A+28*B+35*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*a*(24*A+28*B+35*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/35*a*(A+7*B)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/7*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,4,2/15*a*(8*A+10*B+15*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*a*(A+5*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/5*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,5,2*sqrt(a)*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+2/3*a*(A+3*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/3*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,5,sqrt(a)*(2*B+C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d-a*(2*A-C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))+2*A*sqrt(a+a*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,5,1/4*sqrt(a)*(8*A+4*B+3*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+1/4*a*(4*B+C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))+1/2*C*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,6,1/8*sqrt(a)*(8*A+6*B+5*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+1/12*a*(6*B+C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/3*C*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+1/8*a*(8*A+6*B+5*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,7,1/64*sqrt(a)*(48*A+40*B+35*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+1/24*a*(8*B+C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(5/2)+1/4*C*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(5/2)+1/96*a*(48*A+40*B+35*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/64*a*(48*A+40*B+35*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x,7,16/3465*a^2*(336*A+374*B+429*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+8/3465*a^2*(336*A+374*B+429*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/1155*a^2*(336*A+374*B+429*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/693*a^2*(84*A+110*B+99*C)*sec(d*x+c)^(7/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/99*a*(3*A+11*B)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(9/2)*sin(d*x+c)/d+2/11*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(11/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,6,4/315*a^2*(136*A+156*B+189*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/315*a^2*(136*A+156*B+189*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/315*a^2*(52*A+72*B+63*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/21*a*(A+3*B)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/9*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,5,2/105*a^2*(104*A+126*B+175*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*a^2*(4*A+6*B+5*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/35*a*(3*A+7*B)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,6,2*a^(3/2)*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+2/15*a^2*(12*A+20*B+15*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*a*(3*A+5*B)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,6,a^(3/2)*(2*B+3*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d-1/3*a^2*(8*A+6*B-3*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))+2*a*(A+B)*sqrt(a+a*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,6,1/4*a^(3/2)*(8*A+12*B+7*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d-1/4*a^2*(8*A-4*B-5*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))-1/2*a*(4*A-C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*A*(a+a*cos(d*x+c))^(3/2)*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,6,1/8*a^(3/2)*(24*A+14*B+11*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+1/24*a^2*(24*A+30*B+19*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))+1/4*a*(2*B+C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/3*C*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,7,1/64*a^(3/2)*(112*A+88*B+75*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+1/96*a^2*(48*A+56*B+39*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/24*a*(8*B+3*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+1/4*C*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+1/64*a^2*(112*A+88*B+75*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,8,1/128*a^(3/2)*(176*A+150*B+133*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+1/240*a^2*(80*A+90*B+67*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(5/2)+1/40*a*(10*B+3*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(5/2)+1/5*C*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+1/192*a^2*(176*A+150*B+133*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/128*a^2*(176*A+150*B+133*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(15/2),x,8,16/45045*a^3*(8368*A+9230*B+10439*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+8/45045*a^3*(8368*A+9230*B+10439*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15015*a^3*(8368*A+9230*B+10439*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/9009*a^3*(2224*A+2522*B+2717*C)*sec(d*x+c)^(7/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/1287*a^2*(136*A+182*B+143*C)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(9/2)*sin(d*x+c)/d+2/143*a*(5*A+13*B)*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(11/2)*sin(d*x+c)/d+2/13*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(13/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x,7,4/3465*a^3*(2840*A+3212*B+3795*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/3465*a^3*(2840*A+3212*B+3795*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/3465*a^3*(1160*A+1364*B+1485*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/231*a^2*(32*A+44*B+33*C)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/99*a*(5*A+11*B)*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(9/2)*sin(d*x+c)/d+2/11*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(11/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,6,2/315*a^3*(584*A+690*B+903*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*a^3*(8*A+10*B+11*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/315*a^2*(64*A+90*B+63*C)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/63*a*(5*A+9*B)*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/9*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,7,2*a^(5/2)*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+2/105*a^3*(160*A+224*B+245*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*a^2*(40*A+56*B+35*C)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/35*a*(5*A+7*B)*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,7,a^(5/2)*(2*B+5*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d-1/15*a^3*(64*A+70*B+15*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))+2/5*a^2*(8*A+10*B+5*C)*sqrt(a+a*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*a*(A+B)*(a+a*cos(d*x+c))^(3/2)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,7,1/4*a^(5/2)*(8*A+20*B+19*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d-1/12*a^3*(56*A+12*B-27*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))-1/2*a^2*(8*A+4*B-C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/3*a*(5*A+3*B)*(a+a*cos(d*x+c))^(3/2)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*(a+a*cos(d*x+c))^(5/2)*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,7,1/8*a^(5/2)*(40*A+38*B+25*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d-1/24*a^3*(24*A-54*B-49*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))-1/4*a^2*(8*A-2*B-3*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))-1/3*a*(6*A-C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*A*(a+a*cos(d*x+c))^(5/2)*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,7,1/64*a^(5/2)*(304*A+200*B+163*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+1/192*a^3*(432*A+392*B+299*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))+1/32*a^2*(16*A+24*B+17*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/24*a*(8*B+5*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/4*C*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,8,1/128*a^(5/2)*(400*A+326*B+283*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+1/960*a^3*(1040*A+950*B+787*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/240*a^2*(80*A+110*B+79*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+1/8*a*(2*B+C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+1/5*C*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+1/128*a^3*(400*A+326*B+283*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,9,1/512*a^(5/2)*(1304*A+1132*B+1015*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/d+1/960*a^3*(680*A+628*B+545*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(5/2)+1/480*a^2*(120*A+156*B+115*C)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(5/2)+1/60*a*(12*B+5*C)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+1/6*C*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+1/768*a^3*(1304*A+1132*B+1015*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/512*a^3*(1304*A+1132*B+1015*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2)/sqrt(a+a*cos(d*x+c)),x,9,-sqrt(2)*(A-B+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d+2/315*(257*A-129*B+273*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-2/315*(29*A-93*B+21*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*(19*A-3*B+21*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-2/63*(A-9*B)*sec(d*x+c)^(7/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/9*A*sec(d*x+c)^(9/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/sqrt(a+a*cos(d*x+c)),x,8,sqrt(2)*(A-B+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d-2/105*(43*A-91*B+35*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*(31*A-7*B+35*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-2/35*(A-7*B)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/7*A*sec(d*x+c)^(7/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/sqrt(a+a*cos(d*x+c)),x,7,-sqrt(2)*(A-B+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d+2/15*(13*A-5*B+15*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-2/15*(A-5*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/5*A*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c)),x,6,sqrt(2)*(A-B+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d-2/3*(A-3*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/3*A*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c)),x,7,2*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d-sqrt(2)*(A-B+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d+2*A*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/sqrt(a+a*cos(d*x+c)),x,7,(2*B-C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d+sqrt(2)*(A-B+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d+C*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),x,8,1/4*(8*A-4*B+7*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d-sqrt(2)*(A-B+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d+1/2*C*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/4*(4*B-C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2),x,9,-1/8*(8*A-14*B+9*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d+sqrt(2)*(A-B+C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d+1/3*C*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(5/2)+1/12*(6*B-C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/8*(8*A-2*B+7*C)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)^2)*sqrt(sec(d*x+c))/sqrt(a+a*cos(d*x+c)),x,7,(2*A*b+2*B*a-B*b)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d+sqrt(2)*(a-b)*(A-B)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a)/d+b*B*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(3/2),x,9,1/2*(19*A-15*B+11*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(3/2)/d-1/210*(1201*A-1029*B+665*C)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))+1/210*(397*A-273*B+245*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/70*(67*A-63*B+35*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/2*(A-B+C)*sec(d*x+c)^(7/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/14*(11*A-7*B+7*C)*sec(d*x+c)^(7/2)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x,8,-1/2*(15*A-11*B+7*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(3/2)/d+1/30*(147*A-95*B+75*C)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/30*(39*A-35*B+15*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/2*(A-B+C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/10*(9*A-5*B+5*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x,7,1/2*(11*A-7*B+3*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(3/2)/d-1/6*(19*A-15*B+3*C)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/2*(A-B+C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/6*(7*A-3*B+3*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x,6,-1/2*(7*A-3*B-C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(3/2)/d-1/2*(A-B+C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/2*(5*A-B+C)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+a*cos(d*x+c))^(3/2),x,7,2*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/a^(3/2)/d+1/2*(3*A+B-5*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(3/2)/d-1/2*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c)),x,8,(2*B-3*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/a^(3/2)/d+1/2*(A-5*B+9*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(3/2)/d-1/2*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2)+1/2*(A-B+3*C)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x,9,1/4*(8*A-12*B+19*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/a^(3/2)/d-1/2*(5*A-9*B+13*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(3/2)/d-1/2*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(5/2)+1/2*(A-B+2*C)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)-1/4*(2*A-6*B+7*C)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(5/2),x,9,-1/16*(283*A-163*B+75*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(5/2)/d+1/240*(2671*A-1495*B+735*C)*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))-1/240*(787*A-475*B+195*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))-1/4*(A-B+C)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(21*A-13*B+5*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+1/80*(157*A-85*B+45*C)*sec(d*x+c)^(5/2)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x,8,1/16*(163*A-75*B+19*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(5/2)/d-1/48*(299*A-147*B+27*C)*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))-1/4*(A-B+C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(17*A-9*B+C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+1/48*(95*A-39*B+15*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x,7,-1/16*(75*A-19*B-5*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(5/2)/d-1/4*(A-B+C)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(13*A-5*B-3*C)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+1/16*(49*A-9*B+C)*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+a*cos(d*x+c))^(5/2),x,6,1/16*(19*A+5*B+3*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(5/2)/d-1/4*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)/sqrt(sec(d*x+c))-1/16*(9*A-B-7*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sqrt(sec(d*x+c)),x,8,2*C*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/a^(5/2)/d+1/16*(5*A+3*B-43*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(5/2)/d-1/4*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2)+1/16*(5*A+3*B-11*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x,9,(2*B-5*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/a^(5/2)/d+1/16*(3*A-43*B+115*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(5/2)/d-1/4*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2)+1/16*(A+7*B-15*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2)+1/16*(3*A-11*B+35*C)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x,10,1/4*(8*A-20*B+39*C)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/a^(5/2)/d-1/16*(43*A-115*B+219*C)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))*sqrt(cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(2)/a^(5/2)/d-1/4*(A-B+C)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(7/2)-1/16*(3*A-11*B+19*C)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(5/2)+1/16*(7*A-15*B+31*C)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)-1/16*(11*A-35*B+63*C)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,8,-2/5*b*(3*A+5*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*a*(5*A+7*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*b*(3*A+5*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/21*a*(5*A+7*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*b*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*a*A*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,7,-2/5*a*(3*A+5*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*b*(A+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*a*(3*A+5*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*b*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*a*A*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,6,-2*b*(A-C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*a*(A+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2*A*b*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*a*A*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,6,-2*a*(A-C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*b*(3*A+C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/3*b*C*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*a*A*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,6,2/5*b*(5*A+3*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*a*(3*A+C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*b*C*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/3*a*C*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,7,2/5*a*(5*A+3*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*b*(7*A+5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/7*b*C*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/5*a*C*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/21*b*(7*A+5*C)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,8,2/15*b*(9*A+7*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*a*(7*A+5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/9*b*C*sin(d*x+c)/d/sec(d*x+c)^(7/2)+2/7*a*C*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/45*b*(9*A+7*C)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/21*a*(7*A+5*C)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,9,-2/15*(3*b^2*(3*A+5*C)+a^2*(7*A+9*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/21*a*b*(5*A+7*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/15*(3*b^2*(3*A+5*C)+a^2*(7*A+9*C))*sqrt(sec(d*x+c))*sin(d*x+c)/d+4/21*a*b*(5*A+7*C)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/45*(4*A*b^2+a^2*(7*A+9*C))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+8/63*a*A*b*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/9*A*(a+b*cos(d*x+c))^2*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,8,-4/5*a*b*(3*A+5*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(7*b^2*(A+3*C)+a^2*(5*A+7*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+4/5*a*b*(3*A+5*C)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/21*(4*A*b^2+a^2*(5*A+7*C))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+8/35*a*A*b*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*A*(a+b*cos(d*x+c))^2*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,7,-2/5*(5*b^2*(A-C)+a^2*(3*A+5*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/3*a*b*(A+3*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*(4*A*b^2+a^2*(3*A+5*C))*sqrt(sec(d*x+c))*sin(d*x+c)/d+8/15*a*A*b*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*(a+b*cos(d*x+c))^2*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,7,-4*a*b*(A-C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*(b^2*(3*A+C)+a^2*(A+3*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/3*b^2*(A-C)*sin(d*x+c)/d/sqrt(sec(d*x+c))+8/3*a*A*b*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*(a+b*cos(d*x+c))^2*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,7,-2/5*(5*a^2*(A-C)-b^2*(5*A+3*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/3*a*b*(3*A+C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/5*b^2*(5*A-C)*sin(d*x+c)/d/sec(d*x+c)^(3/2)-4/3*a*b*(3*A-C)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*A*(a+b*cos(d*x+c))^2*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,7,4/5*a*b*(5*A+3*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(7*a^2*(3*A+C)+b^2*(7*A+5*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+8/35*a*b*C*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/21*(4*a^2*C+b^2*(7*A+5*C))*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/7*C*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,8,2/15*(3*a^2*(5*A+3*C)+b^2*(9*A+7*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+4/21*a*b*(7*A+5*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+8/63*a*b*C*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/45*(4*a^2*C+b^2*(9*A+7*C))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/9*C*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(3/2)+4/21*a*b*(7*A+5*C)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))^2*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,9,4/15*a*b*(9*A+7*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/231*(11*a^2*(7*A+5*C)+5*b^2*(11*A+9*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+8/99*a*b*C*sin(d*x+c)/d/sec(d*x+c)^(7/2)+2/77*(4*a^2*C+b^2*(11*A+9*C))*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/11*C*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(5/2)+4/45*a*b*(9*A+7*C)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/231*(11*a^2*(7*A+5*C)+5*b^2*(11*A+9*C))*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,9,-2/15*a*(9*b^2*(3*A+5*C)+a^2*(7*A+9*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*b*(7*b^2*(A+3*C)+3*a^2*(5*A+7*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/15*a*(9*b^2*(3*A+5*C)+a^2*(7*A+9*C))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/63*b*(8*A*b^2+9*a^2*(5*A+7*C))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/315*a*(24*A*b^2+7*a^2*(7*A+9*C))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+4/21*A*b*(a+b*cos(d*x+c))^2*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/9*A*(a+b*cos(d*x+c))^3*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,8,-2/5*b*(5*b^2*(A-C)+3*a^2*(3*A+5*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*a*(21*b^2*(A+3*C)+a^2*(5*A+7*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+6/35*b*(8*A*b^2+7*a^2*(3*A+5*C))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/105*a*(24*A*b^2+5*a^2*(5*A+7*C))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+12/35*A*b*(a+b*cos(d*x+c))^2*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*A*(a+b*cos(d*x+c))^3*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,8,-2/5*a*(15*b^2*(A-C)+a^2*(3*A+5*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*b*(b^2*(3*A+C)+3*a^2*(A+3*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/15*b^3*(9*A-5*C)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/5*a*(8*A*b^2+a^2*(3*A+5*C))*sqrt(sec(d*x+c))*sin(d*x+c)/d+4/5*A*b*(a+b*cos(d*x+c))^2*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*(a+b*cos(d*x+c))^3*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,8,-2/5*b*(15*a^2*(A-C)-b^2*(5*A+3*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*a*(3*b^2*(3*A+C)+a^2*(A+3*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/15*b^3*(35*A-3*C)*sin(d*x+c)/d/sec(d*x+c)^(3/2)-2*a*b^2*(5*A-C)*sin(d*x+c)/d/sqrt(sec(d*x+c))+4*A*b*(a+b*cos(d*x+c))^2*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*(a+b*cos(d*x+c))^3*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,8,-2/5*a*(5*a^2*(A-C)-3*b^2*(5*A+3*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*b*(21*a^2*(3*A+C)+b^2*(7*A+5*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/35*a*b^2*(35*A-11*C)*sin(d*x+c)/d/sec(d*x+c)^(3/2)-2/21*b*(6*a^2*(7*A-3*C)-b^2*(7*A+5*C))*sin(d*x+c)/d/sqrt(sec(d*x+c))-2/7*b*(7*A-C)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*A*(a+b*cos(d*x+c))^3*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,8,2/15*b*(9*a^2*(5*A+3*C)+b^2*(9*A+7*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*a*(7*a^2*(3*A+C)+3*b^2*(7*A+5*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/315*b*(24*a^2*C+7*b^2*(9*A+7*C))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/63*a*(63*A*b^2+8*C*a^2+45*C*b^2)*sin(d*x+c)/d/sqrt(sec(d*x+c))+4/21*a*C*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/9*C*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,9,2/5*a*(a^2*(5*A+3*C)+b^2*(9*A+7*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/231*b*(33*a^2*(7*A+5*C)+5*b^2*(11*A+9*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/231*b*(8*a^2*C+3*b^2*(11*A+9*C))*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/165*a*(99*A*b^2+8*C*a^2+77*C*b^2)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+4/33*a*C*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/11*C*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/231*b*(33*a^2*(7*A+5*C)+5*b^2*(11*A+9*C))*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))^3*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,10,2/195*b*(39*a^2*(9*A+7*C)+7*b^2*(13*A+11*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/231*a*(11*a^2*(7*A+5*C)+15*b^2*(11*A+9*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/1287*b*(24*a^2*C+11*b^2*(13*A+11*C))*sin(d*x+c)/d/sec(d*x+c)^(7/2)+6/1001*a*(143*A*b^2+8*C*a^2+117*C*b^2)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+12/143*a*C*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/13*C*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/585*b*(39*a^2*(9*A+7*C)+7*b^2*(13*A+11*C))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/231*a*(11*a^2*(7*A+5*C)+15*b^2*(11*A+9*C))*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x,10,-8/15*a*b*(3*b^2*(3*A+5*C)+a^2*(7*A+9*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/231*(77*b^4*(A+3*C)+66*a^2*b^2*(5*A+7*C)+5*a^4*(9*A+11*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+8/15*a*b*(3*b^2*(3*A+5*C)+a^2*(7*A+9*C))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/693*(64*A*b^4+15*a^4*(9*A+11*C)+9*a^2*b^2*(101*A+143*C))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+4/3465*a*b*(96*A*b^2+a^2*(673*A+891*C))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/231*(16*A*b^2+3*a^2*(9*A+11*C))*(a+b*cos(d*x+c))^2*sec(d*x+c)^(7/2)*sin(d*x+c)/d+16/99*A*b*(a+b*cos(d*x+c))^3*sec(d*x+c)^(9/2)*sin(d*x+c)/d+2/11*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^(11/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,9,-2/15*(15*b^4*(A-C)+18*a^2*b^2*(3*A+5*C)+a^4*(7*A+9*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+8/21*a*b*(7*b^2*(A+3*C)+a^2*(5*A+7*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/315*(192*A*b^4+21*a^4*(7*A+9*C)+7*a^2*b^2*(155*A+261*C))*sqrt(sec(d*x+c))*sin(d*x+c)/d+4/315*a*b*(32*A*b^2+a^2*(101*A+147*C))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/315*(48*A*b^2+7*a^2*(7*A+9*C))*(a+b*cos(d*x+c))^2*sec(d*x+c)^(5/2)*sin(d*x+c)/d+16/63*A*b*(a+b*cos(d*x+c))^3*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/9*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,9,-8/5*a*b*(5*b^2*(A-C)+a^2*(3*A+5*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(7*b^4*(3*A+C)+42*a^2*b^2*(A+3*C)+a^4*(5*A+7*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/105*b^2*(b^2*(87*A-35*C)+5*a^2*(5*A+7*C))*sin(d*x+c)/d/sqrt(sec(d*x+c))+4/105*a*b*(96*A*b^2+a^2*(101*A+175*C))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/105*(48*A*b^2+5*a^2*(5*A+7*C))*(a+b*cos(d*x+c))^2*sec(d*x+c)^(3/2)*sin(d*x+c)/d+16/35*A*b*(a+b*cos(d*x+c))^3*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,9,-2/5*(30*a^2*b^2*(A-C)-b^4*(5*A+3*C)+a^4*(3*A+5*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+8/3*a*b*(b^2*(3*A+C)+a^2*(A+3*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/15*b^2*(b^2*(59*A-3*C)+3*a^2*(3*A+5*C))*sin(d*x+c)/d/sec(d*x+c)^(3/2)-4/15*a*b*(2*b^2*(33*A-5*C)+3*a^2*(3*A+5*C))*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/5*(16*A*b^2+a^2*(3*A+5*C))*(a+b*cos(d*x+c))^2*sqrt(sec(d*x+c))*sin(d*x+c)/d+16/15*A*b*(a+b*cos(d*x+c))^3*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,9,-8/5*a*b*(5*a^2*(A-C)-b^2*(5*A+3*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(42*a^2*b^2*(3*A+C)+7*a^4*(A+3*C)+b^4*(7*A+5*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-4/105*a*b^3*(175*A-27*C)*sin(d*x+c)/d/sec(d*x+c)^(3/2)-2/21*b^2*(3*a^2*(49*A-13*C)-b^2*(7*A+5*C))*sin(d*x+c)/d/sqrt(sec(d*x+c))-2/7*b^2*(21*A-C)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(sec(d*x+c))+16/3*A*b*(a+b*cos(d*x+c))^3*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,9,-2/15*(15*a^4*(A-C)-18*a^2*b^2*(5*A+3*C)-b^4*(9*A+7*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+8/21*a*b*(7*a^2*(3*A+C)+b^2*(7*A+5*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/315*b^2*(3*a^2*(105*A-41*C)-7*b^2*(9*A+7*C))*sin(d*x+c)/d/sec(d*x+c)^(3/2)-4/63*a*b*(a^2*(63*A-31*C)-6*b^2*(7*A+5*C))*sin(d*x+c)/d/sqrt(sec(d*x+c))-2/21*a*b*(21*A-5*C)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(sec(d*x+c))-2/9*b*(9*A-C)*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*A*(a+b*cos(d*x+c))^4*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,9,8/15*a*b*(3*a^2*(5*A+3*C)+b^2*(9*A+7*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/231*(77*a^4*(3*A+C)+66*a^2*b^2*(7*A+5*C)+5*b^4*(11*A+9*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+4/3465*a*b*(891*A*b^2+96*C*a^2+673*C*b^2)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/693*(64*a^4*C+15*b^4*(11*A+9*C)+9*a^2*b^2*(143*A+101*C))*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/231*(16*a^2*C+3*b^2*(11*A+9*C))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(sec(d*x+c))+16/99*a*C*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/11*C*(a+b*cos(d*x+c))^4*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))^4*(A+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,10,2/195*(39*a^4*(5*A+3*C)+78*a^2*b^2*(9*A+7*C)+7*b^4*(13*A+11*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+8/231*a*b*(11*a^2*(7*A+5*C)+5*b^2*(11*A+9*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+4/9009*a*b*(1573*A*b^2+96*C*a^2+1259*C*b^2)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/6435*(192*a^4*C+77*b^4*(13*A+11*C)+11*a^2*b^2*(637*A+491*C))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/1287*(48*a^2*C+11*b^2*(13*A+11*C))*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(3/2)+16/143*a*C*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/13*C*(a+b*cos(d*x+c))^4*sin(d*x+c)/d/sec(d*x+c)^(3/2)+8/231*a*b*(11*a^2*(7*A+5*C)+5*b^2*(11*A+9*C))*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x,9,-2/5*(5*A*b^2+a^2*(3*A+5*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/d-2/3*A*b*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/d-2*b*(A*b^2+C*a^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a^3/(a+b)/d+2/5*(5*A*b^2+a^2*(3*A+5*C))*sqrt(sec(d*x+c))*sin(d*x+c)/a^3/d-2/3*A*b*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d+2/5*A*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x,8,2*A*b*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^2/d+2/3*A*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d+2*(A*b^2+C*a^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a^2/(a+b)/d-2*A*b*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d+2/3*A*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x,7,-2*A*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/d+2*C*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b/d-2*(A*b^2+C*a^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a/b/(a+b)/d+2*A*sqrt(sec(d*x+c))*sin(d*x+c)/a/d,1],
[(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+b*cos(d*x+c)),x,6,2*C*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b/d-2*a*C*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^2/d+2*(A*b^2+C*a^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/b^2/(a+b)/d,1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sqrt(sec(d*x+c)),x,7,-2*a*C*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b^2/d+2/3*(3*a^2*C+b^2*(3*A+C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^3/d-2*a*(A*b^2+C*a^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/b^3/(a+b)/d+2/3*C*sin(d*x+c)/b/d/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2),x,8,2/5*(5*a^2*C+b^2*(5*A+3*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b^3/d-2/3*a*(3*A*b^2+(3*a^2+b^2)*C)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^4/d+2*a^2*(A*b^2+C*a^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/b^4/(a+b)/d+2/5*C*sin(d*x+c)/b/d/sec(d*x+c)^(3/2)-2/3*a*C*sin(d*x+c)/b^2/d/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(5/2),x,9,-2/5*a*(5*A*b^2+5*C*a^2+3*C*b^2)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b^4/d+2/21*(21*a^4*C+7*a^2*b^2*(3*A+C)+b^4*(7*A+5*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^5/d-2*a^3*(A*b^2+C*a^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/b^5/(a+b)/d+2/7*C*sin(d*x+c)/b/d/sec(d*x+c)^(5/2)-2/5*a*C*sin(d*x+c)/b^2/d/sec(d*x+c)^(3/2)+2/21*(7*a^2*C+b^2*(7*A+5*C))*sin(d*x+c)/b^3/d/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x,9,-b*(5*A*b^2-a^2*(4*A-C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/(a^2-b^2)/d-1/3*(5*A*b^2-a^2*(2*A-3*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/(a^2-b^2)/d-(5*A*b^4-a^2*b^2*(7*A-C)-3*a^4*C)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a^3/(a-b)/(a+b)^2/d+b*(5*A*b^2-a^2*(4*A-C))*sqrt(sec(d*x+c))*sin(d*x+c)/a^3/(a^2-b^2)/d-1/3*(5*A*b^2-a^2*(2*A-3*C))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/(a^2-b^2)/d+(A*b^2+C*a^2)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x,8,(3*A*b^2-a^2*(2*A-C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^2/(a^2-b^2)/d+(A*b^2+C*a^2)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/b/(a^2-b^2)/d+(3*A*b^4-a^4*C-a^2*b^2*(5*A+C))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a^2/(a-b)/b/(a+b)^2/d-(3*A*b^2-a^2*(2*A-C))*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/(a^2-b^2)/d+(A*b^2+C*a^2)*sqrt(sec(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+b*cos(d*x+c))^2,x,7,-(A*b^2+C*a^2)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/b/(a^2-b^2)/d-(A*b^2-C*a^2+2*C*b^2)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^2/(a^2-b^2)/d-(A*b^4+a^4*C-3*a^2*b^2*(A+C))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a/(a-b)/b^2/(a+b)^2/d+(A*b^2+C*a^2)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sqrt(sec(d*x+c)),x,7,(A*b^2+3*C*a^2-2*C*b^2)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b^2/(a^2-b^2)/d+a*(A*b^2-3*C*a^2+4*C*b^2)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^3/(a^2-b^2)/d-(A*b^4-3*a^4*C+a^2*b^2*(A+5*C))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/(a-b)/b^3/(a+b)^2/d-(A*b^2+C*a^2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(3/2),x,8,-a*(A*b^2+5*C*a^2-4*C*b^2)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b^3/(a^2-b^2)/d+1/3*(a^2*b^2*(3*A-16*C)+15*a^4*C-2*b^4*(3*A+C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^4/(a^2-b^2)/d+a*(3*A*b^4-a^2*b^2*(A-7*C)-5*a^4*C)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/(a-b)/b^4/(a+b)^2/d-(A*b^2+C*a^2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2)+1/3*(3*A*b^2+5*C*a^2-2*C*b^2)*sin(d*x+c)/b^2/(a^2-b^2)/d/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(5/2),x,9,1/5*(3*a^2*b^2*(5*A-8*C)+35*a^4*C-2*b^4*(5*A+3*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b^4/(a^2-b^2)/d-1/3*a*(a^2*b^2*(9*A-20*C)+21*a^4*C-4*b^4*(3*A+C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^5/(a^2-b^2)/d-a^2*(5*A*b^4-3*a^2*b^2*(A-3*C)-7*a^4*C)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/(a-b)/b^5/(a+b)^2/d-(A*b^2+C*a^2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))/sec(d*x+c)^(5/2)+1/5*(5*A*b^2+7*C*a^2-2*C*b^2)*sin(d*x+c)/b^2/(a^2-b^2)/d/sec(d*x+c)^(3/2)-1/3*a*(3*A*b^2+7*C*a^2-4*C*b^2)*sin(d*x+c)/b^3/(a^2-b^2)/d/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x,10,1/4*b*(35*A*b^4+3*a^4*(8*A-3*C)-a^2*b^2*(65*A-3*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^4/(a^2-b^2)^2/d+1/12*(35*A*b^4+a^4*(8*A-21*C)-a^2*b^2*(61*A-3*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^3/(a^2-b^2)^2/d+1/4*(35*A*b^6-a^2*b^4*(86*A-3*C)+3*a^4*b^2*(21*A-2*C)+15*a^6*C)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a^4/(a-b)^2/(a+b)^3/d-1/4*b*(35*A*b^4+3*a^4*(8*A-3*C)-a^2*b^2*(65*A-3*C))*sqrt(sec(d*x+c))*sin(d*x+c)/a^4/(a^2-b^2)^2/d+1/12*(35*A*b^4+a^4*(8*A-21*C)-a^2*b^2*(61*A-3*C))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^3/(a^2-b^2)^2/d+1/2*(A*b^2+C*a^2)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/4*(7*A*b^4-5*a^4*C-a^2*b^2*(13*A+C))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x,9,-1/4*(15*A*b^4+a^4*(8*A-5*C)-a^2*b^2*(29*A+C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/(a^2-b^2)^2/d-1/4*(5*A*b^4-3*a^4*C-a^2*b^2*(11*A+3*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/b/(a^2-b^2)^2/d-1/4*(15*A*b^6+3*a^6*C-a^2*b^4*(38*A+C)+5*a^4*b^2*(7*A+2*C))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a^3/(a-b)^2/b/(a+b)^3/d+1/4*(15*A*b^4+a^4*(8*A-5*C)-a^2*b^2*(29*A+C))*sqrt(sec(d*x+c))*sin(d*x+c)/a^3/(a^2-b^2)^2/d+1/2*(A*b^2+C*a^2)*sqrt(sec(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/4*(5*A*b^4-3*a^4*C-a^2*b^2*(11*A+3*C))*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+b*cos(d*x+c))^3,x,8,1/4*(3*A*b^4-a^4*C-a^2*b^2*(9*A+5*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^2/b/(a^2-b^2)^2/d+1/4*(A*b^4+a^4*C-7*a^2*b^2*(A+C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/b^2/(a^2-b^2)^2/d+1/4*(3*A*b^6-3*a^2*b^4*(2*A-C)-a^6*C+5*a^4*b^2*(3*A+2*C))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a^2/(a-b)^2/b^2/(a+b)^3/d+1/2*(A*b^2+C*a^2)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2/sqrt(sec(d*x+c))-1/4*(3*A*b^4-a^4*C-a^2*b^2*(9*A+5*C))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sqrt(sec(d*x+c)),x,8,1/4*(A*b^4-3*a^4*C+a^2*b^2*(5*A+9*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/b^2/(a^2-b^2)^2/d+1/4*(a^2*b^2*(3*A-5*C)+3*a^4*C+b^4*(3*A+8*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^3/(a^2-b^2)^2/d+1/4*(A*b^6-3*a^4*b^2*(A-2*C)-3*a^6*C-5*a^2*b^4*(2*A+3*C))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a/(a-b)^2/b^3/(a+b)^3/d-1/2*(A*b^2+C*a^2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2/sqrt(sec(d*x+c))-1/4*(A*b^4-3*a^4*C+a^2*b^2*(5*A+9*C))*sin(d*x+c)/a/b/(a^2-b^2)^2/d/(a+b*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(3/2),x,8,-1/4*(b^4*(5*A-8*C)-15*a^4*C+a^2*b^2*(A+29*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b^3/(a^2-b^2)^2/d-1/4*a*(15*a^4*C+b^4*(7*A+24*C)-a^2*b^2*(A+33*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^4/(a^2-b^2)^2/d+1/4*(3*A*b^6+15*a^6*C+5*a^2*b^4*(2*A+7*C)-a^4*b^2*(A+38*C))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/(a-b)^2/b^4/(a+b)^3/d-1/2*(A*b^2+C*a^2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2/sec(d*x+c)^(3/2)+1/4*(3*A*b^4-5*a^4*C+a^2*b^2*(3*A+11*C))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(5/2),x,9,-1/4*a*(a^2*b^2*(3*A-65*C)-3*b^4*(3*A-8*C)+35*a^4*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b^4/(a^2-b^2)^2/d+1/12*(a^4*b^2*(9*A-223*C)-a^2*b^4*(15*A-128*C)+105*a^6*C+8*b^6*(3*A+C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^5/(a^2-b^2)^2/d-1/4*a*(15*A*b^6+a^4*b^2*(3*A-86*C)-3*a^2*b^4*(2*A-21*C)+35*a^6*C)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/(a-b)^2/b^5/(a+b)^3/d-1/2*(A*b^2+C*a^2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2/sec(d*x+c)^(5/2)+1/4*(5*A*b^4-7*a^4*C+a^2*b^2*(A+13*C))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2)+1/12*(a^2*b^2*(3*A-61*C)-b^4*(21*A-8*C)+35*a^4*C)*sin(d*x+c)/b^3/(a^2-b^2)^2/d/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(7/2),x,10,-1/20*(a^2*b^4*(145*A-192*C)-3*a^4*b^2*(25*A-187*C)-315*a^6*C-8*b^6*(5*A+3*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b^5/(a^2-b^2)^2/d+1/4*a*(a^2*b^4*(33*A-64*C)-3*a^4*b^2*(5*A-43*C)-63*a^6*C-8*b^6*(3*A+C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^6/(a^2-b^2)^2/d+1/4*a^2*(35*A*b^6-a^2*b^4*(38*A-99*C)+15*a^4*b^2*(A-10*C)+63*a^6*C)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/(a-b)^2/b^6/(a+b)^3/d-1/2*(A*b^2+C*a^2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2/sec(d*x+c)^(7/2)+1/4*(7*A*b^4-a^2*b^2*(A-15*C)-9*a^4*C)*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))/sec(d*x+c)^(5/2)+1/20*(a^2*b^2*(15*A-101*C)-b^4*(45*A-8*C)+63*a^4*C)*sin(d*x+c)/b^3/(a^2-b^2)^2/d/sec(d*x+c)^(3/2)+1/4*a*(b^4*(11*A-8*C)-5*a^2*b^2*(A-7*C)-21*a^4*C)*sin(d*x+c)/b^4/(a^2-b^2)^2/d/sqrt(sec(d*x+c)),1],
[sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,8,-2/315*(a-b)*sqrt(a+b)*(16*A*b^4+6*a^2*b^2*(4*A+7*C)-21*a^4*(7*A+9*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^5/d/sqrt(sec(d*x+c))-2/315*(a-b)*sqrt(a+b)*(12*a*A*b^2+16*A*b^3+6*a^2*b*(6*A+7*C)+21*a^3*(7*A+9*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d/sqrt(sec(d*x+c))+2/315*b*(8*A*b^2+a^2*(13*A+21*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^3/d-2/315*(6*A*b^2-7*a^2*(7*A+9*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/a^2/d+2/63*A*b*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/a/d+2/9*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,7,2/105*(a-b)*b*sqrt(a+b)*(8*A*b^2+a^2*(19*A+35*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d/sqrt(sec(d*x+c))+2/105*(a-b)*sqrt(a+b)*(6*a*A*b+8*A*b^2+5*a^2*(5*A+7*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d/sqrt(sec(d*x+c))-2/105*(4*A*b^2-5*a^2*(5*A+7*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d+2/35*A*b*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d+2/7*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,6,-2/15*(a-b)*sqrt(a+b)*(2*A*b^2-3*a^2*(3*A+5*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d/sqrt(sec(d*x+c))-2/15*(a-b)*sqrt(a+b)*(9*A*a+2*A*b+15*C*a)*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d/sqrt(sec(d*x+c))+2/15*A*b*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d+2/5*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,7,2/3*A*(a-b)*b*sqrt(a+b)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d/sqrt(sec(d*x+c))-2/3*sqrt(a+b)*(A*b-a*(A+3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-2*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))+2/3*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,8,(a-b)*sqrt(a+b)*(2*A-C)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-sqrt(a+b)*(2*A*a-2*A*b-C*a)*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-a*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d/sqrt(sec(d*x+c))+2*A*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d-(2*A-C)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,8,-1/4*(a-b)*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d/sqrt(sec(d*x+c))+1/4*sqrt(a+b)*(8*A*b+(a+2*b)*C)*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d/sqrt(sec(d*x+c))+1/4*sqrt(a+b)*(a^2*C-4*b^2*(2*A+C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))+1/2*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/4*a*C*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b/d,1],
[sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,9,1/24*(a-b)*sqrt(a+b)*(3*a^2*C-8*b^2*(3*A+2*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/d/sqrt(sec(d*x+c))-1/24*sqrt(a+b)*(3*a^2*C-2*a*b*C-8*b^2*(3*A+2*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))-1/8*a*sqrt(a+b)*(8*A*b^2+(a^2+4*b^2)*C)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d/sqrt(sec(d*x+c))-1/4*a*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/3*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d/sqrt(sec(d*x+c))-1/24*(3*a^2*C-8*b^2*(3*A+2*C))*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b^2/d,1],
[sqrt(a+b*cos(d*x+c))*(A+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,10,-1/192*(a-b)*sqrt(a+b)*(48*A*b^2+15*C*a^2+28*C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d/sqrt(sec(d*x+c))+1/192*sqrt(a+b)*(15*a^3*C-10*a^2*b*C+24*b^3*(4*A+3*C)+4*a*b^2*(12*A+7*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d/sqrt(sec(d*x+c))+1/64*sqrt(a+b)*(5*a^4*C+8*a^2*b^2*(2*A+C)-16*b^4*(4*A+3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^4/d/sqrt(sec(d*x+c))+1/4*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d/sec(d*x+c)^(3/2)+1/32*(5*a^2*C+4*b^2*(4*A+3*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d/sqrt(sec(d*x+c))-5/24*a*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^2/d/sqrt(sec(d*x+c))+1/192*a*(48*A*b^2+15*C*a^2+28*C*b^2)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b^3/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,8,2/315*(a-b)*sqrt(a+b)*(8*A*b^4+21*a^4*(7*A+9*C)+3*a^2*b^2*(11*A+21*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d/sqrt(sec(d*x+c))+2/315*(a-b)*sqrt(a+b)*(6*a*A*b^2+8*A*b^3-21*a^3*(7*A+9*C)+a^2*(39*A*b+63*C*b))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d/sqrt(sec(d*x+c))-4/315*b*(2*A*b^2-a^2*(44*A+63*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d+2/315*(3*A*b^2+7*a^2*(7*A+9*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d+2/21*A*b*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/9*A*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,7,-4/105*(a-b)*b*sqrt(a+b)*(3*A*b^2-a^2*(41*A+70*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d/sqrt(sec(d*x+c))+2/105*(a-b)*sqrt(a+b)*(25*A*a^2-57*A*a*b-6*A*b^2+35*C*a^2-105*C*a*b)*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d/sqrt(sec(d*x+c))+2/105*(3*A*b^2+5*a^2*(5*A+7*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d+6/35*A*b*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*A*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,8,2/5*(a-b)*sqrt(a+b)*(A*b^2+a^2*(3*A+5*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d/sqrt(sec(d*x+c))-2/5*sqrt(a+b)*(A*b^2-2*a*b*(2*A+5*C)+a^2*(3*A+5*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-2*b*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))+2/5*A*b*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,9,1/3*(a-b)*b*sqrt(a+b)*(8*A-3*C)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))+1/3*sqrt(a+b)*(6*A*b^2+2*a^2*(A+3*C)-a*(8*A*b-3*C*b))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-3*a*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))+2*A*b*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d-1/3*b*(8*A-3*C)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,9,1/4*(a-b)*sqrt(a+b)*(8*A-5*C)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))-1/4*sqrt(a+b)*(8*A*a-16*A*b-5*C*a-2*C*b)*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))-1/4*sqrt(a+b)*(8*A*b^2+3*C*a^2+4*C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d/sqrt(sec(d*x+c))-1/2*b*(4*A-C)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))-1/4*a*(8*A-5*C)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2*A*(a+b*cos(d*x+c))^(3/2)*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,9,-1/24*(a-b)*sqrt(a+b)*(3*a^2*C+8*b^2*(3*A+2*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d/sqrt(sec(d*x+c))+1/24*sqrt(a+b)*(48*A*a*b+24*A*b^2+3*C*a^2+14*C*a*b+16*C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d/sqrt(sec(d*x+c))-1/8*a*sqrt(a+b)*(24*A*b^2-C*a^2+12*C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))+1/4*a*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/3*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/24*(3*a^2*C+8*b^2*(3*A+2*C))*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,10,-1/64*(a-b)*sqrt(a+b)*(80*A*b^2-3*C*a^2+52*C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))-1/64*sqrt(a+b)*(3*a^3*C-2*a^2*b*C-8*b^3*(4*A+3*C)-4*a*b^2*(20*A+13*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))-1/64*sqrt(a+b)*(3*a^4*C+24*a^2*b^2*(2*A+C)+16*b^4*(4*A+3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d/sqrt(sec(d*x+c))-1/32*(3*a^2*C-4*b^2*(4*A+3*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(sec(d*x+c))-1/8*a*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/4*C*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/64*a*(80*A*b^2-3*C*a^2+52*C*b^2)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b^2/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x,9,2/693*(a-b)*b*sqrt(a+b)*(8*A*b^4+3*a^2*b^2*(17*A+33*C)+a^4*(741*A+957*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d/sqrt(sec(d*x+c))+2/693*(a-b)*sqrt(a+b)*(6*a*A*b^3+8*A*b^4+15*a^4*(9*A+11*C)+3*a^2*b^2*(19*A+33*C)-6*a^3*b*(101*A+132*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d/sqrt(sec(d*x+c))-2/693*(4*A*b^4-15*a^4*(9*A+11*C)-a^2*b^2*(205*A+297*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d+2/693*b*(3*A*b^2+a^2*(229*A+297*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d+2/231*(5*A*b^2+3*a^2*(9*A+11*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/d+10/99*A*b*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(9/2)*sin(d*x+c)/d+2/11*A*(a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(11/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,8,-2/315*(a-b)*sqrt(a+b)*(10*A*b^4-21*a^4*(7*A+9*C)-3*a^2*b^2*(93*A+161*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d/sqrt(sec(d*x+c))-2/315*(a-b)*sqrt(a+b)*(10*A*b^3+21*a^3*(7*A+9*C)+15*a*b^2*(11*A+21*C)-6*a^2*b*(19*A+28*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d/sqrt(sec(d*x+c))+2/315*b*(5*A*b^2+a^2*(163*A+231*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d+2/315*(15*A*b^2+7*a^2*(7*A+9*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+10/63*A*b*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/9*A*(a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,9,2/21*(a-b)*b*sqrt(a+b)*(3*A*b^2+a^2*(29*A+49*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d/sqrt(sec(d*x+c))-2/21*sqrt(a+b)*(3*A*b^3-9*a*b^2*(3*A+7*C)-a^3*(5*A+7*C)+a^2*b*(29*A+49*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-2*b^2*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))+2/21*(3*A*b^2+a^2*(5*A+7*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*A*b*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*A*(a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,10,1/15*(a-b)*sqrt(a+b)*(b^2*(46*A-15*C)+6*a^2*(3*A+5*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))+1/15*sqrt(a+b)*(30*A*b^3-a*b^2*(46*A-15*C)-6*a^3*(3*A+5*C)+a^2*(34*A*b+90*C*b))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-5*a*b*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))+2/5*(5*A*b^2+a^2*(3*A+5*C))*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d-1/15*(b^2*(46*A-15*C)+6*a^2*(3*A+5*C))*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*b*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*(a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,10,1/12*(a-b)*b*sqrt(a+b)*(56*A-27*C)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))+1/12*sqrt(a+b)*(6*b^2*(12*A+C)+8*a^2*(A+3*C)-a*(56*A*b-27*C*b))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))-1/4*sqrt(a+b)*(8*A*b^2+15*C*a^2+4*C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))-1/2*b^2*(8*A-C)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))-1/12*a*b*(56*A-27*C)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+10/3*A*b*(a+b*cos(d*x+c))^(3/2)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*(a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,10,1/24*(a-b)*sqrt(a+b)*(a^2*(48*A-33*C)-8*b^2*(3*A+2*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-1/24*sqrt(a+b)*(a^2*(48*A-33*C)-8*b^2*(3*A+2*C)-2*a*b*(72*A+13*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))-5/8*a*sqrt(a+b)*(8*A*b^2+(a^2+4*b^2)*C)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d/sqrt(sec(d*x+c))-1/4*a*b*(8*A-3*C)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))-1/3*b*(6*A-C)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(sec(d*x+c))-1/24*(a^2*(48*A-33*C)-8*b^2*(3*A+2*C))*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2*A*(a+b*cos(d*x+c))^(5/2)*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,10,-1/192*(a-b)*sqrt(a+b)*(432*A*b^2+15*C*a^2+284*C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d/sqrt(sec(d*x+c))+1/192*sqrt(a+b)*(15*a^3*C+24*b^3*(4*A+3*C)+2*a^2*b*(192*A+59*C)+4*a*b^2*(108*A+71*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d/sqrt(sec(d*x+c))+1/64*sqrt(a+b)*(5*a^4*C-120*a^2*b^2*(2*A+C)-16*b^4*(4*A+3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))+1/32*(5*a^2*C+4*b^2*(4*A+3*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+5/24*a*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/4*C*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/192*a*(432*A*b^2+15*C*a^2+284*C*b^2)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,11,1/1920*(a-b)*sqrt(a+b)*(45*a^4*C-256*b^4*(5*A+4*C)-12*a^2*b^2*(220*A+141*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/d/sqrt(sec(d*x+c))-1/1920*sqrt(a+b)*(45*a^4*C-30*a^3*b*C-256*b^4*(5*A+4*C)-12*a^2*b^2*(220*A+141*C)-8*a*b^3*(260*A+193*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))-1/128*a*sqrt(a+b)*(3*a^4*C+40*a^2*b^2*(2*A+C)+80*b^4*(4*A+3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d/sqrt(sec(d*x+c))+1/320*a*(240*A*b^2-15*C*a^2+172*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(sec(d*x+c))-1/240*(15*a^2*C-16*b^2*(5*A+4*C))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d/sqrt(sec(d*x+c))-3/40*a*C*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/5*C*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b/d/sqrt(sec(d*x+c))-1/1920*(45*a^4*C-256*b^4*(5*A+4*C)-12*a^2*b^2*(220*A+141*C))*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b^2/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/sqrt(a+b*cos(d*x+c)),x,7,-4/105*(a-b)*b*sqrt(a+b)*(24*A*b^2+a^2*(22*A+35*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^5/d/sqrt(sec(d*x+c))-2/105*sqrt(a+b)*(12*a*A*b^2-48*A*b^3-5*a^3*(5*A+7*C)-a^2*(44*A*b+70*C*b))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d/sqrt(sec(d*x+c))+2/105*(24*A*b^2+5*a^2*(5*A+7*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^3/d-12/35*A*b*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/a^2/d+2/7*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/a/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/sqrt(a+b*cos(d*x+c)),x,6,2/15*(a-b)*sqrt(a+b)*(8*A*b^2+3*a^2*(3*A+5*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d/sqrt(sec(d*x+c))+2/15*sqrt(a+b)*(2*a*A*b-8*A*b^2-3*a^2*(3*A+5*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d/sqrt(sec(d*x+c))-8/15*A*b*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d+2/5*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/sqrt(a+b*cos(d*x+c)),x,5,-4/3*A*(a-b)*b*sqrt(a+b)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d/sqrt(sec(d*x+c))+2/3*sqrt(a+b)*(2*A*b+a*(A+3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d/sqrt(sec(d*x+c))+2/3*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/sqrt(a+b*cos(d*x+c)),x,7,2*A*(a-b)*sqrt(a+b)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d/sqrt(sec(d*x+c))-2*A*sqrt(a+b)*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-2*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d/sqrt(sec(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/sqrt(a+b*cos(d*x+c)),x,7,-(a-b)*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d/sqrt(sec(d*x+c))+sqrt(a+b)*(2*A*b+C*a)*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d/sqrt(sec(d*x+c))+a*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))+C*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b/d,1],
[(A+C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c))/sqrt(sec(d*x+c)),x,8,3/4*(a-b)*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))-1/4*(3*a-2*b)*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))-1/4*sqrt(a+b)*(3*a^2*C+4*b^2*(2*A+C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d/sqrt(sec(d*x+c))+1/2*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(sec(d*x+c))-3/4*a*C*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b^2/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x,7,-2/5*(16*A*b^4-2*a^2*b^2*(4*A-5*C)-a^4*(3*A+5*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^5/sqrt(a+b)/d/sqrt(sec(d*x+c))-2/5*(12*a*A*b^2+16*A*b^3+2*a^2*b*(2*A+5*C)+a^3*(3*A+5*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/sqrt(a+b)/d/sqrt(sec(d*x+c))+2/5*b*(8*A*b^2-a^2*(3*A-5*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^3/(a^2-b^2)/d+2*(A*b^2+C*a^2)*sec(d*x+c)^(5/2)*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-2/5*(6*A*b^2-a^2*(A-5*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/a^2/(a^2-b^2)/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x,6,2/3*b*(8*A*b^2-a^2*(5*A-3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/sqrt(a+b)/d/sqrt(sec(d*x+c))+2/3*(6*a*A*b+8*A*b^2+a^2*(A+3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/sqrt(a+b)/d/sqrt(sec(d*x+c))+2*(A*b^2+C*a^2)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-2/3*(4*A*b^2-a^2*(A-3*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/(a^2-b^2)/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x,5,-2*(2*A*b^2-a^2*(A-C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/sqrt(a+b)/d/sqrt(sec(d*x+c))-2*(2*A*b+a*(A-C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/sqrt(a+b)/d/sqrt(sec(d*x+c))+2*(A*b^2+C*a^2)*sqrt(sec(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+b*cos(d*x+c))^(3/2),x,7,2*(A*b^2+C*a^2)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/b/sqrt(a+b)/d/sqrt(sec(d*x+c))+2*(A*b-C*a)*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/sqrt(a+b)/d/sqrt(sec(d*x+c))-2*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))-2*(A*b^2+C*a^2)*sqrt(sec(d*x+c))*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c)),x,8,-(2*A*b^2+3*C*a^2-C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/sqrt(a+b)/d/sqrt(sec(d*x+c))+(2*A*b^2+a*(3*a+b)*C)*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/sqrt(a+b)/d/sqrt(sec(d*x+c))+3*a*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d/sqrt(sec(d*x+c))-2*(A*b^2+C*a^2)*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))/sqrt(sec(d*x+c))+(2*A*b^2+3*C*a^2-C*b^2)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)/d,1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x,9,1/4*(8*A*b^2+15*C*a^2-7*C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/sqrt(a+b)/d/sqrt(sec(d*x+c))-1/4*(8*A*b^2+(15*a^2+5*a*b-2*b^2)*C)*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/sqrt(a+b)/d/sqrt(sec(d*x+c))-1/4*sqrt(a+b)*(8*A*b^2+15*C*a^2+4*C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^4/d/sqrt(sec(d*x+c))-2*(A*b^2+C*a^2)*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))/sec(d*x+c)^(3/2)+1/2*(4*A*b^2+5*C*a^2-C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)/d/sqrt(sec(d*x+c))-1/4*a*(8*A*b^2+15*C*a^2-7*C*b^2)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x,7,-4/3*b*(8*A*b^4+a^4*(4*A-3*C)-a^2*b^2*(14*A-C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^5/sqrt(a+b)/(a^2-b^2)/d/sqrt(sec(d*x+c))-2/3*(12*a*A*b^3+16*A*b^4-2*a^2*b^2*(8*A-C)-a^4*(A+3*C)-a^3*(9*A*b-3*C*b))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/sqrt(a+b)/(a^2-b^2)/d/sqrt(sec(d*x+c))+2/3*(A*b^2+C*a^2)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+4/3*(5*A*a^2*b^2-3*A*b^4+2*C*a^4)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c))+2/3*(8*A*b^4+a^4*(A-5*C)-a^2*b^2*(13*A-C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^3/(a^2-b^2)^2/d,1],
[(A+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x,6,2/3*(8*A*b^4+3*a^4*(A-C)-a^2*b^2*(15*A+C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/sqrt(a+b)/(a^2-b^2)/d/sqrt(sec(d*x+c))+2/3*(6*a*A*b^2+8*A*b^3-3*a^3*(A-C)-a^2*b*(9*A+C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/sqrt(a+b)/(a^2-b^2)/d/sqrt(sec(d*x+c))+2/3*(A*b^2+C*a^2)*sqrt(sec(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)-4/3*(2*A*b^4-a^4*C-a^2*b^2*(4*A+C))*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+b*cos(d*x+c))^(5/2),x,6,-4/3*b*(A*b^2-a^2*(3*A+2*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/(a-b)/(a+b)^(3/2)/d/sqrt(sec(d*x+c))-2/3*(2*A*b^2+3*a*b*(A+C)-a^2*(3*A+C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/sqrt(a+b)/(a^2-b^2)/d/sqrt(sec(d*x+c))+2/3*(A*b^2+C*a^2)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c))+4/3*b*(A*b^2-a^2*(3*A+2*C))*sqrt(sec(d*x+c))*sin(d*x+c)/a/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2)/sqrt(sec(d*x+c)),x,8,-2/3*(A*b^4-3*a^4*C+a^2*b^2*(3*A+7*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/b^2/sqrt(a+b)/(a^2-b^2)/d/sqrt(sec(d*x+c))-2/3*(A*b^3+3*a^3*C+a^2*b*C-3*a*b^2*(A+2*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/(a-b)/b^2/(a+b)^(3/2)/d/sqrt(sec(d*x+c))-2*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d/sqrt(sec(d*x+c))-2/3*(A*b^2+C*a^2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c))+2/3*(A*b^4-3*a^4*C+a^2*b^2*(3*A+7*C))*sqrt(sec(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[(A+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x,9,1/3*(8*A*b^4-(15*a^4-26*a^2*b^2+3*b^4)*C)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/(a-b)/b^3/(a+b)^(3/2)/d/sqrt(sec(d*x+c))-1/3*(6*A*b^4-a*b^3*(2*A-3*C)-15*a^4*C-5*a^3*b*C+21*a^2*b^2*C)*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/(a-b)/b^3/(a+b)^(3/2)/d/sqrt(sec(d*x+c))+5*a*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^4/d/sqrt(sec(d*x+c))-2/3*(A*b^2+C*a^2)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2)+2/3*(3*A*b^4-5*a^4*C+a^2*b^2*(A+9*C))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c))/sqrt(sec(d*x+c))-1/3*(8*A*b^4-(15*a^4-26*a^2*b^2+3*b^4)*C)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)^2/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,8,-2/5*(3*A*b+3*B*a+5*C*b)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(5*A*a+7*B*b+7*C*a)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*(3*A*b+3*B*a+5*C*b)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/21*(5*A*a+7*B*b+7*C*a)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*(A*b+B*a)*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*a*A*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,7,-2/5*(3*A*a+5*B*b+5*C*a)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*(A*b+B*a+3*C*b)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*(3*A*a+5*B*b+5*C*a)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*(A*b+B*a)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*a*A*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,6,-2*(A*b+B*a-C*b)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*(3*b*B+a*(A+3*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2*(A*b+B*a)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*a*A*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,6,2*(b*B-a*(A-C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*(3*A*b+3*B*a+C*b)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/3*b*C*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*a*A*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,6,2/5*(5*A*b+5*B*a+3*C*b)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*(b*B+a*(3*A+C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*b*C*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/3*(B*b+C*a)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,7,2/5*(5*A*a+3*B*b+3*C*a)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(7*A*b+7*B*a+5*C*b)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/7*b*C*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/5*(B*b+C*a)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/21*(7*A*b+7*B*a+5*C*b)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,8,2/15*(9*A*b+9*B*a+7*C*b)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(7*A*a+5*B*b+5*C*a)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/9*b*C*sin(d*x+c)/d/sec(d*x+c)^(7/2)+2/7*(B*b+C*a)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/45*(9*A*b+9*B*a+7*C*b)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/21*(7*A*a+5*B*b+5*C*a)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,9,-2/15*(18*a*b*B+3*b^2*(3*A+5*C)+a^2*(7*A+9*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(10*A*a*b+5*B*a^2+7*B*b^2+14*C*a*b)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/15*(18*a*b*B+3*b^2*(3*A+5*C)+a^2*(7*A+9*C))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/21*(10*A*a*b+5*B*a^2+7*B*b^2+14*C*a*b)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/45*(4*A*b^2+18*a*b*B+a^2*(7*A+9*C))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/63*a*(4*A*b+9*B*a)*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/9*A*(a+b*cos(d*x+c))^2*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,8,-2/5*(6*A*a*b+3*B*a^2+5*B*b^2+10*C*a*b)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(14*a*b*B+7*b^2*(A+3*C)+a^2*(5*A+7*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*(6*A*a*b+3*B*a^2+5*B*b^2+10*C*a*b)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/21*(4*A*b^2+14*a*b*B+a^2*(5*A+7*C))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/35*a*(4*A*b+7*B*a)*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*A*(a+b*cos(d*x+c))^2*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,7,-2/5*(10*a*b*B+5*b^2*(A-C)+a^2*(3*A+5*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*(a^2*B+3*b^2*B+2*a*b*(A+3*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*(4*A*b^2+10*a*b*B+a^2*(3*A+5*C))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/15*a*(4*A*b+5*B*a)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*(a+b*cos(d*x+c))^2*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,7,-2*(a^2*B-b^2*B+2*a*b*(A-C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*(6*a*b*B+b^2*(3*A+C)+a^2*(A+3*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/3*b^2*(A-C)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/3*a*(4*A*b+3*B*a)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*(a+b*cos(d*x+c))^2*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,7,2/5*(10*a*b*B-5*a^2*(A-C)+b^2*(5*A+3*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*(3*a^2*B+b^2*B+2*a*b*(3*A+C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/5*b^2*(5*A-C)*sin(d*x+c)/d/sec(d*x+c)^(3/2)-2/3*b*(6*A*a-B*b-2*C*a)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*A*(a+b*cos(d*x+c))^2*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,7,2/5*(10*A*a*b+5*B*a^2+3*B*b^2+6*C*a*b)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(14*a*b*B+7*a^2*(3*A+C)+b^2*(7*A+5*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/35*b*(7*B*b+4*C*a)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/21*(7*A*b^2+14*B*a*b+4*C*a^2+5*C*b^2)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/7*C*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,8,2/15*(18*a*b*B+3*a^2*(5*A+3*C)+b^2*(9*A+7*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(14*A*a*b+7*B*a^2+5*B*b^2+10*C*a*b)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/63*b*(9*B*b+4*C*a)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/45*(9*A*b^2+18*B*a*b+4*C*a^2+7*C*b^2)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/9*C*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/21*(14*A*a*b+7*B*a^2+5*B*b^2+10*C*a*b)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,9,2/15*(18*A*a*b+9*B*a^2+7*B*b^2+14*C*a*b)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/231*(110*a*b*B+11*a^2*(7*A+5*C)+5*b^2*(11*A+9*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/99*b*(11*B*b+4*C*a)*sin(d*x+c)/d/sec(d*x+c)^(7/2)+2/77*(11*A*b^2+22*B*a*b+4*C*a^2+9*C*b^2)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/11*C*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/45*(18*A*a*b+9*B*a^2+7*B*b^2+14*C*a*b)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/231*(110*a*b*B+11*a^2*(7*A+5*C)+5*b^2*(11*A+9*C))*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,9,-2/15*(27*a^2*b*B+15*b^3*B+9*a*b^2*(3*A+5*C)+a^3*(7*A+9*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(5*a^3*B+21*a*b^2*B+7*b^3*(A+3*C)+3*a^2*b*(5*A+7*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/15*(27*a^2*b*B+15*b^3*B+9*a*b^2*(3*A+5*C)+a^3*(7*A+9*C))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/63*(8*A*b^3+15*a^3*B+54*a*b^2*B+9*a^2*b*(5*A+7*C))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/315*a*(24*A*b^2+99*a*b*B+7*a^2*(7*A+9*C))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/21*(2*A*b+3*B*a)*(a+b*cos(d*x+c))^2*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/9*A*(a+b*cos(d*x+c))^3*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,8,-2/5*(3*a^3*B+15*a*b^2*B+5*b^3*(A-C)+3*a^2*b*(3*A+5*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(21*a^2*b*B+21*b^3*B+21*a*b^2*(A+3*C)+a^3*(5*A+7*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/35*(24*A*b^3+21*a^3*B+98*a*b^2*B+21*a^2*b*(3*A+5*C))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/105*a*(24*A*b^2+63*a*b*B+5*a^2*(5*A+7*C))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/35*(6*A*b+7*B*a)*(a+b*cos(d*x+c))^2*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*A*(a+b*cos(d*x+c))^3*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,8,-2/5*(15*a^2*b*B-5*b^3*B+15*a*b^2*(A-C)+a^3*(3*A+5*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*(a^3*B+9*a*b^2*B+b^3*(3*A+C)+3*a^2*b*(A+3*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/15*b^2*(9*A*b+5*B*a-5*C*b)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/15*a*(24*A*b^2+35*a*b*B+3*a^2*(3*A+5*C))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/15*(6*A*b+5*B*a)*(a+b*cos(d*x+c))^2*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*(a+b*cos(d*x+c))^3*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,8,-2/5*(5*a^3*B-15*a*b^2*B+15*a^2*b*(A-C)-b^3*(5*A+3*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*(9*a^2*b*B+b^3*B+3*a*b^2*(3*A+C)+a^3*(A+3*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/15*b^2*(35*A*b+15*B*a-3*C*b)*sin(d*x+c)/d/sec(d*x+c)^(3/2)-2/3*b*(6*a^2*B-b^2*B+3*a*b*(5*A-C))*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*(2*A*b+B*a)*(a+b*cos(d*x+c))^2*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*(a+b*cos(d*x+c))^3*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,8,2/5*(15*a^2*b*B+3*b^3*B-5*a^3*(A-C)+3*a*b^2*(5*A+3*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(21*a^3*B+21*a*b^2*B+21*a^2*b*(3*A+C)+b^3*(7*A+5*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/35*b^2*(35*A*a-7*B*b-11*C*a)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/21*b*(21*a*b*B-6*a^2*(7*A-3*C)+b^2*(7*A+5*C))*sin(d*x+c)/d/sqrt(sec(d*x+c))-2/7*b*(7*A-C)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*A*(a+b*cos(d*x+c))^3*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,8,2/15*(15*a^3*B+27*a*b^2*B+9*a^2*b*(5*A+3*C)+b^3*(9*A+7*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(21*a^2*b*B+5*b^3*B+7*a^3*(3*A+C)+3*a*b^2*(7*A+5*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/315*b*(63*A*b^2+99*B*a*b+24*C*a^2+49*C*b^2)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/63*(54*a^2*b*B+15*b^3*B+8*a^3*C+9*a*b^2*(7*A+5*C))*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/21*(3*B*b+2*C*a)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/9*C*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,9,2/15*(27*a^2*b*B+7*b^3*B+3*a^3*(5*A+3*C)+3*a*b^2*(9*A+7*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/231*(77*a^3*B+165*a*b^2*B+33*a^2*b*(7*A+5*C)+5*b^3*(11*A+9*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/693*b*(99*A*b^2+143*B*a*b+24*C*a^2+81*C*b^2)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/495*(242*a^2*b*B+77*b^3*B+24*a^3*C+33*a*b^2*(9*A+7*C))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/99*(11*B*b+6*C*a)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/11*C*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/231*(77*a^3*B+165*a*b^2*B+33*a^2*b*(7*A+5*C)+5*b^3*(11*A+9*C))*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,10,2/195*(117*a^3*B+273*a*b^2*B+39*a^2*b*(9*A+7*C)+7*b^3*(13*A+11*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/231*(165*a^2*b*B+45*b^3*B+11*a^3*(7*A+5*C)+15*a*b^2*(11*A+9*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/1287*b*(143*A*b^2+195*B*a*b+24*C*a^2+121*C*b^2)*sin(d*x+c)/d/sec(d*x+c)^(7/2)+2/1001*(338*a^2*b*B+117*b^3*B+24*a^3*C+39*a*b^2*(11*A+9*C))*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/143*(13*B*b+6*C*a)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/13*C*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/585*(117*a^3*B+273*a*b^2*B+39*a^2*b*(9*A+7*C)+7*b^3*(13*A+11*C))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/231*(165*a^2*b*B+45*b^3*B+11*a^3*(7*A+5*C)+15*a*b^2*(11*A+9*C))*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x,10,-2/15*(7*a^4*B+54*a^2*b^2*B+15*b^4*B+12*a*b^3*(3*A+5*C)+4*a^3*b*(7*A+9*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/231*(220*a^3*b*B+308*a*b^3*B+77*b^4*(A+3*C)+66*a^2*b^2*(5*A+7*C)+5*a^4*(9*A+11*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/15*(7*a^4*B+54*a^2*b^2*B+15*b^4*B+12*a*b^3*(3*A+5*C)+4*a^3*b*(7*A+9*C))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/693*(64*A*b^4+660*a^3*b*B+682*a*b^3*B+15*a^4*(9*A+11*C)+9*a^2*b^2*(101*A+143*C))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/3465*a*(192*A*b^3+539*a^3*B+1353*a*b^2*B+2*a^2*b*(673*A+891*C))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/231*(16*A*b^2+55*a*b*B+3*a^2*(9*A+11*C))*(a+b*cos(d*x+c))^2*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/99*(8*A*b+11*B*a)*(a+b*cos(d*x+c))^3*sec(d*x+c)^(9/2)*sin(d*x+c)/d+2/11*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^(11/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,9,-2/15*(36*a^3*b*B+60*a*b^3*B+15*b^4*(A-C)+18*a^2*b^2*(3*A+5*C)+a^4*(7*A+9*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(5*a^4*B+42*a^2*b^2*B+21*b^4*B+28*a*b^3*(A+3*C)+4*a^3*b*(5*A+7*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/315*(192*A*b^4+756*a^3*b*B+1098*a*b^3*B+21*a^4*(7*A+9*C)+7*a^2*b^2*(155*A+261*C))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/315*a*(64*A*b^3+75*a^3*B+261*a*b^2*B+a^2*(202*A*b+294*C*b))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/315*(48*A*b^2+117*a*b*B+7*a^2*(7*A+9*C))*(a+b*cos(d*x+c))^2*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/63*(8*A*b+9*B*a)*(a+b*cos(d*x+c))^3*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/9*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,9,-2/5*(3*a^4*B+30*a^2*b^2*B-5*b^4*B+20*a*b^3*(A-C)+4*a^3*b*(3*A+5*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(28*a^3*b*B+84*a*b^3*B+7*b^4*(3*A+C)+42*a^2*b^2*(A+3*C)+a^4*(5*A+7*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/105*b^2*(98*a*b*B+b^2*(87*A-35*C)+5*a^2*(5*A+7*C))*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/105*a*(192*A*b^3+63*a^3*B+413*a*b^2*B+a^2*(202*A*b+350*C*b))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/105*(48*A*b^2+77*a*b*B+5*a^2*(5*A+7*C))*(a+b*cos(d*x+c))^2*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/35*(8*A*b+7*B*a)*(a+b*cos(d*x+c))^3*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,9,-2/5*(20*a^3*b*B-20*a*b^3*B+30*a^2*b^2*(A-C)-b^4*(5*A+3*C)+a^4*(3*A+5*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*(a^4*B+18*a^2*b^2*B+b^4*B+4*a*b^3*(3*A+C)+4*a^3*b*(A+3*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/15*b^2*(50*a*b*B+b^2*(59*A-3*C)+3*a^2*(3*A+5*C))*sin(d*x+c)/d/sec(d*x+c)^(3/2)-2/15*b*(105*a^2*b*B-5*b^3*B+4*a*b^2*(33*A-5*C)+6*a^3*(3*A+5*C))*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/5*(16*A*b^2+15*a*b*B+a^2*(3*A+5*C))*(a+b*cos(d*x+c))^2*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/15*(8*A*b+5*B*a)*(a+b*cos(d*x+c))^3*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,9,-2/5*(5*a^4*B-30*a^2*b^2*B-3*b^4*B+20*a^3*b*(A-C)-4*a*b^3*(5*A+3*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(84*a^3*b*B+28*a*b^3*B+42*a^2*b^2*(3*A+C)+7*a^4*(A+3*C)+b^4*(7*A+5*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d-2/105*b^2*(350*A*a*b+105*B*a^2-21*B*b^2-54*C*a*b)*sin(d*x+c)/d/sec(d*x+c)^(3/2)-2/21*b*(42*a^3*B-28*a*b^2*B+3*a^2*b*(49*A-13*C)-b^3*(7*A+5*C))*sin(d*x+c)/d/sqrt(sec(d*x+c))-2/7*b*(21*A*b+7*B*a-C*b)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/3*(8*A*b+3*B*a)*(a+b*cos(d*x+c))^3*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*(a+b*cos(d*x+c))^4*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,9,2/15*(60*a^3*b*B+36*a*b^3*B-15*a^4*(A-C)+18*a^2*b^2*(5*A+3*C)+b^4*(9*A+7*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/21*(21*a^4*B+42*a^2*b^2*B+5*b^4*B+28*a^3*b*(3*A+C)+4*a*b^3*(7*A+5*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/315*b^2*(162*a*b*B-a^2*(315*A-123*C)+7*b^2*(9*A+7*C))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/63*b*(117*a^2*b*B+15*b^3*B-a^3*(126*A-62*C)+12*a*b^2*(7*A+5*C))*sin(d*x+c)/d/sqrt(sec(d*x+c))-2/21*b*(21*A*a-3*B*b-5*C*a)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(sec(d*x+c))-2/9*b*(9*A-C)*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*A*(a+b*cos(d*x+c))^4*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,9,2/15*(15*a^4*B+54*a^2*b^2*B+7*b^4*B+12*a^3*b*(5*A+3*C)+4*a*b^3*(9*A+7*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/231*(308*a^3*b*B+220*a*b^3*B+77*a^4*(3*A+C)+66*a^2*b^2*(7*A+5*C)+5*b^4*(11*A+9*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/3465*b*(1353*a^2*b*B+539*b^3*B+192*a^3*C+2*a*b^2*(891*A+673*C))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/693*(682*a^3*b*B+660*a*b^3*B+64*a^4*C+15*b^4*(11*A+9*C)+9*a^2*b^2*(143*A+101*C))*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/231*(33*A*b^2+55*B*a*b+16*C*a^2+27*C*b^2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/99*(11*B*b+8*C*a)*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/11*C*(a+b*cos(d*x+c))^4*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,10,2/195*(468*a^3*b*B+364*a*b^3*B+39*a^4*(5*A+3*C)+78*a^2*b^2*(9*A+7*C)+7*b^4*(13*A+11*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/231*(77*a^4*B+330*a^2*b^2*B+45*b^4*B+44*a^3*b*(7*A+5*C)+20*a*b^3*(11*A+9*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/9009*b*(2171*a^2*b*B+1053*b^3*B+192*a^3*C+2*a*b^2*(1573*A+1259*C))*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/6435*(3458*a^3*b*B+4004*a*b^3*B+192*a^4*C+77*b^4*(13*A+11*C)+11*a^2*b^2*(637*A+491*C))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/1287*(143*A*b^2+221*B*a*b+48*C*a^2+121*C*b^2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/143*(13*B*b+8*C*a)*(a+b*cos(d*x+c))^3*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/13*C*(a+b*cos(d*x+c))^4*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/231*(77*a^4*B+330*a^2*b^2*B+45*b^4*B+44*a^3*b*(7*A+5*C)+20*a*b^3*(11*A+9*C))*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c)),x,9,-2/5*(5*A*b^2-5*a*b*B+a^2*(3*A+5*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/d-2/3*(A*b-B*a)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/d-2*b*(A*b^2-a*(B*b-C*a))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a^3/(a+b)/d+2/5*(5*A*b^2-5*a*b*B+a^2*(3*A+5*C))*sqrt(sec(d*x+c))*sin(d*x+c)/a^3/d-2/3*(A*b-B*a)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d+2/5*A*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x,8,2*(A*b-B*a)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^2/d+2/3*A*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d+2*(A*b^2-a*(B*b-C*a))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a^2/(a+b)/d-2*(A*b-B*a)*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d+2/3*A*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x,7,-2*A*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/d+2*C*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b/d-2*(A*b^2-a*(B*b-C*a))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a/b/(a+b)/d+2*A*sqrt(sec(d*x+c))*sin(d*x+c)/a/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+b*cos(d*x+c)),x,6,2*C*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b/d+2*(B*b-C*a)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^2/d+2*(A*b^2-a*(B*b-C*a))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/b^2/(a+b)/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sqrt(sec(d*x+c)),x,7,2*(B*b-C*a)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b^2/d+2/3*(b^2*(3*A+C)-3*a*(B*b-C*a))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^3/d-2*a*(A*b^2-a*(B*b-C*a))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/b^3/(a+b)/d+2/3*C*sin(d*x+c)/b/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2),x,8,2/5*(5*A*b^2-5*B*a*b+5*C*a^2+3*C*b^2)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b^3/d+2/3*(3*a^2*b*B+b^3*B-3*a^3*C-a*b^2*(3*A+C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^4/d+2*a^2*(A*b^2-a*(B*b-C*a))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/b^4/(a+b)/d+2/5*C*sin(d*x+c)/b/d/sec(d*x+c)^(3/2)+2/3*(B*b-C*a)*sin(d*x+c)/b^2/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))/sec(d*x+c)^(5/2),x,9,2/5*(5*a^2*b*B+3*b^3*B-5*a^3*C-a*b^2*(5*A+3*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b^4/d-2/21*(21*a^3*b*B+7*a*b^3*B-21*a^4*C-7*a^2*b^2*(3*A+C)-b^4*(7*A+5*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^5/d-2*a^3*(A*b^2-a*(B*b-C*a))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/b^5/(a+b)/d+2/7*C*sin(d*x+c)/b/d/sec(d*x+c)^(5/2)+2/5*(B*b-C*a)*sin(d*x+c)/b^2/d/sec(d*x+c)^(3/2)+2/21*(7*A*b^2-7*B*a*b+7*C*a^2+5*C*b^2)*sin(d*x+c)/b^3/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x,9,-(5*A*b^3+2*a^3*B-3*a*b^2*B-a^2*b*(4*A-C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/(a^2-b^2)/d-1/3*(5*A*b^2-3*a*b*B-a^2*(2*A-3*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/(a^2-b^2)/d-(5*A*b^4+5*a^3*b*B-3*a*b^3*B-a^2*b^2*(7*A-C)-3*a^4*C)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a^3/(a-b)/(a+b)^2/d+(5*A*b^3+2*a^3*B-3*a*b^2*B-a^2*b*(4*A-C))*sqrt(sec(d*x+c))*sin(d*x+c)/a^3/(a^2-b^2)/d-1/3*(5*A*b^2-3*a*b*B-a^2*(2*A-3*C))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/(a^2-b^2)/d+(A*b^2-a*(B*b-C*a))*sec(d*x+c)^(3/2)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x,8,(3*A*b^2-a*b*B-a^2*(2*A-C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^2/(a^2-b^2)/d+(A*b^2-a*(B*b-C*a))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/b/(a^2-b^2)/d+(3*A*b^4+3*a^3*b*B-a*b^3*B-a^4*C-a^2*b^2*(5*A+C))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a^2/(a-b)/b/(a+b)^2/d-(3*A*b^2-a*b*B-a^2*(2*A-C))*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/(a^2-b^2)/d+(A*b^2-a*(B*b-C*a))*sqrt(sec(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+b*cos(d*x+c))^2,x,7,-(A*b^2-a*(B*b-C*a))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/b/(a^2-b^2)/d-(A*b^2-B*a*b-C*a^2+2*C*b^2)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^2/(a^2-b^2)/d-(A*b^4+a^3*b*B+a*b^3*B+a^4*C-3*a^2*b^2*(A+C))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a/(a-b)/b^2/(a+b)^2/d+(A*b^2-a*(B*b-C*a))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sqrt(sec(d*x+c)),x,7,(A*b^2-B*a*b+3*C*a^2-2*C*b^2)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b^2/(a^2-b^2)/d+(a^2*b*B-2*b^3*B-3*a^3*C+a*b^2*(A+4*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^3/(a^2-b^2)/d-(A*b^4+a^3*b*B-3*a*b^3*B-3*a^4*C+a^2*b^2*(A+5*C))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/(a-b)/b^3/(a+b)^2/d-(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(3/2),x,8,(3*a^2*b*B-2*b^3*B-a*b^2*(A-4*C)-5*a^3*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b^3/(a^2-b^2)/d-1/3*(9*a^3*b*B-12*a*b^3*B-a^2*b^2*(3*A-16*C)-15*a^4*C+2*b^4*(3*A+C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^4/(a^2-b^2)/d+a*(3*A*b^4+3*a^3*b*B-5*a*b^3*B-a^2*b^2*(A-7*C)-5*a^4*C)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/(a-b)/b^4/(a+b)^2/d-(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2)+1/3*(3*A*b^2-3*B*a*b+5*C*a^2-2*C*b^2)*sin(d*x+c)/b^2/(a^2-b^2)/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^2/sec(d*x+c)^(5/2),x,9,-1/5*(25*a^3*b*B-20*a*b^3*B-3*a^2*b^2*(5*A-8*C)-35*a^4*C+2*b^4*(5*A+3*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b^4/(a^2-b^2)/d+1/3*(15*a^4*b*B-16*a^2*b^3*B-2*b^5*B-a^3*b^2*(9*A-20*C)-21*a^5*C+4*a*b^4*(3*A+C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^5/(a^2-b^2)/d-a^2*(5*A*b^4+5*a^3*b*B-7*a*b^3*B-3*a^2*b^2*(A-3*C)-7*a^4*C)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/(a-b)/b^5/(a+b)^2/d-(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))/sec(d*x+c)^(5/2)+1/5*(5*A*b^2-5*B*a*b+7*C*a^2-2*C*b^2)*sin(d*x+c)/b^2/(a^2-b^2)/d/sec(d*x+c)^(3/2)+1/3*(5*a^2*b*B-2*b^3*B-a*b^2*(3*A-4*C)-7*a^3*C)*sin(d*x+c)/b^3/(a^2-b^2)/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x,10,1/4*(35*A*b^5-8*a^5*B+29*a^3*b^2*B-15*a*b^4*B+3*a^4*b*(8*A-3*C)-a^2*b^3*(65*A-3*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^4/(a^2-b^2)^2/d+1/12*(35*A*b^4+33*a^3*b*B-15*a*b^3*B+a^4*(8*A-21*C)-a^2*b^2*(61*A-3*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^3/(a^2-b^2)^2/d+1/4*(35*A*b^6-35*a^5*b*B+38*a^3*b^3*B-15*a*b^5*B-a^2*b^4*(86*A-3*C)+3*a^4*b^2*(21*A-2*C)+15*a^6*C)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a^4/(a-b)^2/(a+b)^3/d-1/4*(35*A*b^5-8*a^5*B+29*a^3*b^2*B-15*a*b^4*B+3*a^4*b*(8*A-3*C)-a^2*b^3*(65*A-3*C))*sqrt(sec(d*x+c))*sin(d*x+c)/a^4/(a^2-b^2)^2/d+1/12*(35*A*b^4+33*a^3*b*B-15*a*b^3*B+a^4*(8*A-21*C)-a^2*b^2*(61*A-3*C))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^3/(a^2-b^2)^2/d+1/2*(A*b^2-a*(B*b-C*a))*sec(d*x+c)^(3/2)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/4*(7*A*b^4+9*a^3*b*B-3*a*b^3*B-5*a^4*C-a^2*b^2*(13*A+C))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x,9,-1/4*(15*A*b^4+9*a^3*b*B-3*a*b^3*B+a^4*(8*A-5*C)-a^2*b^2*(29*A+C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^3/(a^2-b^2)^2/d-1/4*(5*A*b^4+7*a^3*b*B-a*b^3*B-3*a^4*C-a^2*b^2*(11*A+3*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/b/(a^2-b^2)^2/d-1/4*(15*A*b^6-15*a^5*b*B+6*a^3*b^3*B-3*a*b^5*B+3*a^6*C-a^2*b^4*(38*A+C)+5*a^4*b^2*(7*A+2*C))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a^3/(a-b)^2/b/(a+b)^3/d+1/4*(15*A*b^4+9*a^3*b*B-3*a*b^3*B+a^4*(8*A-5*C)-a^2*b^2*(29*A+C))*sqrt(sec(d*x+c))*sin(d*x+c)/a^3/(a^2-b^2)^2/d+1/2*(A*b^2-a*(B*b-C*a))*sqrt(sec(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/4*(5*A*b^4+7*a^3*b*B-a*b^3*B-3*a^4*C-a^2*b^2*(11*A+3*C))*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+b*cos(d*x+c))^3,x,8,1/4*(3*A*b^4+5*a^3*b*B+a*b^3*B-a^4*C-a^2*b^2*(9*A+5*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a^2/b/(a^2-b^2)^2/d+1/4*(A*b^4+3*a^3*b*B+3*a*b^3*B+a^4*C-7*a^2*b^2*(A+C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/b^2/(a^2-b^2)^2/d+1/4*(3*A*b^6-3*a^5*b*B-10*a^3*b^3*B+a*b^5*B-3*a^2*b^4*(2*A-C)-a^6*C+5*a^4*b^2*(3*A+2*C))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a^2/(a-b)^2/b^2/(a+b)^3/d+1/2*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2/sqrt(sec(d*x+c))-1/4*(3*A*b^4+5*a^3*b*B+a*b^3*B-a^4*C-a^2*b^2*(9*A+5*C))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sqrt(sec(d*x+c)),x,8,1/4*(A*b^4-a^3*b*B-5*a*b^3*B-3*a^4*C+a^2*b^2*(5*A+9*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/b^2/(a^2-b^2)^2/d+1/4*(a^3*b*B-7*a*b^3*B+a^2*b^2*(3*A-5*C)+3*a^4*C+b^4*(3*A+8*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^3/(a^2-b^2)^2/d+1/4*(A*b^6-a^5*b*B+10*a^3*b^3*B+3*a*b^5*B-3*a^4*b^2*(A-2*C)-3*a^6*C-5*a^2*b^4*(2*A+3*C))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/a/(a-b)^2/b^3/(a+b)^3/d-1/2*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2/sqrt(sec(d*x+c))-1/4*(A*b^4-a^3*b*B-5*a*b^3*B-3*a^4*C+a^2*b^2*(5*A+9*C))*sin(d*x+c)/a/b/(a^2-b^2)^2/d/(a+b*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(3/2),x,8,-1/4*(3*a^3*b*B-9*a*b^3*B+b^4*(5*A-8*C)-15*a^4*C+a^2*b^2*(A+29*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b^3/(a^2-b^2)^2/d+1/4*(3*a^4*b*B-5*a^2*b^3*B+8*b^5*B-15*a^5*C-a*b^4*(7*A+24*C)+a^3*b^2*(A+33*C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^4/(a^2-b^2)^2/d+1/4*(3*A*b^6-3*a^5*b*B+6*a^3*b^3*B-15*a*b^5*B+15*a^6*C+5*a^2*b^4*(2*A+7*C)-a^4*b^2*(A+38*C))*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/(a-b)^2/b^4/(a+b)^3/d-1/2*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2/sec(d*x+c)^(3/2)+1/4*(3*A*b^4+a^3*b*B-7*a*b^3*B-5*a^4*C+a^2*b^2*(3*A+11*C))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(5/2),x,9,1/4*(15*a^4*b*B-29*a^2*b^3*B+8*b^5*B-a^3*b^2*(3*A-65*C)+3*a*b^4*(3*A-8*C)-35*a^5*C)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b^4/(a^2-b^2)^2/d-1/12*(45*a^5*b*B-99*a^3*b^3*B+72*a*b^5*B-a^4*b^2*(9*A-223*C)+a^2*b^4*(15*A-128*C)-105*a^6*C-8*b^6*(3*A+C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^5/(a^2-b^2)^2/d-1/4*a*(15*A*b^6-15*a^5*b*B+38*a^3*b^3*B-35*a*b^5*B+a^4*b^2*(3*A-86*C)-3*a^2*b^4*(2*A-21*C)+35*a^6*C)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/(a-b)^2/b^5/(a+b)^3/d-1/2*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2/sec(d*x+c)^(5/2)+1/4*(5*A*b^4+3*a^3*b*B-9*a*b^3*B-7*a^4*C+a^2*b^2*(A+13*C))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2)-1/12*(15*a^3*b*B-33*a*b^3*B-a^2*b^2*(3*A-61*C)+b^4*(21*A-8*C)-35*a^4*C)*sin(d*x+c)/b^3/(a^2-b^2)^2/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^3/sec(d*x+c)^(7/2),x,10,-1/20*(175*a^5*b*B-325*a^3*b^3*B+120*a*b^5*B+a^2*b^4*(145*A-192*C)-3*a^4*b^2*(25*A-187*C)-315*a^6*C-8*b^6*(5*A+3*C))*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/b^5/(a^2-b^2)^2/d+1/12*(105*a^6*b*B-223*a^4*b^3*B+128*a^2*b^5*B+8*b^7*B+3*a^3*b^4*(33*A-64*C)-9*a^5*b^2*(5*A-43*C)-189*a^7*C-24*a*b^6*(3*A+C))*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b^6/(a^2-b^2)^2/d+1/4*a^2*(35*A*b^6-35*a^5*b*B+86*a^3*b^3*B-63*a*b^5*B-a^2*b^4*(38*A-99*C)+15*a^4*b^2*(A-10*C)+63*a^6*C)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))*sqrt(sec(d*x+c))/(a-b)^2/b^6/(a+b)^3/d-1/2*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2/sec(d*x+c)^(7/2)+1/4*(7*A*b^4+5*a^3*b*B-11*a*b^3*B-a^2*b^2*(A-15*C)-9*a^4*C)*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))/sec(d*x+c)^(5/2)-1/20*(35*a^3*b*B-65*a*b^3*B-a^2*b^2*(15*A-101*C)+b^4*(45*A-8*C)-63*a^4*C)*sin(d*x+c)/b^3/(a^2-b^2)^2/d/sec(d*x+c)^(3/2)+1/12*(35*a^4*b*B-61*a^2*b^3*B+8*b^5*B+3*a*b^4*(11*A-8*C)-15*a^3*b^2*(A-7*C)-63*a^5*C)*sin(d*x+c)/b^4/(a^2-b^2)^2/d/sqrt(sec(d*x+c)),1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,8,-2/315*(a-b)*sqrt(a+b)*(16*A*b^4-57*a^3*b*B-24*a*b^3*B+6*a^2*b^2*(4*A+7*C)-21*a^4*(7*A+9*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^5/d/sqrt(sec(d*x+c))-2/315*(a-b)*sqrt(a+b)*(16*A*b^3+12*a*b^2*(A-2*B)+6*a^2*b*(6*A-3*B+7*C)+3*a^3*(49*A-25*B+63*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d/sqrt(sec(d*x+c))+2/315*(8*A*b^3+75*a^3*B-12*a*b^2*B+a^2*b*(13*A+21*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^3/d-2/315*(6*A*b^2-9*a*b*B-7*a^2*(7*A+9*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/a^2/d+2/63*(A*b+9*B*a)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/a/d+2/9*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,7,2/105*(a-b)*sqrt(a+b)*(8*A*b^3+63*a^3*B-14*a*b^2*B+a^2*b*(19*A+35*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d/sqrt(sec(d*x+c))+2/105*(a-b)*sqrt(a+b)*(8*A*b^2+2*a*b*(3*A-7*B)+a^2*(25*A-63*B+35*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d/sqrt(sec(d*x+c))-2/105*(4*A*b^2-7*a*b*B-5*a^2*(5*A+7*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d+2/35*(A*b+7*B*a)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d+2/7*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,6,-2/15*(a-b)*sqrt(a+b)*(2*A*b^2-5*a*b*B-3*a^2*(3*A+5*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d/sqrt(sec(d*x+c))-2/15*(a-b)*sqrt(a+b)*(2*A*b+a*(9*A-5*B+15*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d/sqrt(sec(d*x+c))+2/15*(A*b+5*B*a)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d+2/5*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,7,2/3*(a-b)*sqrt(a+b)*(A*b+3*B*a)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d/sqrt(sec(d*x+c))-2/3*sqrt(a+b)*(b*(A-3*B)-a*(A-3*B+3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-2*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))+2/3*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,8,(a-b)*sqrt(a+b)*(2*A-C)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))+sqrt(a+b)*(2*A*b-a*(2*A-2*B-C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-sqrt(a+b)*(2*B*b+C*a)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d/sqrt(sec(d*x+c))+2*A*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d-(2*A-C)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,8,-1/4*(a-b)*sqrt(a+b)*(4*B*b+C*a)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d/sqrt(sec(d*x+c))+1/4*sqrt(a+b)*(8*A*b+a*C+2*b*(2*B+C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d/sqrt(sec(d*x+c))-1/4*sqrt(a+b)*(8*A*b^2+4*B*a*b-C*a^2+4*C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))+1/2*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/4*(4*B*b+C*a)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b/d,1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,9,-1/24*(a-b)*sqrt(a+b)*(8*b^2*(3*A+2*C)+3*a*(2*B*b-C*a))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/d/sqrt(sec(d*x+c))+1/24*sqrt(a+b)*(24*A*b^2+(a+2*b)*(6*B*b-3*C*a+8*C*b))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))+1/8*sqrt(a+b)*(2*a^2*b*B-8*b^3*B-a^3*C-4*a*b^2*(2*A+C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d/sqrt(sec(d*x+c))+1/4*(2*B*b-C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/3*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/24*(8*b^2*(3*A+2*C)+3*a*(2*B*b-C*a))*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b^2/d,1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sec(d*x+c)^(3/2),x,10,1/192*(a-b)*sqrt(a+b)*(24*a^2*b*B-128*b^3*B-15*a^3*C-4*a*b^2*(12*A+7*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^3/d/sqrt(sec(d*x+c))+1/192*sqrt(a+b)*(15*a^3*C-2*a^2*b*(12*B+5*C)+4*a*b^2*(12*A+4*B+7*C)+8*b^3*(12*A+16*B+9*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d/sqrt(sec(d*x+c))-1/64*sqrt(a+b)*(8*a^3*b*B+32*a*b^3*B-5*a^4*C-8*a^2*b^2*(2*A+C)+16*b^4*(4*A+3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^4/d/sqrt(sec(d*x+c))+1/4*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d/sec(d*x+c)^(3/2)+1/32*(16*A*b^2-8*B*a*b+5*C*a^2+12*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d/sqrt(sec(d*x+c))+1/24*(8*B*b-5*C*a)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^2/d/sqrt(sec(d*x+c))-1/192*(24*a^2*b*B-128*b^3*B-15*a^3*C-4*a*b^2*(12*A+7*C))*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b^3/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,8,2/315*(a-b)*sqrt(a+b)*(8*A*b^4+246*a^3*b*B-18*a*b^3*B+21*a^4*(7*A+9*C)+3*a^2*b^2*(11*A+21*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d/sqrt(sec(d*x+c))+2/315*(a-b)*sqrt(a+b)*(8*A*b^3+6*a*b^2*(A-3*B)+3*a^2*b*(13*A-57*B+21*C)-3*a^3*(49*A-25*B+63*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d/sqrt(sec(d*x+c))-2/315*(4*A*b^3-75*a^3*B-9*a*b^2*B-2*a^2*b*(44*A+63*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d+2/315*(3*A*b^2+72*a*b*B+7*a^2*(7*A+9*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d+2/21*(A*b+3*B*a)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/9*A*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,7,-2/105*(a-b)*sqrt(a+b)*(6*A*b^3-63*a^3*B-21*a*b^2*B-2*a^2*b*(41*A+70*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d/sqrt(sec(d*x+c))-2/105*(a-b)*sqrt(a+b)*(6*A*b^2-a^2*(25*A-63*B+35*C)+3*a*b*(19*A-7*B+35*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d/sqrt(sec(d*x+c))+2/105*(3*A*b^2+42*a*b*B+5*a^2*(5*A+7*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d+2/35*(3*A*b+7*B*a)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*A*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,8,2/15*(a-b)*sqrt(a+b)*(3*A*b^2+20*a*b*B+3*a^2*(3*A+5*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d/sqrt(sec(d*x+c))-2/15*sqrt(a+b)*(3*b^2*(A-5*B)-2*a*b*(6*A-10*B+15*C)+a^2*(9*A-5*B+15*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-2*b*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))+2/15*(3*A*b+5*B*a)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,9,1/3*(a-b)*sqrt(a+b)*(8*A*b+6*B*a-3*C*b)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))+1/3*sqrt(a+b)*(6*A*b^2+2*a^2*(A-3*B+3*C)-a*b*(8*A-12*B-3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-sqrt(a+b)*(2*B*b+3*C*a)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))+2*(A*b+B*a)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d-1/3*(8*A*b+6*B*a-3*C*b)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,9,1/4*(a-b)*sqrt(a+b)*(8*A*a-4*B*b-5*C*a)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-1/4*sqrt(a+b)*(a*(8*A-8*B-5*C)-2*b*(8*A+2*B+C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))-1/4*sqrt(a+b)*(8*A*b^2+12*B*a*b+3*C*a^2+4*C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d/sqrt(sec(d*x+c))-1/2*b*(4*A-C)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))-1/4*(8*A*a-4*B*b-5*C*a)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2*A*(a+b*cos(d*x+c))^(3/2)*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,9,-1/24*(a-b)*sqrt(a+b)*(24*A*b^2+30*B*a*b+3*C*a^2+16*C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d/sqrt(sec(d*x+c))+1/24*sqrt(a+b)*(3*a^2*C+4*b^2*(6*A+3*B+4*C)+2*a*b*(24*A+15*B+7*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d/sqrt(sec(d*x+c))-1/8*sqrt(a+b)*(6*a^2*b*B+8*b^3*B-a^3*C+12*a*b^2*(2*A+C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))+1/4*(2*B*b+C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/3*C*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/24*(24*A*b^2+30*B*a*b+3*C*a^2+16*C*b^2)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,10,-1/192*(a-b)*sqrt(a+b)*(24*a^2*b*B+128*b^3*B-9*a^3*C+12*a*b^2*(20*A+13*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/d/sqrt(sec(d*x+c))-1/192*sqrt(a+b)*(9*a^3*C-6*a^2*b*(4*B+C)-8*b^3*(12*A+16*B+9*C)-4*a*b^2*(60*A+28*B+39*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))+1/64*sqrt(a+b)*(8*a^3*b*B-96*a*b^3*B-3*a^4*C-24*a^2*b^2*(2*A+C)-16*b^4*(4*A+3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d/sqrt(sec(d*x+c))+1/32*(4*b^2*(4*A+3*C)+a*(8*B*b-3*C*a))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/24*(8*B*b-3*C*a)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/4*C*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/192*(24*a^2*b*B+128*b^3*B-9*a^3*C+12*a*b^2*(20*A+13*C))*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b^2/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(13/2),x,9,2/3465*(a-b)*sqrt(a+b)*(40*A*b^5+1617*a^5*B+3069*a^3*b^2*B-110*a*b^4*B+15*a^2*b^3*(17*A+33*C)+15*a^4*b*(247*A+319*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d/sqrt(sec(d*x+c))+2/3465*(a-b)*sqrt(a+b)*(40*A*b^4+10*a*b^3*(3*A-11*B)+15*a^2*b^2*(19*A-121*B+33*C)+3*a^4*(225*A-539*B+275*C)-6*a^3*b*(505*A-209*B+660*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d/sqrt(sec(d*x+c))-2/3465*(20*A*b^4-1793*a^3*b*B-55*a*b^3*B-75*a^4*(9*A+11*C)-5*a^2*b^2*(205*A+297*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d+2/3465*(15*A*b^3+539*a^3*B+825*a*b^2*B+5*a^2*b*(229*A+297*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d+2/231*(5*A*b^2+44*a*b*B+3*a^2*(9*A+11*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/99*(5*A*b+11*B*a)*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(9/2)*sin(d*x+c)/d+2/11*A*(a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(11/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(11/2),x,8,-2/315*(a-b)*sqrt(a+b)*(10*A*b^4-435*a^3*b*B-45*a*b^3*B-21*a^4*(7*A+9*C)-3*a^2*b^2*(93*A+161*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d/sqrt(sec(d*x+c))-2/315*(a-b)*sqrt(a+b)*(10*A*b^3+15*a*b^2*(11*A-3*B+21*C)-6*a^2*b*(19*A-60*B+28*C)+3*a^3*(49*A-25*B+63*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d/sqrt(sec(d*x+c))+2/315*(5*A*b^3+75*a^3*B+135*a*b^2*B+a^2*b*(163*A+231*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d+2/315*(15*A*b^2+90*a*b*B+7*a^2*(7*A+9*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/63*(5*A*b+9*B*a)*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/9*A*(a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(9/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2),x,9,2/105*(a-b)*sqrt(a+b)*(15*A*b^3+63*a^3*B+161*a*b^2*B+5*a^2*b*(29*A+49*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d/sqrt(sec(d*x+c))-2/105*sqrt(a+b)*(15*b^3*(A-7*B)-a^3*(25*A-63*B+35*C)+a^2*b*(145*A-119*B+245*C)-a*b^2*(135*A-161*B+315*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-2*b^2*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))+2/105*(15*A*b^2+56*a*b*B+5*a^2*(5*A+7*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/35*(5*A*b+7*B*a)*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*A*(a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2),x,10,1/15*(a-b)*sqrt(a+b)*(70*a*b*B+b^2*(46*A-15*C)+6*a^2*(3*A+5*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))+1/15*sqrt(a+b)*(30*A*b^3-2*a^3*(9*A-5*B+15*C)+2*a^2*b*(17*A-35*B+45*C)-a*b^2*(46*A-90*B-15*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-b*sqrt(a+b)*(2*B*b+5*C*a)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))+2/5*(5*A*b^2+10*a*b*B+a^2*(3*A+5*C))*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d-1/15*(70*a*b*B+b^2*(46*A-15*C)+6*a^2*(3*A+5*C))*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*(A*b+B*a)*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*(a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2),x,10,1/12*(a-b)*sqrt(a+b)*(24*a^2*B-12*b^2*B+a*b*(56*A-27*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-1/12*sqrt(a+b)*(a*b*(56*A-72*B-27*C)-6*b^2*(12*A+2*B+C)-8*a^2*(A-3*B+3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))-1/4*sqrt(a+b)*(8*A*b^2+20*B*a*b+15*C*a^2+4*C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))-1/2*b*(8*A*b+4*B*a-C*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))-1/12*(24*a^2*B-12*b^2*B+a*b*(56*A-27*C))*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*(5*A*b+3*B*a)*(a+b*cos(d*x+c))^(3/2)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*(a+b*cos(d*x+c))^(5/2)*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2),x,10,-1/24*(a-b)*sqrt(a+b)*(54*a*b*B-a^2*(48*A-33*C)+8*b^2*(3*A+2*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-1/24*sqrt(a+b)*(a^2*(48*A-48*B-33*C)-4*b^2*(6*A+3*B+4*C)-2*a*b*(72*A+27*B+13*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))-1/8*sqrt(a+b)*(30*a^2*b*B+8*b^3*B+5*a^3*C+20*a*b^2*(2*A+C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d/sqrt(sec(d*x+c))-1/4*b*(8*A*a-2*B*b-3*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))-1/3*b*(6*A-C)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/24*(54*a*b*B-a^2*(48*A-33*C)+8*b^2*(3*A+2*C))*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2*A*(a+b*cos(d*x+c))^(5/2)*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c)),x,10,-1/192*(a-b)*sqrt(a+b)*(264*a^2*b*B+128*b^3*B+15*a^3*C+4*a*b^2*(108*A+71*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d/sqrt(sec(d*x+c))+1/192*sqrt(a+b)*(15*a^3*C+8*b^3*(12*A+16*B+9*C)+2*a^2*b*(192*A+132*B+59*C)+4*a*b^2*(108*A+52*B+71*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d/sqrt(sec(d*x+c))-1/64*sqrt(a+b)*(40*a^3*b*B+160*a*b^3*B-5*a^4*C+120*a^2*b^2*(2*A+C)+16*b^4*(4*A+3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))+1/32*(16*A*b^2+24*B*a*b+5*C*a^2+12*C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/24*(8*B*b+5*C*a)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/4*C*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/192*(264*a^2*b*B+128*b^3*B+15*a^3*C+4*a*b^2*(108*A+71*C))*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(sec(d*x+c)),x,11,-1/1920*(a-b)*sqrt(a+b)*(150*a^3*b*B+2840*a*b^3*B-45*a^4*C+256*b^4*(5*A+4*C)+12*a^2*b^2*(220*A+141*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/d/sqrt(sec(d*x+c))-1/1920*sqrt(a+b)*(45*a^4*C-30*a^3*b*(5*B+C)-16*b^4*(80*A+45*B+64*C)-8*a*b^3*(260*A+355*B+193*C)-4*a^2*b^2*(660*A+295*B+423*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))+1/128*sqrt(a+b)*(10*a^4*b*B-240*a^2*b^3*B-96*b^5*B-3*a^5*C-40*a^3*b^2*(2*A+C)-80*a*b^4*(4*A+3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d/sqrt(sec(d*x+c))+1/320*(50*a^2*b*B+120*b^3*B-15*a^3*C+4*a*b^2*(60*A+43*C))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/240*(80*A*b^2+50*B*a*b-15*C*a^2+64*C*b^2)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/40*(10*B*b-3*C*a)*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/5*C*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/1920*(150*a^3*b*B+2840*a*b^3*B-45*a^4*C+256*b^4*(5*A+4*C)+12*a^2*b^2*(220*A+141*C))*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b^2/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(9/2)/sqrt(a+b*cos(d*x+c)),x,7,-2/105*(a-b)*sqrt(a+b)*(48*A*b^3-63*a^3*B-56*a*b^2*B+a^2*(44*A*b+70*C*b))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^5/d/sqrt(sec(d*x+c))+2/105*sqrt(a+b)*(48*A*b^3-4*a*b^2*(3*A+14*B)+a^3*(25*A-63*B+35*C)+2*a^2*b*(22*A+7*B+35*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d/sqrt(sec(d*x+c))+2/105*(24*A*b^2-28*a*b*B+5*a^2*(5*A+7*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^3/d-2/35*(6*A*b-7*B*a)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/a^2/d+2/7*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/a/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/sqrt(a+b*cos(d*x+c)),x,6,2/15*(a-b)*sqrt(a+b)*(8*A*b^2-10*a*b*B+3*a^2*(3*A+5*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/d/sqrt(sec(d*x+c))-2/15*sqrt(a+b)*(8*A*b^2-2*a*b*(A+5*B)+a^2*(9*A-5*B+15*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d/sqrt(sec(d*x+c))-2/15*(4*A*b-5*B*a)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d+2/5*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/sqrt(a+b*cos(d*x+c)),x,5,-2/3*(a-b)*sqrt(a+b)*(2*A*b-3*B*a)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/d/sqrt(sec(d*x+c))+2/3*sqrt(a+b)*(2*A*b+a*(A-3*B+3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d/sqrt(sec(d*x+c))+2/3*A*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/sqrt(a+b*cos(d*x+c)),x,6,2*A*(a-b)*sqrt(a+b)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/d/sqrt(sec(d*x+c))-2*sqrt(a+b)*(A-B)*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))-2*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/sqrt(a+b*cos(d*x+c)),x,7,-(a-b)*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d/sqrt(sec(d*x+c))+sqrt(a+b)*(2*A*b+C*a)*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/d/sqrt(sec(d*x+c))-sqrt(a+b)*(2*B*b-C*a)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))+C*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c))/sqrt(sec(d*x+c)),x,8,-1/4*(a-b)*sqrt(a+b)*(4*B*b-3*C*a)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/d/sqrt(sec(d*x+c))-1/4*sqrt(a+b)*(3*a*C-2*b*(2*B+C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))-1/4*sqrt(a+b)*(8*A*b^2-4*B*a*b+3*C*a^2+4*C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d/sqrt(sec(d*x+c))+1/2*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/4*(4*B*b-3*C*a)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b^2/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/sqrt(a+b*cos(d*x+c))/sec(d*x+c)^(3/2),x,9,-1/24*(a-b)*sqrt(a+b)*(24*A*b^2-18*B*a*b+15*C*a^2+16*C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^3/d/sqrt(sec(d*x+c))+1/24*sqrt(a+b)*(24*A*b^2-18*B*a*b+12*B*b^2+15*C*a^2-10*C*a*b+16*C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d/sqrt(sec(d*x+c))-1/8*sqrt(a+b)*(6*a^2*b*B+8*b^3*B-5*a^3*C-4*a*b^2*(2*A+C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^4/d/sqrt(sec(d*x+c))+1/3*C*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sec(d*x+c)^(3/2)+1/12*(6*B*b-5*C*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d/sqrt(sec(d*x+c))+1/24*(24*A*b^2-18*B*a*b+15*C*a^2+16*C*b^2)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b^3/d,1],
[(a*A+(A*b+B*a)*cos(d*x+c)+b*B*cos(d*x+c)^2)*sqrt(sec(d*x+c))/sqrt(a+b*cos(d*x+c)),x,8,-(a-b)*sqrt(a+b)*B*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/d/sqrt(sec(d*x+c))+sqrt(a+b)*(2*A+B)*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/d/sqrt(sec(d*x+c))-sqrt(a+b)*(2*A*b+B*a)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b/d/sqrt(sec(d*x+c))+B*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(7/2)/(a+b*cos(d*x+c))^(3/2),x,7,-2/15*(48*A*b^4+25*a^3*b*B-40*a*b^3*B-6*a^2*b^2*(4*A-5*C)-3*a^4*(3*A+5*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^5/sqrt(a+b)/d/sqrt(sec(d*x+c))-2/15*(48*A*b^3+4*a*b^2*(9*A-10*B)+6*a^2*b*(2*A-5*B+5*C)+a^3*(9*A-5*B+15*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/sqrt(a+b)/d/sqrt(sec(d*x+c))+2/15*(24*A*b^3+5*a^3*B-20*a*b^2*B-a^2*(9*A*b-15*C*b))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^3/(a^2-b^2)/d+2*(A*b^2-a*(B*b-C*a))*sec(d*x+c)^(5/2)*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-2/5*(6*A*b^2-5*a*b*B-a^2*(A-5*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/a^2/(a^2-b^2)/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x,6,2/3*(8*A*b^3+3*a^3*B-6*a*b^2*B-a^2*(5*A*b-3*C*b))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/sqrt(a+b)/d/sqrt(sec(d*x+c))+2/3*(8*A*b^2+6*a*b*(A-B)+a^2*(A-3*B+3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/sqrt(a+b)/d/sqrt(sec(d*x+c))+2*(A*b^2-a*(B*b-C*a))*sec(d*x+c)^(3/2)*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))-2/3*(4*A*b^2-3*a*b*B-a^2*(A-3*C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/(a^2-b^2)/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x,5,-2*(2*A*b^2-a*b*B-a^2*(A-C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/sqrt(a+b)/d/sqrt(sec(d*x+c))-2*(2*A*b+a*(A-B-C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/sqrt(a+b)/d/sqrt(sec(d*x+c))+2*(A*b^2-a*(B*b-C*a))*sqrt(sec(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+b*cos(d*x+c))^(3/2),x,7,2*(A*b^2-a*(B*b-C*a))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/b/sqrt(a+b)/d/sqrt(sec(d*x+c))+2*(A*b+B*b-C*a)*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b/sqrt(a+b)/d/sqrt(sec(d*x+c))-2*sqrt(a+b)*C*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^2/d/sqrt(sec(d*x+c))-2*(A*b^2-a*(B*b-C*a))*sqrt(sec(d*x+c))*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c)),x,8,-(2*A*b^2-2*B*a*b+3*C*a^2-C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/sqrt(a+b)/d/sqrt(sec(d*x+c))+(2*A*b^2-a*(b*(2*B-C)-3*a*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^2/sqrt(a+b)/d/sqrt(sec(d*x+c))-sqrt(a+b)*(2*B*b-3*C*a)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/d/sqrt(sec(d*x+c))-2*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))/sqrt(sec(d*x+c))+(2*A*b^2-2*B*a*b+3*C*a^2-C*b^2)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x,9,-1/4*(12*a^2*b*B-4*b^3*B-a*b^2*(8*A-7*C)-15*a^3*C)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a/b^3/sqrt(a+b)/d/sqrt(sec(d*x+c))-1/4*(8*A*b^2-a*b*(12*B-5*C)+15*a^2*C-2*b^2*(2*B+C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^3/sqrt(a+b)/d/sqrt(sec(d*x+c))-1/4*sqrt(a+b)*(8*A*b^2-12*B*a*b+15*C*a^2+4*C*b^2)*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticPi(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),(a+b)/b,sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/b^4/d/sqrt(sec(d*x+c))-2*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))/sec(d*x+c)^(3/2)+1/2*(4*A*b^2-4*B*a*b+5*C*a^2-C*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)/d/sqrt(sec(d*x+c))+1/4*(12*a^2*b*B-4*b^3*B-a*b^2*(8*A-7*C)-15*a^3*C)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x,7,-2/3*(16*A*b^5-3*a^5*B+15*a^3*b^2*B-8*a*b^4*B-2*a^2*b^3*(14*A-C)+a^4*(8*A*b-6*C*b))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^5/sqrt(a+b)/(a^2-b^2)/d/sqrt(sec(d*x+c))-2/3*(16*A*b^4+4*a*b^3*(3*A-2*B)-3*a^3*b*(3*A-3*B-C)-2*a^2*b^2*(8*A+3*B-C)-a^4*(A-3*B+3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/sqrt(a+b)/(a^2-b^2)/d/sqrt(sec(d*x+c))+2/3*(A*b^2-a*(B*b-C*a))*sec(d*x+c)^(3/2)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+2/3*(10*A*a^2*b^2-6*A*b^4-7*B*a^3*b+3*B*a*b^3+4*C*a^4)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c))+2/3*(8*A*b^4+8*a^3*b*B-4*a*b^3*B+a^4*(A-5*C)-a^2*b^2*(13*A-C))*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^3/(a^2-b^2)^2/d,1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x,6,2/3*(8*A*b^4+6*a^3*b*B-2*a*b^3*B+3*a^4*(A-C)-a^2*b^2*(15*A+C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^4/sqrt(a+b)/(a^2-b^2)/d/sqrt(sec(d*x+c))+2/3*(8*A*b^3+2*a*b^2*(3*A-B)-3*a^3*(A-B-C)-a^2*b*(9*A+3*B+C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/sqrt(a+b)/(a^2-b^2)/d/sqrt(sec(d*x+c))+2/3*(A*b^2-a*(B*b-C*a))*sqrt(sec(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)-2/3*(4*A*b^4+5*a^3*b*B-a*b^3*B-2*a^4*C-2*a^2*b^2*(4*A+C))*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c)+C*cos(d*x+c)^2)*sqrt(sec(d*x+c))/(a+b*cos(d*x+c))^(5/2),x,6,-2/3*(2*A*b^3+3*a^3*B+a*b^2*B-2*a^2*b*(3*A+2*C))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c)))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^3/(a-b)/(a+b)^(3/2)/d/sqrt(sec(d*x+c))-2/3*(2*A*b^2-a^2*(3*A+3*B+C)+a*b*(3*A+B+3*C))*sqrt(cos(d*x+c))*csc(d*x+c)*InverseJacobiAM(arcsin(sqrt(a+b*cos(d*x+c))/sqrt(a+b)/sqrt(cos(d*x+c))),sqrt(-(a+b)/(a-b)))*sqrt(a*(1-sec(d*x+c))/(a+b))*sqrt(a*(1+sec(d*x+c))/(a-b))/a^2/sqrt(a+b)/(a^2-b^2)/d/sqrt(sec(d*x+c))+2/3*(A*b^2-a*(B*b-C*a))*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c))+2/3*(2*A*b^3+3*a^3*B+a*b^2*B-2*a^2*b*(3*A+2*C))*sqrt(sec(d*x+c))*sin(d*x+c)/a/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1]]: