lst:=[[cos(d*x+c)^3*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x,8,3/8*a*(A+B)*x+1/5*a*(5*A+4*B)*sin(d*x+c)/d+3/8*a*(A+B)*cos(d*x+c)*sin(d*x+c)/d+1/4*a*(A+B)*cos(d*x+c)^3*sin(d*x+c)/d+1/5*a*B*cos(d*x+c)^4*sin(d*x+c)/d-1/15*a*(5*A+4*B)*sin(d*x+c)^3/d,1],
[cos(d*x+c)^2*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x,7,1/8*a*(4*A+3*B)*x+a*(A+B)*sin(d*x+c)/d+1/8*a*(4*A+3*B)*cos(d*x+c)*sin(d*x+c)/d+1/4*a*B*cos(d*x+c)^3*sin(d*x+c)/d-1/3*a*(A+B)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x,3,1/2*a*(A+B)*x+1/3*a*(3*A+2*B)*sin(d*x+c)/d+1/2*a*(A+B)*cos(d*x+c)*sin(d*x+c)/d+1/3*a*B*cos(d*x+c)^2*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x,1,1/2*a*(2*A+B)*x+a*(A+B)*sin(d*x+c)/d+1/2*a*B*cos(d*x+c)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c),x,4,a*(A+B)*x+a*A*arctanh(sin(d*x+c))/d+a*B*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^2,x,4,a*B*x+a*(A+B)*arctanh(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))*sec(d*x+c)^3,x,6,1/2*a*(A+2*B)*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))*sec(d*x+c)^4,x,7,1/2*a*(A+B)*arctanh(sin(d*x+c))/d+1/3*a*(2*A+3*B)*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))*sec(d*x+c)^5,x,7,1/8*a*(3*A+4*B)*arctanh(sin(d*x+c))/d+a*(A+B)*tan(d*x+c)/d+1/8*a*(3*A+4*B)*sec(d*x+c)*tan(d*x+c)/d+1/4*a*A*sec(d*x+c)^3*tan(d*x+c)/d+1/3*a*(A+B)*tan(d*x+c)^3/d,1],
[cos(d*x+c)^3*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)),x,9,1/16*a^2*(12*A+11*B)*x+1/5*a^2*(9*A+8*B)*sin(d*x+c)/d+1/16*a^2*(12*A+11*B)*cos(d*x+c)*sin(d*x+c)/d+1/24*a^2*(12*A+11*B)*cos(d*x+c)^3*sin(d*x+c)/d+1/30*a^2*(6*A+7*B)*cos(d*x+c)^4*sin(d*x+c)/d+1/6*B*cos(d*x+c)^4*(a^2+a^2*cos(d*x+c))*sin(d*x+c)/d-1/15*a^2*(9*A+8*B)*sin(d*x+c)^3/d,1],
[cos(d*x+c)^2*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)),x,8,1/8*a^2*(7*A+6*B)*x+1/5*a^2*(10*A+9*B)*sin(d*x+c)/d+1/8*a^2*(7*A+6*B)*cos(d*x+c)*sin(d*x+c)/d+1/20*a^2*(5*A+6*B)*cos(d*x+c)^3*sin(d*x+c)/d+1/5*B*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)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c)),x,4,1/8*a^2*(8*A+7*B)*x+1/6*a^2*(8*A+7*B)*sin(d*x+c)/d+1/24*a^2*(8*A+7*B)*cos(d*x+c)*sin(d*x+c)/d+1/12*(4*A-B)*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+1/4*B*(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)),x,2,1/2*a^2*(3*A+2*B)*x+2/3*a^2*(3*A+2*B)*sin(d*x+c)/d+1/6*a^2*(3*A+2*B)*cos(d*x+c)*sin(d*x+c)/d+1/3*B*(a+a*cos(d*x+c))^2*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c),x,5,1/2*a^2*(4*A+3*B)*x+a^2*A*arctanh(sin(d*x+c))/d+1/2*a^2*(2*A+3*B)*sin(d*x+c)/d+1/2*B*(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))*sec(d*x+c)^2,x,5,a^2*(A+2*B)*x+a^2*(2*A+B)*arctanh(sin(d*x+c))/d-a^2*(A-B)*sin(d*x+c)/d+A*(a^2+a^2*cos(d*x+c))*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^3,x,5,a^2*B*x+1/2*a^2*(3*A+4*B)*arctanh(sin(d*x+c))/d+1/2*a^2*(3*A+2*B)*tan(d*x+c)/d+1/2*A*(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*(A+B*cos(d*x+c))*sec(d*x+c)^4,x,7,1/2*a^2*(2*A+3*B)*arctanh(sin(d*x+c))/d+1/3*a^2*(5*A+6*B)*tan(d*x+c)/d+1/6*a^2*(4*A+3*B)*sec(d*x+c)*tan(d*x+c)/d+1/3*A*(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*(A+B*cos(d*x+c))*sec(d*x+c)^5,x,8,1/8*a^2*(7*A+8*B)*arctanh(sin(d*x+c))/d+1/3*a^2*(4*A+5*B)*tan(d*x+c)/d+1/8*a^2*(7*A+8*B)*sec(d*x+c)*tan(d*x+c)/d+1/12*a^2*(5*A+4*B)*sec(d*x+c)^2*tan(d*x+c)/d+1/4*A*(a^2+a^2*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*(A+B*cos(d*x+c)),x,9,1/16*a^3*(26*A+23*B)*x+1/5*a^3*(19*A+17*B)*sin(d*x+c)/d+1/16*a^3*(26*A+23*B)*cos(d*x+c)*sin(d*x+c)/d+1/40*a^3*(22*A+21*B)*cos(d*x+c)^3*sin(d*x+c)/d+1/6*a*B*cos(d*x+c)^3*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+1/15*(3*A+4*B)*cos(d*x+c)^3*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d-1/15*a^3*(19*A+17*B)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)),x,10,1/8*a^3*(15*A+13*B)*x+1/5*a^3*(15*A+13*B)*sin(d*x+c)/d+3/40*a^3*(15*A+13*B)*cos(d*x+c)*sin(d*x+c)/d+1/20*(5*A-B)*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+1/5*B*(a+a*cos(d*x+c))^4*sin(d*x+c)/a/d-1/60*a^3*(15*A+13*B)*sin(d*x+c)^3/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c)),x,8,5/8*a^3*(4*A+3*B)*x+a^3*(4*A+3*B)*sin(d*x+c)/d+3/8*a^3*(4*A+3*B)*cos(d*x+c)*sin(d*x+c)/d+1/4*B*(a+a*cos(d*x+c))^3*sin(d*x+c)/d-1/12*a^3*(4*A+3*B)*sin(d*x+c)^3/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c),x,6,1/2*a^3*(7*A+5*B)*x+a^3*A*arctanh(sin(d*x+c))/d+5/2*a^3*(A+B)*sin(d*x+c)/d+1/3*a*B*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+1/6*(3*A+5*B)*(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))*sec(d*x+c)^2,x,6,1/2*a^3*(6*A+7*B)*x+a^3*(3*A+B)*arctanh(sin(d*x+c))/d+5/2*a^3*B*sin(d*x+c)/d-1/2*(2*A-B)*(a^3+a^3*cos(d*x+c))*sin(d*x+c)/d+a*A*(a+a*cos(d*x+c))^2*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^3,x,6,a^3*(A+3*B)*x+1/2*a^3*(7*A+6*B)*arctanh(sin(d*x+c))/d-5/2*a^3*A*sin(d*x+c)/d+(2*A+B)*(a^3+a^3*cos(d*x+c))*tan(d*x+c)/d+1/2*a*A*(a+a*cos(d*x+c))^2*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^4,x,6,a^3*B*x+1/2*a^3*(5*A+7*B)*arctanh(sin(d*x+c))/d+5/2*a^3*(A+B)*tan(d*x+c)/d+1/6*(5*A+3*B)*(a^3+a^3*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/3*a*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))^3*(A+B*cos(d*x+c))*sec(d*x+c)^5,x,8,5/8*a^3*(3*A+4*B)*arctanh(sin(d*x+c))/d+1/3*a^3*(9*A+11*B)*tan(d*x+c)/d+1/24*a^3*(27*A+28*B)*sec(d*x+c)*tan(d*x+c)/d+1/6*(3*A+2*B)*(a^3+a^3*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d+1/4*a*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))^3*(A+B*cos(d*x+c))*sec(d*x+c)^6,x,9,1/8*a^3*(13*A+15*B)*arctanh(sin(d*x+c))/d+1/15*a^3*(38*A+45*B)*tan(d*x+c)/d+1/8*a^3*(13*A+15*B)*sec(d*x+c)*tan(d*x+c)/d+1/60*a^3*(43*A+45*B)*sec(d*x+c)^2*tan(d*x+c)/d+1/20*(7*A+5*B)*(a^3+a^3*cos(d*x+c))*sec(d*x+c)^3*tan(d*x+c)/d+1/5*a*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))^4*(A+B*cos(d*x+c)),x,10,1/16*a^4*(49*A+44*B)*x+1/35*a^4*(252*A+227*B)*sin(d*x+c)/d+1/16*a^4*(49*A+44*B)*cos(d*x+c)*sin(d*x+c)/d+1/280*a^4*(301*A+276*B)*cos(d*x+c)^3*sin(d*x+c)/d+1/7*a*B*cos(d*x+c)^3*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+1/42*(7*A+10*B)*cos(d*x+c)^3*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/d+7/15*(A+B)*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)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)),x,13,7/16*a^4*(8*A+7*B)*x+4/5*a^4*(8*A+7*B)*sin(d*x+c)/d+27/80*a^4*(8*A+7*B)*cos(d*x+c)*sin(d*x+c)/d+1/40*a^4*(8*A+7*B)*cos(d*x+c)^3*sin(d*x+c)/d+1/30*(6*A-B)*(a+a*cos(d*x+c))^4*sin(d*x+c)/d+1/6*B*(a+a*cos(d*x+c))^5*sin(d*x+c)/a/d-2/15*a^4*(8*A+7*B)*sin(d*x+c)^3/d,1],
[(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c)),x,11,7/8*a^4*(5*A+4*B)*x+8/5*a^4*(5*A+4*B)*sin(d*x+c)/d+27/40*a^4*(5*A+4*B)*cos(d*x+c)*sin(d*x+c)/d+1/20*a^4*(5*A+4*B)*cos(d*x+c)^3*sin(d*x+c)/d+1/5*B*(a+a*cos(d*x+c))^4*sin(d*x+c)/d-4/15*a^4*(5*A+4*B)*sin(d*x+c)^3/d,1],
[(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c),x,7,1/8*a^4*(48*A+35*B)*x+a^4*A*arctanh(sin(d*x+c))/d+5/8*a^4*(8*A+7*B)*sin(d*x+c)/d+1/4*a*B*(a+a*cos(d*x+c))^3*sin(d*x+c)/d+1/12*(4*A+7*B)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/d+1/24*(32*A+35*B)*(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))*sec(d*x+c)^2,x,7,1/2*a^4*(13*A+12*B)*x+a^4*(4*A+B)*arctanh(sin(d*x+c))/d+5/2*a^4*(A+2*B)*sin(d*x+c)/d-1/3*(3*A-B)*(a^2+a^2*cos(d*x+c))^2*sin(d*x+c)/d-1/6*(3*A-8*B)*(a^4+a^4*cos(d*x+c))*sin(d*x+c)/d+a*A*(a+a*cos(d*x+c))^3*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^3,x,7,1/2*a^4*(8*A+13*B)*x+1/2*a^4*(13*A+8*B)*arctanh(sin(d*x+c))/d-5/2*a^4*(A-B)*sin(d*x+c)/d-1/2*(6*A+B)*(a^4+a^4*cos(d*x+c))*sin(d*x+c)/d+1/2*(5*A+2*B)*(a^2+a^2*cos(d*x+c))^2*tan(d*x+c)/d+1/2*a*A*(a+a*cos(d*x+c))^3*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^4,x,7,a^4*(A+4*B)*x+1/2*a^4*(12*A+13*B)*arctanh(sin(d*x+c))/d-5/2*a^4*(2*A+B)*sin(d*x+c)/d+1/3*(11*A+9*B)*(a^4+a^4*cos(d*x+c))*tan(d*x+c)/d+1/2*(2*A+B)*(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],
[(a+a*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^5,x,7,a^4*B*x+1/8*a^4*(35*A+48*B)*arctanh(sin(d*x+c))/d+5/8*a^4*(7*A+8*B)*tan(d*x+c)/d+1/24*(35*A+32*B)*(a^4+a^4*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/12*(7*A+4*B)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^2*tan(d*x+c)/d+1/4*a*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))^4*(A+B*cos(d*x+c))*sec(d*x+c)^6,x,9,7/8*a^4*(4*A+5*B)*arctanh(sin(d*x+c))/d+1/15*a^4*(83*A+100*B)*tan(d*x+c)/d+1/120*a^4*(244*A+275*B)*sec(d*x+c)*tan(d*x+c)/d+1/30*(26*A+25*B)*(a^4+a^4*cos(d*x+c))*sec(d*x+c)^2*tan(d*x+c)/d+1/20*(8*A+5*B)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^3*tan(d*x+c)/d+1/5*a*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))^4*(A+B*cos(d*x+c))*sec(d*x+c)^7,x,10,7/16*a^4*(7*A+8*B)*arctanh(sin(d*x+c))/d+1/15*a^4*(72*A+83*B)*tan(d*x+c)/d+7/16*a^4*(7*A+8*B)*sec(d*x+c)*tan(d*x+c)/d+1/120*a^4*(159*A+176*B)*sec(d*x+c)^2*tan(d*x+c)/d+1/120*(73*A+72*B)*(a^4+a^4*cos(d*x+c))*sec(d*x+c)^3*tan(d*x+c)/d+1/10*(3*A+2*B)*(a^2+a^2*cos(d*x+c))^2*sec(d*x+c)^4*tan(d*x+c)/d+1/6*a*A*(a+a*cos(d*x+c))^3*sec(d*x+c)^5*tan(d*x+c)/d,1],
[cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x,7,-3/8*(4*A-5*B)*x/a+4*(A-B)*sin(d*x+c)/a/d-3/8*(4*A-5*B)*cos(d*x+c)*sin(d*x+c)/a/d-1/4*(4*A-5*B)*cos(d*x+c)^3*sin(d*x+c)/a/d+(A-B)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))-4/3*(A-B)*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x,6,3/2*(A-B)*x/a-(3*A-4*B)*sin(d*x+c)/a/d+3/2*(A-B)*cos(d*x+c)*sin(d*x+c)/a/d+(A-B)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))+1/3*(3*A-4*B)*sin(d*x+c)^3/a/d,1],
[cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x,2,-(A-B)*x/a+1/2*B*x/a+(A-B)*sin(d*x+c)/a/d+1/2*B*cos(d*x+c)*sin(d*x+c)/a/d+(A-B)*sin(d*x+c)/a/d/(1+cos(d*x+c)),1],
[cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x,5,(A-B)*x/a+B*sin(d*x+c)/a/d-(A-B)*sin(d*x+c)/a/d/(1+cos(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x,2,B*x/a+(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*sec(d*x+c)/(a+a*cos(d*x+c)),x,3,A*arctanh(sin(d*x+c))/a/d-(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*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)*tan(d*x+c)/a/d-(A-B)*tan(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c)),x,6,1/2*(3*A-2*B)*arctanh(sin(d*x+c))/a/d-2*(A-B)*tan(d*x+c)/a/d+1/2*(3*A-2*B)*sec(d*x+c)*tan(d*x+c)/a/d-(A-B)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*sec(d*x+c)^4/(a+a*cos(d*x+c)),x,6,-3/2*(A-B)*arctanh(sin(d*x+c))/a/d+(4*A-3*B)*tan(d*x+c)/a/d-3/2*(A-B)*sec(d*x+c)*tan(d*x+c)/a/d-(A-B)*sec(d*x+c)^2*tan(d*x+c)/d/(a+a*cos(d*x+c))+1/3*(4*A-3*B)*tan(d*x+c)^3/a/d,1],
[cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x,7,1/2*(7*A-10*B)*x/a^2-4*(2*A-3*B)*sin(d*x+c)/a^2/d+1/2*(7*A-10*B)*cos(d*x+c)*sin(d*x+c)/a^2/d+1/3*(7*A-10*B)*cos(d*x+c)^3*sin(d*x+c)/a^2/d/(1+cos(d*x+c))+1/3*(A-B)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))^2+4/3*(2*A-3*B)*sin(d*x+c)^3/a^2/d,1],
[cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x,3,-1/2*(4*A-7*B)*x/a^2+2/3*(5*A-8*B)*sin(d*x+c)/a^2/d-1/2*(4*A-7*B)*cos(d*x+c)*sin(d*x+c)/a^2/d+1/3*(5*A-8*B)*cos(d*x+c)^2*sin(d*x+c)/a^2/d/(1+cos(d*x+c))+1/3*(A-B)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x,6,(A-2*B)*x/a^2-1/3*(A-4*B)*sin(d*x+c)/a^2/d-(A-2*B)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))+1/3*(A-B)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x,4,B*x/a^2+1/3*(2*A-5*B)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x,2,1/3*(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2+1/3*(A+2*B)*sin(d*x+c)/d/(a^2+a^2*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*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)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+B*cos(d*x+c))*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+2/3*(5*A-2*B)*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)*tan(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^2,x,7,1/2*(7*A-4*B)*arctanh(sin(d*x+c))/a^2/d-2/3*(8*A-5*B)*tan(d*x+c)/a^2/d+1/2*(7*A-4*B)*sec(d*x+c)*tan(d*x+c)/a^2/d-1/3*(8*A-5*B)*sec(d*x+c)*tan(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A-B)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+B*cos(d*x+c))*sec(d*x+c)^4/(a+a*cos(d*x+c))^2,x,7,-1/2*(10*A-7*B)*arctanh(sin(d*x+c))/a^2/d+4*(3*A-2*B)*tan(d*x+c)/a^2/d-1/2*(10*A-7*B)*sec(d*x+c)*tan(d*x+c)/a^2/d-1/3*(10*A-7*B)*sec(d*x+c)^2*tan(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A-B)*sec(d*x+c)^2*tan(d*x+c)/d/(a+a*cos(d*x+c))^2+4/3*(3*A-2*B)*tan(d*x+c)^3/a^2/d,1],
[cos(d*x+c)^5*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x,8,1/2*(13*A-23*B)*x/a^3-4/5*(19*A-34*B)*sin(d*x+c)/a^3/d+1/2*(13*A-23*B)*cos(d*x+c)*sin(d*x+c)/a^3/d+1/5*(A-B)*cos(d*x+c)^5*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/15*(8*A-13*B)*cos(d*x+c)^4*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+1/3*(13*A-23*B)*cos(d*x+c)^3*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c))+4/15*(19*A-34*B)*sin(d*x+c)^3/a^3/d,1],
[cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x,4,-1/2*(6*A-13*B)*x/a^3+8/15*(9*A-19*B)*sin(d*x+c)/a^3/d-1/2*(6*A-13*B)*cos(d*x+c)*sin(d*x+c)/a^3/d+1/5*(A-B)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/15*(6*A-11*B)*cos(d*x+c)^3*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+4/15*(9*A-19*B)*cos(d*x+c)^2*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x,7,(A-3*B)*x/a^3-1/15*(7*A-27*B)*sin(d*x+c)/a^3/d+1/5*(A-B)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/15*(4*A-9*B)*cos(d*x+c)^2*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-(A-3*B)*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))/(a+a*cos(d*x+c))^3,x,5,B*x/a^3+1/5*(A-B)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(2*A-7*B)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+1/15*(4*A-29*B)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x,4,-1/5*(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/15*(3*A-8*B)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+1/15*(3*A+7*B)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x,3,1/5*(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/15*(2*A+3*B)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+1/15*(2*A+3*B)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*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)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(7*A-2*B)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-2/15*(11*A-B)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*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)*tan(d*x+c)/a^3/d-1/5*(A-B)*tan(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(9*A-4*B)*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))*sec(d*x+c)^3/(a+a*cos(d*x+c))^3,x,8,1/2*(13*A-6*B)*arctanh(sin(d*x+c))/a^3/d-8/15*(19*A-9*B)*tan(d*x+c)/a^3/d+1/2*(13*A-6*B)*sec(d*x+c)*tan(d*x+c)/a^3/d-1/5*(A-B)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(11*A-6*B)*sec(d*x+c)*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^2-4/15*(19*A-9*B)*sec(d*x+c)*tan(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[cos(d*x+c)^5*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x,5,-1/2*(8*A-21*B)*x/a^4+8/105*(83*A-216*B)*sin(d*x+c)/a^4/d-1/2*(8*A-21*B)*cos(d*x+c)*sin(d*x+c)/a^4/d+1/105*(52*A-129*B)*cos(d*x+c)^3*sin(d*x+c)/a^4/d/(1+cos(d*x+c))^2+4/105*(83*A-216*B)*cos(d*x+c)^2*sin(d*x+c)/a^4/d/(1+cos(d*x+c))+1/7*(A-B)*cos(d*x+c)^5*sin(d*x+c)/d/(a+a*cos(d*x+c))^4+1/5*(A-2*B)*cos(d*x+c)^4*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^3,1],
[cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x,8,(A-4*B)*x/a^4-1/105*(55*A-244*B)*sin(d*x+c)/a^4/d+1/105*(25*A-88*B)*cos(d*x+c)^2*sin(d*x+c)/a^4/d/(1+cos(d*x+c))^2-(A-4*B)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))+1/7*(A-B)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))^4+1/35*(5*A-12*B)*cos(d*x+c)^3*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))/(a+a*cos(d*x+c))^4,x,6,B*x/a^4-1/105*(6*A-55*B)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))^2+1/105*(12*A-215*B)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))+1/7*(A-B)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))^4+1/35*(3*A-10*B)*cos(d*x+c)^2*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))/(a+a*cos(d*x+c))^4,x,5,-2/105*(A+27*B)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))^2+1/105*(13*A+36*B)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))+1/7*(A-B)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c))^4-1/35*(A-8*B)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^3,1],
[cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x,5,-1/7*(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c))^4+1/35*(4*A-11*B)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^3+1/105*(8*A+13*B)*sin(d*x+c)/d/(a^2+a^2*cos(d*x+c))^2+1/105*(8*A+13*B)*sin(d*x+c)/d/(a^4+a^4*cos(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^4,x,4,1/7*(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c))^4+1/35*(3*A+4*B)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^3+2/105*(3*A+4*B)*sin(d*x+c)/d/(a^2+a^2*cos(d*x+c))^2+2/105*(3*A+4*B)*sin(d*x+c)/d/(a^4+a^4*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*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)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))^2-2/105*(80*A-3*B)*sin(d*x+c)/a^4/d/(1+cos(d*x+c))-1/7*(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c))^4-1/35*(10*A-3*B)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^3,1],
[(A+B*cos(d*x+c))*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+8/105*(83*A-20*B)*tan(d*x+c)/a^4/d-1/105*(88*A-25*B)*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)*tan(d*x+c)/d/(a+a*cos(d*x+c))^4-1/35*(12*A-5*B)*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^3,1],
[(A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^4,x,9,1/2*(21*A-8*B)*arctanh(sin(d*x+c))/a^4/d-8/105*(216*A-83*B)*tan(d*x+c)/a^4/d+1/2*(21*A-8*B)*sec(d*x+c)*tan(d*x+c)/a^4/d-1/105*(129*A-52*B)*sec(d*x+c)*tan(d*x+c)/a^4/d/(1+cos(d*x+c))^2-4/105*(216*A-83*B)*sec(d*x+c)*tan(d*x+c)/a^4/d/(1+cos(d*x+c))-1/7*(A-B)*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],
[cos(d*x+c)^3*sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x,5,4/45*a*(9*A+8*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/63*a*(9*A+8*B)*cos(d*x+c)^3*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/9*a*B*cos(d*x+c)^4*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-8/315*(9*A+8*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+4/105*(9*A+8*B)*(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)),x,4,2/15*a*(7*A+6*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/7*a*B*cos(d*x+c)^3*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-4/105*(7*A+6*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/35*(7*A+6*B)*(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)),x,4,2/15*a*(5*A+7*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*(5*A-2*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/5*B*(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)),x,2,2/3*a*(3*A+B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/3*B*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))*sec(d*x+c),x,3,2*sqrt(a)*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+2*a*B*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^2,x,3,sqrt(a)*(A+2*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+a*A*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^3,x,4,1/4*sqrt(a)*(3*A+4*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/4*a*(3*A+4*B)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/2*a*A*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^4,x,5,1/8*sqrt(a)*(5*A+6*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/8*a*(5*A+6*B)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/12*a*(5*A+6*B)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/3*a*A*sec(d*x+c)^2*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)^3*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x,6,4/495*a^2*(187*A+168*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/693*a^2*(187*A+168*B)*cos(d*x+c)^3*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/99*a^2*(11*A+12*B)*cos(d*x+c)^4*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-8/3465*a*(187*A+168*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/11*a*B*cos(d*x+c)^4*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+4/1155*(187*A+168*B)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[cos(d*x+c)^2*(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x,5,2/45*a^2*(39*A+34*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/63*a^2*(9*A+10*B)*cos(d*x+c)^3*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-4/315*a*(39*A+34*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/9*a*B*cos(d*x+c)^3*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/105*(39*A+34*B)*(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)),x,5,8/105*a^2*(21*A+19*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*a*(21*A+19*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/35*(7*A-2*B)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/7*B*(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)),x,3,8/15*a^2*(5*A+3*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*a*(5*A+3*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/5*B*(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))*sec(d*x+c),x,4,2*a^(3/2)*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+2/3*a^2*(3*A+4*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/3*a*B*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x,4,a^(3/2)*(3*A+2*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-a^2*(A-2*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+a*A*sqrt(a+a*cos(d*x+c))*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x,4,1/4*a^(3/2)*(7*A+12*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/4*a^2*(5*A+4*B)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/2*a*A*sqrt(a+a*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x,5,1/8*a^(3/2)*(11*A+14*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/8*a^2*(11*A+14*B)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/12*a^2*(7*A+6*B)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/3*a*A*sqrt(a+a*cos(d*x+c))*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))*sec(d*x+c)^5,x,6,1/64*a^(3/2)*(75*A+88*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/64*a^2*(75*A+88*B)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/96*a^2*(75*A+88*B)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/24*a^2*(9*A+8*B)*sec(d*x+c)^2*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)^3*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)),x,6,2/495*a^3*(803*A+710*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/693*a^3*(209*A+194*B)*cos(d*x+c)^3*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-4/3465*a^2*(803*A+710*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/99*a^2*(11*A+14*B)*cos(d*x+c)^3*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/1155*a*(803*A+710*B)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/11*a*B*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))^(5/2)*(A+B*cos(d*x+c)),x,6,64/315*a^3*(15*A+13*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+16/315*a^2*(15*A+13*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/105*a*(15*A+13*B)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/63*(9*A-2*B)*(a+a*cos(d*x+c))^(5/2)*sin(d*x+c)/d+2/9*B*(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)),x,4,64/105*a^3*(7*A+5*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+16/105*a^2*(7*A+5*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/35*a*(7*A+5*B)*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d+2/7*B*(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))*sec(d*x+c),x,5,2*a^(5/2)*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+2/15*a^3*(35*A+32*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*a^2*(5*A+8*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2/5*a*B*(a+a*cos(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))*sec(d*x+c)^2,x,5,a^(5/2)*(5*A+2*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/3*a^3*(3*A+14*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/3*a^2*(3*A-2*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+a*A*(a+a*cos(d*x+c))^(3/2)*tan(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x,5,1/4*a^(5/2)*(19*A+20*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/4*a^3*(9*A-4*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/4*a^2*(7*A+4*B)*sqrt(a+a*cos(d*x+c))*tan(d*x+c)/d+1/2*a*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))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x,5,1/8*a^(5/2)*(25*A+38*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/24*a^3*(49*A+54*B)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/4*a^2*(3*A+2*B)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/3*a*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))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^5,x,6,1/64*a^(5/2)*(163*A+200*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/64*a^3*(163*A+200*B)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/96*a^3*(95*A+104*B)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/24*a^2*(11*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+a*cos(d*x+c))^(3/2)*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))*sec(d*x+c)^6,x,7,1/128*a^(5/2)*(283*A+326*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/128*a^3*(283*A+326*B)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/192*a^3*(283*A+326*B)*sec(d*x+c)*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/240*a^3*(157*A+170*B)*sec(d*x+c)^2*tan(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/40*a^2*(13*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+a*cos(d*x+c))^(3/2)*sec(d*x+c)^4*tan(d*x+c)/d,1],
[cos(d*x+c)^3*(A+B*cos(d*x+c))/sqrt(a+a*cos(d*x+c)),x,7,-sqrt(2)*(A-B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+4/105*(49*A-37*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/35*(7*A-B)*cos(d*x+c)^2*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/7*B*cos(d*x+c)^3*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-2/105*(7*A-31*B)*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))/sqrt(a+a*cos(d*x+c)),x,6,sqrt(2)*(A-B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-4/15*(5*A-7*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/5*B*cos(d*x+c)^2*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*(5*A-B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a/d,1],
[cos(d*x+c)*(A+B*cos(d*x+c))/sqrt(a+a*cos(d*x+c)),x,5,-sqrt(2)*(A-B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+2/3*(3*A-2*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/3*B*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a/d,1],
[(A+B*cos(d*x+c))/sqrt(a+a*cos(d*x+c)),x,3,sqrt(2)*(A-B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+2*B*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*sec(d*x+c)/sqrt(a+a*cos(d*x+c)),x,5,2*A*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-sqrt(2)*(A-B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d,1],
[(A+B*cos(d*x+c))*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)*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))*sec(d*x+c)^3/sqrt(a+a*cos(d*x+c)),x,7,1/4*(7*A-4*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-sqrt(2)*(A-B)*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],
[cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x,8,-1/2*(15*A-19*B)*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)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/105*(651*A-799*B)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))+1/70*(63*A-67*B)*cos(d*x+c)^2*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/14*(7*A-11*B)*cos(d*x+c)^3*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/210*(273*A-397*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a^2/d,1],
[cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x,7,1/2*(11*A-15*B)*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)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)-1/15*(65*A-93*B)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/10*(5*A-9*B)*cos(d*x+c)^2*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))+1/30*(35*A-39*B)*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))/(a+a*cos(d*x+c))^(3/2),x,6,-1/2*(7*A-11*B)*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)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/3*(9*A-13*B)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/6*(3*A-7*B)*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))/(a+a*cos(d*x+c))^(3/2),x,5,1/2*(3*A-7*B)*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)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+2*B*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x,3,1/2*(A+3*B)*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)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+B*cos(d*x+c))*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)*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)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+B*cos(d*x+c))*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)*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)*tan(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/2*(3*A-B)*tan(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^(3/2),x,8,1/4*(19*A-12*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(3/2)/d-1/2*(13*A-9*B)*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)*tan(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/2*(A-B)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/2*(2*A-B)*sec(d*x+c)*tan(d*x+c)/a/d/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x,8,1/16*(163*A-283*B)*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)*cos(d*x+c)^4*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)+1/16*(13*A-21*B)*cos(d*x+c)^3*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)-1/120*(985*A-1729*B)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))-1/80*(85*A-157*B)*cos(d*x+c)^2*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))+1/240*(475*A-787*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/a^3/d,1],
[cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x,7,-1/16*(75*A-163*B)*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)*cos(d*x+c)^3*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)+1/16*(9*A-17*B)*cos(d*x+c)^2*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+1/24*(93*A-197*B)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))-1/48*(39*A-95*B)*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))/(a+a*cos(d*x+c))^(5/2),x,6,1/16*(19*A-75*B)*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)*cos(d*x+c)^2*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(5*A-13*B)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)-1/4*(A-9*B)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x,5,1/16*(5*A+19*B)*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)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)+1/16*(5*A-13*B)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x,4,1/16*(3*A+5*B)*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)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)+1/16*(3*A+5*B)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+B*cos(d*x+c))*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)*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)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(11*A-3*B)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+B*cos(d*x+c))*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)*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)*tan(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(15*A-7*B)*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+1/16*(35*A-11*B)*tan(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*sec(d*x+c)^3/(a+a*cos(d*x+c))^(5/2),x,9,1/4*(39*A-20*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(5/2)/d-1/16*(219*A-115*B)*arctanh(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(5/2)/d-7/16*(9*A-5*B)*tan(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))-1/4*(A-B)*sec(d*x+c)*tan(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(19*A-11*B)*sec(d*x+c)*tan(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)+1/16*(31*A-15*B)*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+B*cos(d*x+c)),x,8,2/15*a*(9*A+7*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+10/21*a*(A+B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+10/21*a*(A+B)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*a*(9*A+7*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*a*(A+B)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/9*a*B*cos(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x,7,6/5*a*(A+B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*a*(7*A+5*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*a*(7*A+5*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*a*(A+B)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*a*B*cos(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x,6,2/5*a*(5*A+3*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*a*(A+B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*a*(A+B)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*a*B*cos(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c))/sqrt(cos(d*x+c)),x,5,2*a*(A+B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*a*(3*A+B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*a*B*sqrt(cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x,5,-2*a*(A-B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2*a*(A+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)),1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x,6,-2*a*(A+B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*a*(A+3*B)*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))/cos(d*x+c)^(7/2),x,7,-2/5*a*(3*A+5*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*a*(A+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*(A+B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*a*(3*A+5*B)*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)),x,8,4/15*a^2*(9*A+8*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^2*(6*A+5*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/21*a^2*(6*A+5*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d+4/45*a^2*(9*A+8*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/63*a^2*(9*A+11*B)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/9*B*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)),x,7,4/5*a^2*(4*A+3*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^2*(7*A+6*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/21*a^2*(7*A+6*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/35*a^2*(7*A+9*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*B*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))/sqrt(cos(d*x+c)),x,6,4/5*a^2*(5*A+4*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/3*a^2*(2*A+B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/15*a^2*(5*A+7*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*B*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))/cos(d*x+c)^(3/2),x,6,4*a^2*B*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/3*a^2*(3*A+2*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-2/3*a^2*(3*A-B)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2*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+B*cos(d*x+c))/cos(d*x+c)^(5/2),x,6,-4*a^2*A*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/3*a^2*(2*A+3*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*a^2*(5*A+3*B)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*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+B*cos(d*x+c))/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)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/15*a^2*(7*A+5*B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+4/5*a^2*(4*A+5*B)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/5*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+B*cos(d*x+c))/cos(d*x+c)^(9/2),x,8,-4/5*a^2*(3*A+4*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^2*(6*A+7*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/35*a^2*(9*A+7*B)*sin(d*x+c)/d/cos(d*x+c)^(5/2)+4/21*a^2*(6*A+7*B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+4/5*a^2*(3*A+4*B)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/7*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+B*cos(d*x+c)),x,9,4/15*a^3*(17*A+15*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/231*a^3*(121*A+105*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/231*a^3*(121*A+105*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d+4/45*a^3*(17*A+15*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+20/693*a^3*(22*A+21*B)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/11*a*B*cos(d*x+c)^(5/2)*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+2/99*(11*A+15*B)*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)),x,8,4/15*a^3*(21*A+17*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^3*(13*A+11*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/21*a^3*(13*A+11*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d+4/105*a^3*(24*A+23*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/9*a*B*cos(d*x+c)^(3/2)*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+2/63*(9*A+13*B)*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))/sqrt(cos(d*x+c)),x,7,4/5*a^3*(9*A+7*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^3*(21*A+13*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/105*a^3*(42*A+41*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/7*a*B*sqrt(cos(d*x+c))*(a+a*cos(d*x+c))^2*sin(d*x+c)/d+2/35*(7*A+11*B)*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))/cos(d*x+c)^(3/2),x,7,4/5*a^3*(5*A+9*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/3*a^3*(5*A+3*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-4/15*a^3*(5*A-6*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2*a*A*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/sqrt(cos(d*x+c))-2/5*(5*A-B)*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))/cos(d*x+c)^(5/2),x,7,-4*a^3*(A-B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+20/3*a^3*(A+B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-4/3*a^3*(4*A+B)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/3*a*A*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/3*(7*A+3*B)*(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))/cos(d*x+c)^(7/2),x,7,-4/5*a^3*(9*A+5*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/3*a^3*(3*A+5*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/15*a^3*(21*A+20*B)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/5*a*A*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/15*(9*A+5*B)*(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))/cos(d*x+c)^(9/2),x,8,-4/5*a^3*(7*A+9*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^3*(13*A+21*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/105*a^3*(41*A+42*B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+4/5*a^3*(7*A+9*B)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/7*a*A*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/35*(11*A+7*B)*(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))/cos(d*x+c)^(11/2),x,9,-4/15*a^3*(17*A+21*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+4/21*a^3*(11*A+13*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+4/105*a^3*(23*A+24*B)*sin(d*x+c)/d/cos(d*x+c)^(5/2)+4/21*a^3*(11*A+13*B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+4/15*a^3*(17*A+21*B)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/9*a*A*(a+a*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(9/2)+2/63*(13*A+9*B)*(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))/(a+a*cos(d*x+c)),x,6,-3/5*(5*A-7*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d+5/3*(A-B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d+5/3*(A-B)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d-1/5*(5*A-7*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/a/d+(A-B)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x,5,3*(A-B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d-1/3*(3*A-5*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d-1/3*(3*A-5*B)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d+(A-B)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c))/(a+a*cos(d*x+c)),x,4,-(A-3*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d+(A-B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d+(A-B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c))/sqrt(cos(d*x+c))/(a+a*cos(d*x+c)),x,4,(A-B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d+(A+B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d-(A-B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x,5,-(3*A-B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d-(A-B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d+(3*A-B)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))-(A-B)*sin(d*x+c)/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x,6,3*(A-B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d+1/3*(5*A-3*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d+1/3*(5*A-3*B)*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)-3*(A-B)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))-(A-B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c)),1],
[cos(d*x+c)^(7/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x,7,-7/5*(5*A-8*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d+5/3*(2*A-3*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d+5/3*(2*A-3*B)*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d-7/15*(5*A-8*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/a^2/d+(2*A-3*B)*cos(d*x+c)^(5/2)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))+1/3*(A-B)*cos(d*x+c)^(7/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x,6,(4*A-7*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d-5/3*(A-2*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d-5/3*(A-2*B)*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d+1/3*(4*A-7*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/a^2/d/(1+cos(d*x+c))+1/3*(A-B)*cos(d*x+c)^(5/2)*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))/(a+a*cos(d*x+c))^2,x,5,-(A-4*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d+1/3*(2*A-5*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d+1/3*(2*A-5*B)*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d/(1+cos(d*x+c))+1/3*(A-B)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2,x,5,-B*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d+1/3*(A+2*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d+B*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d/(1+cos(d*x+c))+1/3*(A-B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+B*cos(d*x+c))/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^2,x,5,A*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d+1/3*(2*A+B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d-A*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d/(1+cos(d*x+c))-1/3*(A-B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^2,1],
[(A+B*cos(d*x+c))/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)*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)*sin(d*x+c)/a^2/d/sqrt(cos(d*x+c))/(1+cos(d*x+c))-1/3*(A-B)*sin(d*x+c)/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^2,1],
[(A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^2,x,7,(7*A-4*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d+5/3*(2*A-B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d+5/3*(2*A-B)*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2)-(7*A-4*B)*sin(d*x+c)/a^2/d/sqrt(cos(d*x+c))-1/3*(7*A-4*B)*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2)/(1+cos(d*x+c))-1/3*(A-B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,1],
[cos(d*x+c)^(9/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x,8,-7/10*(17*A-33*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d+1/2*(11*A-21*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d+1/2*(11*A-21*B)*sqrt(cos(d*x+c))*sin(d*x+c)/a^3/d-7/30*(17*A-33*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/a^3/d+1/5*(A-B)*cos(d*x+c)^(9/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/15*(7*A-12*B)*cos(d*x+c)^(7/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+3/10*(11*A-21*B)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/(a^3+a^3*cos(d*x+c)),1],
[cos(d*x+c)^(7/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3,x,7,7/10*(7*A-17*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d-1/6*(13*A-33*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d-1/6*(13*A-33*B)*sqrt(cos(d*x+c))*sin(d*x+c)/a^3/d+1/5*(A-B)*cos(d*x+c)^(7/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/3*(A-2*B)*cos(d*x+c)^(5/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+7/30*(7*A-17*B)*cos(d*x+c)^(3/2)*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))/(a+a*cos(d*x+c))^3,x,6,-1/10*(9*A-49*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d+1/6*(3*A-13*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d+1/5*(A-B)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/15*(3*A-8*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+1/6*(3*A-13*B)*sqrt(cos(d*x+c))*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))/(a+a*cos(d*x+c))^3,x,6,-1/10*(A+9*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d+1/6*(A+3*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d+1/5*(A-B)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/15*(A-6*B)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2+1/10*(A+9*B)*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))/(a+a*cos(d*x+c))^3,x,6,1/10*(A-B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d+1/6*(A+B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d+1/5*(A-B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^3+1/15*(A+4*B)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/10*(A-B)*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))/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^3,x,6,1/10*(9*A+B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d+1/6*(3*A+B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d-1/5*(A-B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^3-1/15*(6*A-B)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^2-1/10*(9*A+B)*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))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x,7,-1/10*(49*A-9*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d-1/6*(13*A-3*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d+1/10*(49*A-9*B)*sin(d*x+c)/a^3/d/sqrt(cos(d*x+c))-1/5*(A-B)*sin(d*x+c)/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^3-1/15*(8*A-3*B)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^2-1/6*(13*A-3*B)*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))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^3,x,8,7/10*(17*A-7*B)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d+1/6*(33*A-13*B)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d+1/6*(33*A-13*B)*sin(d*x+c)/a^3/d/cos(d*x+c)^(3/2)-7/10*(17*A-7*B)*sin(d*x+c)/a^3/d/sqrt(cos(d*x+c))-1/5*(A-B)*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))^2-7/30*(17*A-7*B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/(a^3+a^3*cos(d*x+c)),1],
[cos(d*x+c)^(5/2)*sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x,6,5/64*sqrt(a)*(8*A+7*B)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+5/64*a*(8*A+7*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+5/96*a*(8*A+7*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/24*a*(8*A+7*B)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/4*a*B*cos(d*x+c)^(7/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x,5,1/8*sqrt(a)*(6*A+5*B)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/8*a*(6*A+5*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/12*a*(6*A+5*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/3*a*B*cos(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c)),x,4,1/4*sqrt(a)*(4*A+3*B)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/4*a*(4*A+3*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/2*a*B*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c))/sqrt(cos(d*x+c)),x,3,sqrt(a)*(2*A+B)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+a*B*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x,3,2*sqrt(a)*B*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+2*a*A*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x,2,2/3*a*A*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+2/3*a*(2*A+3*B)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x,3,2/5*a*A*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+2/15*a*(4*A+5*B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+4/15*a*(4*A+5*B)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x,4,2/7*a*A*sin(d*x+c)/d/cos(d*x+c)^(7/2)/sqrt(a+a*cos(d*x+c))+2/35*a*(6*A+7*B)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+8/105*a*(6*A+7*B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+16/105*a*(6*A+7*B)*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+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x,6,1/64*a^(3/2)*(88*A+75*B)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/64*a^2*(88*A+75*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/96*a^2*(88*A+75*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/24*a^2*(8*A+9*B)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/4*a*B*cos(d*x+c)^(5/2)*sqrt(a+a*cos(d*x+c))*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)),x,5,1/8*a^(3/2)*(14*A+11*B)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/8*a^2*(14*A+11*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/12*a^2*(6*A+7*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/3*a*B*cos(d*x+c)^(3/2)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/sqrt(cos(d*x+c)),x,4,1/4*a^(3/2)*(12*A+7*B)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/4*a^2*(4*A+5*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/2*a*B*sqrt(cos(d*x+c))*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x,4,a^(3/2)*(2*A+3*B)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-a^2*(2*A-B)*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)),1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x,4,2*a^(3/2)*B*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+2/3*a^2*(4*A+3*B)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/3*a*A*sqrt(a+a*cos(d*x+c))*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))/cos(d*x+c)^(7/2),x,3,2/15*a^2*(6*A+5*B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+2/15*a^2*(18*A+25*B)*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)^(5/2),1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x,4,2/35*a^2*(8*A+7*B)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+2/105*a^2*(52*A+63*B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+4/105*a^2*(52*A+63*B)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/7*a*A*sqrt(a+a*cos(d*x+c))*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))/cos(d*x+c)^(11/2),x,5,2/63*a^2*(10*A+9*B)*sin(d*x+c)/d/cos(d*x+c)^(7/2)/sqrt(a+a*cos(d*x+c))+2/105*a^2*(34*A+39*B)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+8/315*a^2*(34*A+39*B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+16/315*a^2*(34*A+39*B)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/9*a*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))^(5/2)*(A+B*cos(d*x+c)),x,7,1/128*a^(5/2)*(326*A+283*B)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/128*a^3*(326*A+283*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/192*a^3*(326*A+283*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/240*a^3*(170*A+157*B)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/40*a^2*(10*A+13*B)*cos(d*x+c)^(5/2)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+1/5*a*B*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))^(5/2)*(A+B*cos(d*x+c)),x,6,1/64*a^(5/2)*(200*A+163*B)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/64*a^3*(200*A+163*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/96*a^3*(104*A+95*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/24*a^2*(8*A+11*B)*cos(d*x+c)^(3/2)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+1/4*a*B*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))^(5/2)*(A+B*cos(d*x+c))/sqrt(cos(d*x+c)),x,5,1/8*a^(5/2)*(38*A+25*B)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+1/24*a^3*(54*A+49*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/4*a^2*(2*A+3*B)*sqrt(cos(d*x+c))*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+1/3*a*B*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))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x,5,1/4*a^(5/2)*(20*A+19*B)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/4*a^3*(4*A-9*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-1/2*a^2*(4*A-B)*sqrt(cos(d*x+c))*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d+2*a*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))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x,5,a^(5/2)*(2*A+5*B)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d-1/3*a^3*(14*A+3*B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2*a^2*(2*A+B)*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),1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x,5,2*a^(5/2)*B*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/d+2/15*a^3*(32*A+35*B)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/15*a^2*(8*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+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))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x,4,2/15*a^3*(10*A+11*B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+2/105*a^3*(230*A+301*B)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/35*a^2*(10*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+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))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x,5,2/315*a^3*(124*A+135*B)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+2/315*a^3*(292*A+345*B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+4/315*a^3*(292*A+345*B)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/21*a^2*(4*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+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))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(13/2),x,6,2/693*a^3*(194*A+209*B)*sin(d*x+c)/d/cos(d*x+c)^(7/2)/sqrt(a+a*cos(d*x+c))+2/1155*a^3*(710*A+803*B)*sin(d*x+c)/d/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c))+8/3465*a^3*(710*A+803*B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))+16/3465*a^3*(710*A+803*B)*sin(d*x+c)/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c))+2/99*a^2*(14*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+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+B*cos(d*x+c))/sqrt(a+a*cos(d*x+c)),x,7,-1/4*(4*A-7*B)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+sqrt(2)*(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)*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+1/2*B*cos(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c))/sqrt(a+a*cos(d*x+c)),x,6,(2*A-B)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d-sqrt(2)*(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+B*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c))/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),x,5,2*B*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/sqrt(a)/d+sqrt(2)*(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],
[(A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c)),x,4,-sqrt(2)*(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+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))/cos(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c)),x,5,sqrt(2)*(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+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))/cos(d*x+c)^(7/2)/sqrt(a+a*cos(d*x+c)),x,6,-sqrt(2)*(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+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)*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+B*cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x,7,(2*A-3*B)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(3/2)/d-1/2*(5*A-9*B)*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)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)-1/2*(A-3*B)*sqrt(cos(d*x+c))*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))/(a+a*cos(d*x+c))^(3/2),x,6,2*B*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(3/2)/d+1/2*(A-5*B)*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)*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))/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^(3/2),x,4,1/2*(3*A+B)*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)*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))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x,5,-1/2*(7*A-3*B)*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)*sin(d*x+c)/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^(3/2)+1/2*(5*A-B)*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))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x,6,1/2*(11*A-7*B)*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)*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)*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)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x,8,(2*A-5*B)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(5/2)/d-1/16*(43*A-115*B)*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)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)+1/16*(7*A-15*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)-1/16*(11*A-35*B)*sqrt(cos(d*x+c))*sin(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))/(a+a*cos(d*x+c))^(5/2),x,7,2*B*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(5/2)/d+1/16*(3*A-43*B)*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)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)+1/16*(3*A-11*B)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2),1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x,5,1/16*(5*A+3*B)*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)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)+1/16*(A+7*B)*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))/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^(5/2),x,5,1/16*(19*A+5*B)*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)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(9*A-B)*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))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x,6,-1/16*(75*A-19*B)*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)*sin(d*x+c)/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^(5/2)-1/16*(13*A-5*B)*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)*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))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x,7,1/16*(163*A-75*B)*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)*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)*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)*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)*sin(d*x+c)/a^2/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)^(7/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2),x,9,(2*A-7*B)*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(7/2)/d-1/64*(177*A-637*B)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(7/2)/d+1/6*(A-B)*cos(d*x+c)^(7/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(7/2)+1/16*(3*A-7*B)*cos(d*x+c)^(5/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(5/2)+1/192*(79*A-259*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/a^2/d/(a+a*cos(d*x+c))^(3/2)-7/64*(7*A-27*B)*sqrt(cos(d*x+c))*sin(d*x+c)/a^3/d/sqrt(a+a*cos(d*x+c)),1],
[cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2),x,8,2*B*arcsin(sqrt(a)*sin(d*x+c)/sqrt(a+a*cos(d*x+c)))/a^(7/2)/d+1/64*(5*A-177*B)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(7/2)/d+1/6*(A-B)*cos(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(7/2)+1/48*(5*A-17*B)*cos(d*x+c)^(3/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(5/2)+1/64*(5*A-49*B)*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d/(a+a*cos(d*x+c))^(3/2),1],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2),x,6,1/64*(7*A+5*B)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(7/2)/d+1/6*(A-B)*cos(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(7/2)+1/48*(A-13*B)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(5/2)+1/192*(17*A+67*B)*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d/(a+a*cos(d*x+c))^(3/2),1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2),x,6,1/64*(13*A+7*B)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(7/2)/d+1/6*(A-B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^(7/2)+1/16*(A+3*B)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(5/2)-1/192*(5*A-17*B)*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+B*cos(d*x+c))/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^(7/2),x,6,1/64*(63*A+13*B)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(7/2)/d-1/6*(A-B)*sqrt(cos(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^(7/2)-1/16*(5*A-B)*sqrt(cos(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(5/2)-1/192*(103*A+5*B)*sqrt(cos(d*x+c))*sin(d*x+c)/a^2/d/(a+a*cos(d*x+c))^(3/2),1],
[(A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(7/2),x,7,-3/64*(121*A-21*B)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(7/2)/d-1/6*(A-B)*sin(d*x+c)/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^(7/2)-1/48*(19*A-7*B)*sin(d*x+c)/a/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^(5/2)-1/192*(199*A-43*B)*sin(d*x+c)/a^2/d/sqrt(cos(d*x+c))/(a+a*cos(d*x+c))^(3/2)+1/192*(691*A-103*B)*sin(d*x+c)/a^3/d/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(7/2),x,8,1/64*(1015*A-363*B)*arctan(sqrt(a)*sin(d*x+c)/sqrt(2)/sqrt(cos(d*x+c))/sqrt(a+a*cos(d*x+c)))/sqrt(2)/a^(7/2)/d-1/6*(A-B)*sin(d*x+c)/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(7/2)-1/48*(23*A-11*B)*sin(d*x+c)/a/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2)-1/64*(109*A-41*B)*sin(d*x+c)/a^2/d/cos(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2)+1/192*(579*A-199*B)*sin(d*x+c)/a^3/d/cos(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c))-1/192*(1887*A-691*B)*sin(d*x+c)/a^3/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+B*cos(d*x+c)),x,7,1/8*(4*A*a+3*B*b)*x+(A*b+B*a)*sin(d*x+c)/d+1/8*(4*A*a+3*B*b)*cos(d*x+c)*sin(d*x+c)/d+1/4*b*B*cos(d*x+c)^3*sin(d*x+c)/d-1/3*(A*b+B*a)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x,3,1/2*(A*b+B*a)*x+1/3*(3*A*a+2*B*b)*sin(d*x+c)/d+1/2*(A*b+B*a)*cos(d*x+c)*sin(d*x+c)/d+1/3*b*B*cos(d*x+c)^2*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x,1,1/2*(2*A*a+B*b)*x+(A*b+B*a)*sin(d*x+c)/d+1/2*b*B*cos(d*x+c)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c),x,4,(A*b+B*a)*x+a*A*arctanh(sin(d*x+c))/d+b*B*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^2,x,4,b*B*x+(A*b+B*a)*arctanh(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))*sec(d*x+c)^3,x,6,1/2*(A*a+2*B*b)*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))*sec(d*x+c)^4,x,7,1/2*(A*b+B*a)*arctanh(sin(d*x+c))/d+1/3*(2*A*a+3*B*b)*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))*sec(d*x+c)^5,x,7,1/8*(3*A*a+4*B*b)*arctanh(sin(d*x+c))/d+(A*b+B*a)*tan(d*x+c)/d+1/8*(3*A*a+4*B*b)*sec(d*x+c)*tan(d*x+c)/d+1/4*a*A*sec(d*x+c)^3*tan(d*x+c)/d+1/3*(A*b+B*a)*tan(d*x+c)^3/d,1],
[cos(d*x+c)^2*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x,7,1/8*(4*A*a^2+3*A*b^2+6*B*a*b)*x+1/5*(4*b^2*B+5*a*(2*A*b+B*a))*sin(d*x+c)/d+1/8*(4*A*a^2+3*A*b^2+6*B*a*b)*cos(d*x+c)*sin(d*x+c)/d+1/20*b*(5*A*b+6*B*a)*cos(d*x+c)^3*sin(d*x+c)/d+1/5*b*B*cos(d*x+c)^3*(a+b*cos(d*x+c))*sin(d*x+c)/d-1/15*(4*b^2*B+5*a*(2*A*b+B*a))*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x,4,1/8*(8*A*a*b+4*B*a^2+3*B*b^2)*x+1/6*(4*A*a^2*b+4*A*b^3-B*a^3+8*B*a*b^2)*sin(d*x+c)/b/d+1/24*(8*A*a*b-2*B*a^2+9*B*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/12*(4*A*b-B*a)*(a+b*cos(d*x+c))^2*sin(d*x+c)/b/d+1/4*B*(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)),x,2,1/2*(2*A*a^2+A*b^2+2*B*a*b)*x+2/3*(3*A*a*b+B*a^2+B*b^2)*sin(d*x+c)/d+1/6*b*(3*A*b+2*B*a)*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],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c),x,4,1/2*(4*A*a*b+2*B*a^2+B*b^2)*x+a^2*A*arctanh(sin(d*x+c))/d+1/2*b*(2*A*b+3*B*a)*sin(d*x+c)/d+1/2*b*B*(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^2,x,4,b*(A*b+2*B*a)*x+a*(2*A*b+B*a)*arctanh(sin(d*x+c))/d+b^2*B*sin(d*x+c)/d+a^2*A*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^3,x,4,b^2*B*x+1/2*(A*a^2+2*A*b^2+4*B*a*b)*arctanh(sin(d*x+c))/d+a*(2*A*b+B*a)*tan(d*x+c)/d+1/2*a^2*A*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^4,x,6,1/2*(2*A*a*b+B*a^2+2*B*b^2)*arctanh(sin(d*x+c))/d+1/3*(2*A*a^2+3*A*b^2+6*B*a*b)*tan(d*x+c)/d+1/2*a*(2*A*b+B*a)*sec(d*x+c)*tan(d*x+c)/d+1/3*a^2*A*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^5,x,7,1/8*(3*A*a^2+4*A*b^2+8*B*a*b)*arctanh(sin(d*x+c))/d+1/3*(4*A*a*b+2*B*a^2+3*B*b^2)*tan(d*x+c)/d+1/8*(3*A*a^2+4*A*b^2+8*B*a*b)*sec(d*x+c)*tan(d*x+c)/d+1/3*a*(2*A*b+B*a)*sec(d*x+c)^2*tan(d*x+c)/d+1/4*a^2*A*sec(d*x+c)^3*tan(d*x+c)/d,1],
[cos(d*x+c)^2*(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)),x,8,1/16*(8*A*a^3+18*A*a*b^2+18*B*a^2*b+5*B*b^3)*x+1/5*(15*A*a^2*b+4*A*b^3+5*B*a^3+12*B*a*b^2)*sin(d*x+c)/d+1/16*(8*A*a^3+18*A*a*b^2+18*B*a^2*b+5*B*b^3)*cos(d*x+c)*sin(d*x+c)/d+1/24*b*(18*A*a*b+14*B*a^2+5*B*b^2)*cos(d*x+c)^3*sin(d*x+c)/d+1/15*b^2*(3*A*b+4*B*a)*cos(d*x+c)^4*sin(d*x+c)/d+1/6*b*B*cos(d*x+c)^3*(a+b*cos(d*x+c))^2*sin(d*x+c)/d-1/15*(15*A*a^2*b+4*A*b^3+5*B*a^3+12*B*a*b^2)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)),x,5,1/8*(12*A*a^2*b+3*A*b^3+4*B*a^3+9*B*a*b^2)*x+1/30*(15*A*a^3*b+60*A*a*b^3-3*B*a^4+52*B*a^2*b^2+16*B*b^4)*sin(d*x+c)/b/d+1/120*(30*A*a^2*b+45*A*b^3-6*B*a^3+71*B*a*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/60*(15*A*a*b-3*B*a^2+16*B*b^2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/b/d+1/20*(5*A*b-B*a)*(a+b*cos(d*x+c))^3*sin(d*x+c)/b/d+1/5*B*(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)),x,3,1/8*(8*A*a^3+12*A*a*b^2+12*B*a^2*b+3*B*b^3)*x+1/6*(16*A*a^2*b+4*A*b^3+3*B*a^3+12*B*a*b^2)*sin(d*x+c)/d+1/24*b*(20*A*a*b+6*B*a^2+9*B*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/12*(4*A*b+3*B*a)*(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))^3*(A+B*cos(d*x+c))*sec(d*x+c),x,5,1/2*(6*A*a^2*b+A*b^3+2*B*a^3+3*B*a*b^2)*x+a^3*A*arctanh(sin(d*x+c))/d+1/3*b*(9*A*a*b+8*B*a^2+2*B*b^2)*sin(d*x+c)/d+1/6*b^2*(3*A*b+5*B*a)*cos(d*x+c)*sin(d*x+c)/d+1/3*b*B*(a+b*cos(d*x+c))^2*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^2,x,5,1/2*b*(6*A*a*b+6*B*a^2+B*b^2)*x+a^2*(3*A*b+B*a)*arctanh(sin(d*x+c))/d-b*(2*A*a^2-A*b^2-3*B*a*b)*sin(d*x+c)/d-1/2*b^2*(2*A*a-B*b)*cos(d*x+c)*sin(d*x+c)/d+a*A*(a+b*cos(d*x+c))^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^3,x,5,b^2*(A*b+3*B*a)*x+1/2*a*(A*a^2+6*A*b^2+6*B*a*b)*arctanh(sin(d*x+c))/d-1/2*b^2*(A*a-2*B*b)*sin(d*x+c)/d+a^2*(2*A*b+B*a)*tan(d*x+c)/d+1/2*a*A*(a+b*cos(d*x+c))^2*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^4,x,5,b^3*B*x+1/2*(3*A*a^2*b+2*A*b^3+B*a^3+6*B*a*b^2)*arctanh(sin(d*x+c))/d+1/3*a*(2*A*a^2+8*A*b^2+9*B*a*b)*tan(d*x+c)/d+1/6*a^2*(5*A*b+3*B*a)*sec(d*x+c)*tan(d*x+c)/d+1/3*a*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))^3*(A+B*cos(d*x+c))*sec(d*x+c)^5,x,7,1/8*(3*A*a^3+12*A*a*b^2+12*B*a^2*b+8*B*b^3)*arctanh(sin(d*x+c))/d+1/3*(6*A*a^2*b+3*A*b^3+2*B*a^3+9*B*a*b^2)*tan(d*x+c)/d+1/8*a*(3*A*a^2+10*A*b^2+12*B*a*b)*sec(d*x+c)*tan(d*x+c)/d+1/6*a^2*(3*A*b+2*B*a)*sec(d*x+c)^2*tan(d*x+c)/d+1/4*a*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))^3*(A+B*cos(d*x+c))*sec(d*x+c)^6,x,8,1/8*(9*A*a^2*b+4*A*b^3+3*B*a^3+12*B*a*b^2)*arctanh(sin(d*x+c))/d+1/15*(8*A*a^3+30*A*a*b^2+30*B*a^2*b+15*B*b^3)*tan(d*x+c)/d+1/8*(9*A*a^2*b+4*A*b^3+3*B*a^3+12*B*a*b^2)*sec(d*x+c)*tan(d*x+c)/d+1/15*a*(4*A*a^2+12*A*b^2+15*B*a*b)*sec(d*x+c)^2*tan(d*x+c)/d+1/20*a^2*(7*A*b+5*B*a)*sec(d*x+c)^3*tan(d*x+c)/d+1/5*a*A*(a+b*cos(d*x+c))^2*sec(d*x+c)^4*tan(d*x+c)/d,1],
[cos(d*x+c)^2*(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)),x,9,1/16*(8*A*a^4+36*A*a^2*b^2+5*A*b^4+24*B*a^3*b+20*B*a*b^3)*x+1/35*(140*A*a^3*b+112*A*a*b^3+35*B*a^4+168*B*a^2*b^2+24*B*b^4)*sin(d*x+c)/d+1/16*(8*A*a^4+36*A*a^2*b^2+5*A*b^4+24*B*a^3*b+20*B*a*b^3)*cos(d*x+c)*sin(d*x+c)/d+1/168*b*(224*A*a^2*b+35*A*b^3+104*B*a^3+140*B*a*b^2)*cos(d*x+c)^3*sin(d*x+c)/d+1/105*b^2*(49*A*a*b+31*B*a^2+18*B*b^2)*cos(d*x+c)^4*sin(d*x+c)/d+1/42*b*(7*A*b+10*B*a)*cos(d*x+c)^3*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+1/7*b*B*cos(d*x+c)^3*(a+b*cos(d*x+c))^3*sin(d*x+c)/d-1/105*(140*A*a^3*b+112*A*a*b^3+35*B*a^4+168*B*a^2*b^2+24*B*b^4)*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c)),x,6,1/16*(32*A*a^3*b+24*A*a*b^3+8*B*a^4+36*B*a^2*b^2+5*B*b^4)*x+1/60*(24*A*a^4*b+224*A*a^2*b^3+32*A*b^5-4*B*a^5+121*B*a^3*b^2+128*B*a*b^4)*sin(d*x+c)/b/d+1/240*(48*A*a^3*b+232*A*a*b^3-8*B*a^4+178*B*a^2*b^2+75*B*b^4)*cos(d*x+c)*sin(d*x+c)/d+1/120*(24*A*a^2*b+32*A*b^3-4*B*a^3+53*B*a*b^2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/b/d+1/120*(24*A*a*b-4*B*a^2+25*B*b^2)*(a+b*cos(d*x+c))^3*sin(d*x+c)/b/d+1/30*(6*A*b-B*a)*(a+b*cos(d*x+c))^4*sin(d*x+c)/b/d+1/6*B*(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)),x,4,1/8*(8*A*a^4+24*A*a^2*b^2+3*A*b^4+16*B*a^3*b+12*B*a*b^3)*x+1/30*(95*A*a^3*b+80*A*a*b^3+12*B*a^4+112*B*a^2*b^2+16*B*b^4)*sin(d*x+c)/d+1/120*b*(130*A*a^2*b+45*A*b^3+24*B*a^3+116*B*a*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/60*(35*A*a*b+12*B*a^2+16*B*b^2)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+1/20*(5*A*b+4*B*a)*(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))^4*(A+B*cos(d*x+c))*sec(d*x+c),x,6,1/8*(32*A*a^3*b+16*A*a*b^3+8*B*a^4+24*B*a^2*b^2+3*B*b^4)*x+a^4*A*arctanh(sin(d*x+c))/d+1/6*b*(34*A*a^2*b+4*A*b^3+19*B*a^3+16*B*a*b^2)*sin(d*x+c)/d+1/24*b^2*(32*A*a*b+26*B*a^2+9*B*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/12*b*(4*A*b+7*B*a)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+1/4*b*B*(a+b*cos(d*x+c))^3*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^2,x,6,1/2*b*(12*A*a^2*b+A*b^3+8*B*a^3+4*B*a*b^2)*x+a^3*(4*A*b+B*a)*arctanh(sin(d*x+c))/d-1/3*b*(6*A*a^3-12*A*a*b^2-17*B*a^2*b-2*B*b^3)*sin(d*x+c)/d-1/6*b^2*(6*A*a^2-3*A*b^2-8*B*a*b)*cos(d*x+c)*sin(d*x+c)/d-1/3*b*(3*A*a-B*b)*(a+b*cos(d*x+c))^2*sin(d*x+c)/d+a*A*(a+b*cos(d*x+c))^3*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^3,x,6,1/2*b^2*(8*A*a*b+12*B*a^2+B*b^2)*x+1/2*a^2*(A*a^2+12*A*b^2+8*B*a*b)*arctanh(sin(d*x+c))/d-1/2*b*(13*A*a^2*b-2*A*b^3+4*B*a^3-8*B*a*b^2)*sin(d*x+c)/d-1/2*b^2*(6*A*a*b+2*B*a^2-B*b^2)*cos(d*x+c)*sin(d*x+c)/d+1/2*a*(5*A*b+2*B*a)*(a+b*cos(d*x+c))^2*tan(d*x+c)/d+1/2*a*A*(a+b*cos(d*x+c))^3*sec(d*x+c)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^4,x,6,b^3*(A*b+4*B*a)*x+1/2*a*(4*A*a^2*b+8*A*b^3+B*a^3+12*B*a*b^2)*arctanh(sin(d*x+c))/d-1/6*b^2*(8*A*a*b+3*B*a^2-6*B*b^2)*sin(d*x+c)/d+1/3*a^2*(2*A*a^2+9*A*b^2+9*B*a*b)*tan(d*x+c)/d+1/2*a*(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*(a+b*cos(d*x+c))^3*sec(d*x+c)^2*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^5,x,6,b^4*B*x+1/8*(3*A*a^4+24*A*a^2*b^2+8*A*b^4+16*B*a^3*b+32*B*a*b^3)*arctanh(sin(d*x+c))/d+1/6*a*(16*A*a^2*b+19*A*b^3+4*B*a^3+34*B*a*b^2)*tan(d*x+c)/d+1/24*a^2*(9*A*a^2+26*A*b^2+32*B*a*b)*sec(d*x+c)*tan(d*x+c)/d+1/12*a*(7*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*(a+b*cos(d*x+c))^3*sec(d*x+c)^3*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^6,x,8,1/8*(12*A*a^3*b+16*A*a*b^3+3*B*a^4+24*B*a^2*b^2+8*B*b^4)*arctanh(sin(d*x+c))/d+1/15*(8*A*a^4+60*A*a^2*b^2+15*A*b^4+40*B*a^3*b+60*B*a*b^3)*tan(d*x+c)/d+1/40*a*(60*A*a^2*b+56*A*b^3+15*B*a^3+110*B*a*b^2)*sec(d*x+c)*tan(d*x+c)/d+1/30*a^2*(8*A*a^2+18*A*b^2+25*B*a*b)*sec(d*x+c)^2*tan(d*x+c)/d+1/20*a*(8*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*(a+b*cos(d*x+c))^3*sec(d*x+c)^4*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^4*(A+B*cos(d*x+c))*sec(d*x+c)^7,x,9,1/16*(5*A*a^4+36*A*a^2*b^2+8*A*b^4+24*B*a^3*b+32*B*a*b^3)*arctanh(sin(d*x+c))/d+1/15*(32*A*a^3*b+40*A*a*b^3+8*B*a^4+60*B*a^2*b^2+15*B*b^4)*tan(d*x+c)/d+1/16*(5*A*a^4+36*A*a^2*b^2+8*A*b^4+24*B*a^3*b+32*B*a*b^3)*sec(d*x+c)*tan(d*x+c)/d+1/15*a*(16*A*a^2*b+13*A*b^3+4*B*a^3+27*B*a*b^2)*sec(d*x+c)^2*tan(d*x+c)/d+1/120*a^2*(25*A*a^2+48*A*b^2+72*B*a*b)*sec(d*x+c)^3*tan(d*x+c)/d+1/10*a*(3*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*(a+b*cos(d*x+c))^3*sec(d*x+c)^5*tan(d*x+c)/d,1],
[cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x,6,1/2*(2*a^2+b^2)*(A*b-B*a)*x/b^4-2*a^3*(A*b-B*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*a*b-3*B*a^2-2*B*b^2)*sin(d*x+c)/b^3/d+1/2*(A*b-B*a)*cos(d*x+c)*sin(d*x+c)/b^2/d+1/3*B*cos(d*x+c)^2*sin(d*x+c)/b/d,1],
[cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x,5,-1/2*(2*A*a*b-2*B*a^2-B*b^2)*x/b^3+2*a^2*(A*b-B*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+(A*b-B*a)*sin(d*x+c)/b^2/d+1/2*B*cos(d*x+c)*sin(d*x+c)/b/d,1],
[cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x,6,(A*b-B*a)*x/b^2-2*a*(A*b-B*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+B*sin(d*x+c)/b/d,1],
[(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x,3,B*x/b+2*(A*b-B*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],
[(A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c)),x,4,-2*(A*b-B*a)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a/sqrt(a-b)/sqrt(a+b)/d+A*arctanh(sin(d*x+c))/a/d,1],
[(A+B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c)),x,6,2*b*(A*b-B*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))*sec(d*x+c)^3/(a+b*cos(d*x+c)),x,6,-2*b^2*(A*b-B*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*(A*a^2+2*A*b^2-2*B*a*b)*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))*sec(d*x+c)^4/(a+b*cos(d*x+c)),x,7,2*b^3*(A*b-B*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*(a^2+2*b^2)*(A*b-B*a)*arctanh(sin(d*x+c))/a^4/d+1/3*(2*A*a^2+3*A*b^2-3*B*a*b)*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],
[cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x,6,-1/2*(4*A*a*b-6*B*a^2-B*b^2)*x/b^4+2*a^2*(2*A*a^2*b-3*A*b^3-3*B*a^3+4*B*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*A*a^2*b-A*b^3-3*B*a^3+2*B*a*b^2)*sin(d*x+c)/b^3/(a^2-b^2)/d-1/2*(2*A*a*b-3*B*a^2+B*b^2)*cos(d*x+c)*sin(d*x+c)/b^2/(a^2-b^2)/d+a*(A*b-B*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)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x,5,(A*b-2*B*a)*x/b^3-2*a*(A*a^2*b-2*A*b^3-2*B*a^3+3*B*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+B*sin(d*x+c)/b^2/d-a^2*(A*b-B*a)*sin(d*x+c)/b^2/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x,5,B*x/b^2-2*(A*b^3+B*a^3-2*B*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*(A*b-B*a)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x,4,2*(A*a-B*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-(A*b-B*a)*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*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)*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+b*(A*b-B*a)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x,6,2*b*(3*A*a^2*b-2*A*b^3-2*B*a^3+B*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*A*b-B*a)*arctanh(sin(d*x+c))/a^3/d+(A*a^2-2*A*b^2+B*a*b)*tan(d*x+c)/a^2/(a^2-b^2)/d+b*(A*b-B*a)*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x,7,-2*b^2*(4*A*a^2*b-3*A*b^3-3*B*a^3+2*B*a*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*(A*a^2+6*A*b^2-4*B*a*b)*arctanh(sin(d*x+c))/a^4/d-(2*A*a^2*b-3*A*b^3-B*a^3+2*B*a*b^2)*tan(d*x+c)/a^3/(a^2-b^2)/d+1/2*(A*a^2-3*A*b^2+2*B*a*b)*sec(d*x+c)*tan(d*x+c)/a^2/(a^2-b^2)/d+b*(A*b-B*a)*sec(d*x+c)*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^4*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x,7,-1/2*(6*A*a*b-12*B*a^2-B*b^2)*x/b^5+a^2*(6*A*a^4*b-15*A*a^2*b^3+12*A*b^5-12*B*a^5+29*B*a^3*b^2-20*B*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*A*a^4*b-11*A*a^2*b^3+2*A*b^5-12*B*a^5+21*B*a^3*b^2-6*B*a*b^4)*sin(d*x+c)/b^4/(a^2-b^2)^2/d-1/2*(3*A*a^3*b-6*A*a*b^3-6*B*a^4+10*B*a^2*b^2-B*b^4)*cos(d*x+c)*sin(d*x+c)/b^3/(a^2-b^2)^2/d+1/2*a*(A*b-B*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*A*a^2*b-5*A*b^3-4*B*a^3+7*B*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)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x,6,(A*b-3*B*a)*x/b^4-a*(2*A*a^4*b-5*A*a^2*b^3+6*A*b^5-6*B*a^5+15*B*a^3*b^2-12*B*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*(A*a*b-3*B*a^2+2*B*b^2)*sin(d*x+c)/b^3/(a^2-b^2)/d+1/2*a*(A*b-B*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*a^2*b-4*A*b^3-3*B*a^3+6*B*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)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x,5,B*x/b^3+(A*a^2*b^3+2*A*b^5-2*B*a^5+5*B*a^3*b^2-6*B*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*(A*b-B*a)*sin(d*x+c)/b^2/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/2*a*(A*a^2*b-4*A*b^3-3*B*a^3+6*B*a*b^2)*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x,6,-(3*A*a*b-B*a^2-2*B*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*(A*b-B*a)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/2*(A*a^2*b+2*A*b^3+B*a^3-4*B*a*b^2)*sin(d*x+c)/b/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x,5,(2*A*a^2+A*b^2-3*B*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*(A*b-B*a)*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c))^2-1/2*(3*A*a*b-B*a^2-2*B*b^2)*sin(d*x+c)/(a^2-b^2)^2/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^3,x,6,-(6*A*a^4*b-5*A*a^2*b^3+2*A*b^5-2*B*a^5-B*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+A*arctanh(sin(d*x+c))/a^3/d+1/2*b*(A*b-B*a)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/2*b*(5*A*a^2*b-2*A*b^3-3*B*a^3)*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))*sec(d*x+c)^2/(a+b*cos(d*x+c))^3,x,7,b*(12*A*a^4*b-15*A*a^2*b^3+6*A*b^5-6*B*a^5+5*B*a^3*b^2-2*B*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*A*b-B*a)*arctanh(sin(d*x+c))/a^4/d+1/2*(2*A*a^4-11*A*a^2*b^2+6*A*b^4+5*B*a^3*b-2*B*a*b^3)*tan(d*x+c)/a^3/(a^2-b^2)^2/d+1/2*b*(A*b-B*a)*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/2*b*(6*A*a^2*b-3*A*b^3-4*B*a^3+B*a*b^2)*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))*sec(d*x+c)^3/(a+b*cos(d*x+c))^3,x,8,-b^2*(20*A*a^4*b-29*A*a^2*b^3+12*A*b^5-12*B*a^5+15*B*a^3*b^2-6*B*a*b^4)*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*(A*a^2+12*A*b^2-6*B*a*b)*arctanh(sin(d*x+c))/a^5/d-1/2*(6*A*a^4*b-21*A*a^2*b^3+12*A*b^5-2*B*a^5+11*B*a^3*b^2-6*B*a*b^4)*tan(d*x+c)/a^4/(a^2-b^2)^2/d+1/2*(A*a^4-10*A*a^2*b^2+6*A*b^4+6*B*a^3*b-3*B*a*b^3)*sec(d*x+c)*tan(d*x+c)/a^3/(a^2-b^2)^2/d+1/2*b*(A*b-B*a)*sec(d*x+c)*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^2+1/2*b*(7*A*a^2*b-4*A*b^3-5*B*a^3+2*B*a*b^2)*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))/(a+b*cos(d*x+c))^4,x,7,(A*b-4*B*a)*x/b^5-a*(2*A*a^6*b-7*A*a^4*b^3+8*A*a^2*b^5-8*A*b^7-8*B*a^7+28*B*a^5*b^2-35*B*a^3*b^4+20*B*a*b^6)*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*(3*A*a^3*b-8*A*a*b^3-12*B*a^4+23*B*a^2*b^2-6*B*b^4)*sin(d*x+c)/b^4/(a^2-b^2)^2/d+1/3*a*(A*b-B*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*a*(A*a^2*b-6*A*b^3-4*B*a^3+9*B*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))^2-1/2*a^2*(A*a^4*b-2*A*a^2*b^3+6*A*b^5-4*B*a^5+11*B*a^3*b^2-12*B*a*b^4)*sin(d*x+c)/b^4/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^4,x,6,B*x/b^4-(3*A*a^2*b^5+2*A*b^7+2*B*a^7-7*B*a^5*b^2+8*B*a^3*b^4-8*B*a*b^6)*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*(A*b-B*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*(5*A*b^3+3*B*a^3-8*B*a*b^2)*sin(d*x+c)/b^3/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2-1/6*a*(A*a^2*b^3-16*A*b^5+9*B*a^5-28*B*a^3*b^2+34*B*a*b^4)*sin(d*x+c)/b^3/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^4,x,6,(A*a^3+4*A*a*b^2-3*B*a^2*b-2*B*b^3)*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^2*(A*b-B*a)*sin(d*x+c)/b^2/(a^2-b^2)/d/(a+b*cos(d*x+c))^3+1/6*a*(A*a^2*b-6*A*b^3-4*B*a^3+9*B*a*b^2)*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2+1/6*(A*a^4*b-10*A*a^2*b^3-6*A*b^5+2*B*a^5-5*B*a^3*b^2+18*B*a*b^4)*sin(d*x+c)/b^2/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^4,x,7,-(4*A*a^2*b+A*b^3-B*a^3-4*B*a*b^2)*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-B*a)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^3+1/6*(2*A*a^2*b+3*A*b^3+B*a^3-6*B*a*b^2)*sin(d*x+c)/b/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2+1/6*(2*A*a^3*b+13*A*a*b^3+B*a^4-10*B*a^2*b^2-6*B*b^4)*sin(d*x+c)/b/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^4,x,6,(2*A*a^3+3*A*a*b^2-4*B*a^2*b-B*b^3)*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-B*a)*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c))^3-1/6*(5*A*a*b-2*B*a^2-3*B*b^2)*sin(d*x+c)/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2-1/6*(11*A*a^2*b+4*A*b^3-2*B*a^3-13*B*a*b^2)*sin(d*x+c)/(a^2-b^2)^3/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^4,x,7,-(8*A*a^6*b-8*A*a^4*b^3+7*A*a^2*b^5-2*A*b^7-2*B*a^7-3*B*a^5*b^2)*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*b*(A*b-B*a)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^3+1/6*b*(8*A*a^2*b-3*A*b^3-5*B*a^3)*sin(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2+1/6*b*(26*A*a^4*b-17*A*a^2*b^3+6*A*b^5-11*B*a^5-4*B*a^3*b^2)*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))*sec(d*x+c)^2/(a+b*cos(d*x+c))^4,x,8,b*(20*A*a^6*b-35*A*a^4*b^3+28*A*a^2*b^5-8*A*b^7-8*B*a^7+8*B*a^5*b^2-7*B*a^3*b^4+2*B*a*b^6)*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*(6*A*a^6-65*A*a^4*b^2+68*A*a^2*b^4-24*A*b^6+26*B*a^5*b-17*B*a^3*b^3+6*B*a*b^5)*tan(d*x+c)/a^4/(a^2-b^2)^3/d+1/3*b*(A*b-B*a)*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^3+1/6*b*(9*A*a^2*b-4*A*b^3-6*B*a^3+B*a*b^2)*tan(d*x+c)/a^2/(a^2-b^2)^2/d/(a+b*cos(d*x+c))^2+1/2*b*(12*A*a^4*b-11*A*a^2*b^3+4*A*b^5-6*B*a^5+2*B*a^3*b^2-B*a*b^4)*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))*sec(d*x+c)^3/(a+b*cos(d*x+c))^4,x,9,-b^2*(40*A*a^6*b-84*A*a^4*b^3+69*A*a^2*b^5-20*A*b^7-20*B*a^7+35*B*a^5*b^2-28*B*a^3*b^4+8*B*a*b^6)*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/a^6/(a-b)^(7/2)/(a+b)^(7/2)/d+1/2*(A*a^2+20*A*b^2-8*B*a*b)*arctanh(sin(d*x+c))/a^6/d-1/6*(24*A*a^6*b-146*A*a^4*b^3+167*A*a^2*b^5-60*A*b^7-6*B*a^7+65*B*a^5*b^2-68*B*a^3*b^4+24*B*a*b^6)*tan(d*x+c)/a^5/(a^2-b^2)^3/d+1/2*(A*a^6-23*A*a^4*b^2+27*A*a^2*b^4-10*A*b^6+12*B*a^5*b-11*B*a^3*b^3+4*B*a*b^5)*sec(d*x+c)*tan(d*x+c)/a^4/(a^2-b^2)^3/d+1/3*b*(A*b-B*a)*sec(d*x+c)*tan(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^3+1/6*b*(10*A*a^2*b-5*A*b^3-7*B*a^3+2*B*a*b^2)*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*b*(48*A*a^4*b-53*A*a^2*b^3+20*A*b^5-27*B*a^5+20*B*a^3*b^2-8*B*a*b^4)*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*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x,3,B*sin(d*x+c)/d-1/3*B*sin(d*x+c)^3/d,1],
[cos(d*x+c)^2*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x,3,1/2*B*x+1/2*B*cos(d*x+c)*sin(d*x+c)/d,1],
[cos(d*x+c)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x,2,B*sin(d*x+c)/d,1],
[(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x,1,B*x,1],
[(a*B+b*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c)),x,2,B*arctanh(sin(d*x+c))/d,1],
[(a*B+b*B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c)),x,3,B*tan(d*x+c)/d,1],
[(a*B+b*B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c)),x,3,1/2*B*arctanh(sin(d*x+c))/d+1/2*B*sec(d*x+c)*tan(d*x+c)/d,1],
[(a*B+b*B*cos(d*x+c))*sec(d*x+c)^4/(a+b*cos(d*x+c)),x,3,B*tan(d*x+c)/d+1/3*B*tan(d*x+c)^3/d,1],
[cos(d*x+c)^3*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x,6,1/2*(2*a^2+b^2)*B*x/b^3-2*a^3*B*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*B*sin(d*x+c)/b^2/d+1/2*B*cos(d*x+c)*sin(d*x+c)/b/d,1],
[cos(d*x+c)^2*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x,6,-a*B*x/b^2+2*a^2*B*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b^2/sqrt(a+b)/d+B*sin(d*x+c)/b/d,1],
[cos(d*x+c)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x,4,B*x/b-2*a*B*arctan(sqrt(a-b)*tan(1/2*d*x+1/2*c)/sqrt(a+b))/sqrt(a-b)/b/sqrt(a+b)/d,1],
[(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x,3,2*B*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*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^2,x,5,-2*b*B*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],
[(a*B+b*B*cos(d*x+c))*sec(d*x+c)^2/(a+b*cos(d*x+c))^2,x,7,2*b^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-b*B*arctanh(sin(d*x+c))/a^2/d+B*tan(d*x+c)/a/d,1],
[(a*B+b*B*cos(d*x+c))*sec(d*x+c)^3/(a+b*cos(d*x+c))^2,x,7,-2*b^3*B*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*(a^2+2*b^2)*B*arctanh(sin(d*x+c))/a^3/d-b*B*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)^3*sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x,9,2/315*(24*A*a^3*b+57*A*a*b^3-16*B*a^4-24*B*a^2*b^2+147*B*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/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/315*(a^2-b^2)*(24*A*a^2*b+75*A*b^3-16*B*a^3-36*B*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))+2/315*(24*A*a^2*b+75*A*b^3-16*B*a^3-36*B*a*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/d-2/315*(36*A*a*b-24*B*a^2-49*B*b^2)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^3/d+2/21*(3*A*b-2*B*a)*cos(d*x+c)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^2/d+2/9*B*cos(d*x+c)^2*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d,1],
[cos(d*x+c)^2*sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x,8,-2/105*(14*A*a^2*b-63*A*b^3-8*B*a^3-19*B*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*A*a*b-8*B*a^2-25*B*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*A*a*b-8*B*a^2-25*B*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d+2/35*(7*A*b-4*B*a)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^2/d+2/7*B*cos(d*x+c)*(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)),x,8,2/15*(5*A*a*b-2*B*a^2+9*B*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*A*b-2*B*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*A*b-2*B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+2/5*B*(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)),x,6,2/3*(3*A*b+B*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)*B*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*B*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))*sec(d*x+c),x,8,2*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))+2*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))+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)),1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^2,x,9,-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))+(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))*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)*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*A*a^2-A*b^2+4*B*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*(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))*sec(d*x+c)^4,x,11,-1/24*(16*A*a^2-3*A*b^2+6*B*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))+1/24*(16*A*a^2-A*b^2+18*B*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))+1/8*(4*A*a^2*b+A*b^3+8*B*a^3-2*B*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^2/d/sqrt(a+b*cos(d*x+c))+1/24*(16*A*a^2-3*A*b^2+6*B*a*b)*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)),x,9,-2/315*(18*A*a^3*b-246*A*a*b^3-8*B*a^4-33*B*a^2*b^2-147*B*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*A*a^2*b-75*A*b^3-8*B*a^3-39*B*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*A*a^2*b-75*A*b^3-8*B*a^3-39*B*a*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d-2/315*(18*A*a*b-8*B*a^2-49*B*b^2)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^2/d+2/63*(9*A*b-4*B*a)*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b^2/d+2/9*B*cos(d*x+c)*(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)),x,9,2/105*(21*A*a^2*b+63*A*b^3-6*B*a^3+82*B*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*A*a*b-6*B*a^2+25*B*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*A*a*b-6*B*a^2+25*B*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+2/35*(7*A*b-2*B*a)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d+2/7*B*(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)),x,7,2/15*(20*A*a*b+3*B*a^2+9*B*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*A*b+3*B*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*A*b+3*B*a)*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],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c),x,9,2/3*(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)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+2/3*(3*A*a*b-B*a^2+B*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*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*b*B*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^2,x,9,-(A*a-2*B*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))+(A*a^2+2*A*b^2+2*B*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*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*A*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x,10,-1/4*(5*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)))/d/sqrt((a+b*cos(d*x+c))/(a+b))+1/4*(7*A*a*b+4*B*a^2+8*B*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*A*a^2+3*A*b^2+12*B*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*A*b+4*B*a)*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/d+1/2*a*A*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)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x,11,-1/24*(16*A*a^2+3*A*b^2+30*B*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*A*a^2+17*A*b^2+42*B*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*A*a^2*b-A*b^3+8*B*a^3+6*B*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*A*a^2+3*A*b^2+30*B*a*b)*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a/d+1/12*(7*A*b+6*B*a)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/3*a*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))^(5/2)*(A+B*cos(d*x+c)),x,10,-2/3465*(110*A*a^4*b-3069*A*a^2*b^3-1617*A*b^5-40*B*a^5-255*B*a^3*b^2-3705*B*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*A*a^3*b-1254*A*a*b^3-40*B*a^4-285*B*a^2*b^2-675*B*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*A*a^3*b-1254*A*a*b^3-40*B*a^4-285*B*a^2*b^2-675*B*b^4)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d-2/3465*(110*A*a^2*b-539*A*b^3-40*B*a^3-335*B*a*b^2)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b^2/d-2/693*(22*A*a*b-8*B*a^2-81*B*b^2)*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b^2/d+2/99*(11*A*b-4*B*a)*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b^2/d+2/11*B*cos(d*x+c)*(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)),x,10,2/315*(45*A*a^3*b+435*A*a*b^3-10*B*a^4+279*B*a^2*b^2+147*B*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*A*a^2*b+75*A*b^3-10*B*a^3+114*B*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*A*a^2*b+75*A*b^3-10*B*a^3+114*B*a*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+2/315*(45*A*a*b-10*B*a^2+49*B*b^2)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d+2/63*(9*A*b-2*B*a)*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d+2/9*B*(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)),x,8,2/105*(161*A*a^2*b+63*A*b^3+15*B*a^3+145*B*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*A*a*b+15*B*a^2+25*B*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*A*a*b+15*B*a^2+25*B*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+2/35*(7*A*b+5*B*a)*(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],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c),x,10,2/15*(35*A*a*b+23*B*a^2+9*B*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*A*a^2*b+5*A*b^3-8*B*a^3+8*B*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*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*b*(5*A*b+8*B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+2/5*b*B*(a+b*cos(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))*sec(d*x+c)^2,x,10,-1/3*(3*A*a^2-6*A*b^2-14*B*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*A*a^3+12*A*a*b^2+4*B*a^2*b+2*B*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*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*a-2*B*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+a*A*(a+b*cos(d*x+c))^(3/2)*tan(d*x+c)/d,1],
[(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^3,x,10,-1/4*(9*A*a*b+4*B*a^2-8*B*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*A*a^2*b+8*A*b^3+4*B*a^3+16*B*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*A*a^2+15*A*b^2+20*B*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*A*b+4*B*a)*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/d+1/2*a*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))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^4,x,11,-1/24*(16*A*a^2+33*A*b^2+54*B*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*A*a^3+59*A*a*b^2+66*B*a^2*b+48*B*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*A*a^2*b+5*A*b^3+8*B*a^3+30*B*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*A*a^2+33*A*b^2+54*B*a*b)*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/d+1/4*a*(3*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*(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)*(A+B*cos(d*x+c))*sec(d*x+c)^5,x,12,-1/192*(284*A*a^2*b+15*A*b^3+128*B*a^3+264*B*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*A*a^2*b+133*A*b^3+128*B*a^3+472*B*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*A*a^4+120*A*a^2*b^2-5*A*b^4+160*B*a^3*b+40*B*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*A*a^2*b+15*A*b^3+128*B*a^3+264*B*a*b^2)*sqrt(a+b*cos(d*x+c))*tan(d*x+c)/a/d+1/96*(36*A*a^2+59*A*b^2+104*B*a*b)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)*tan(d*x+c)/d+1/24*a*(11*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*(a+b*cos(d*x+c))^(3/2)*sec(d*x+c)^3*tan(d*x+c)/d,1],
[cos(d*x+c)^3*(A+B*cos(d*x+c))/sqrt(a+b*cos(d*x+c)),x,8,2/105*(56*A*a^2*b+63*A*b^3-48*B*a^3-44*B*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^4/d/sqrt((a+b*cos(d*x+c))/(a+b))-2/105*(56*A*a^3*b+49*A*a*b^3-48*B*a^4-32*B*a^2*b^2-25*B*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/d/sqrt(a+b*cos(d*x+c))-2/105*(28*A*a*b-24*B*a^2-25*B*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/d+2/35*(7*A*b-6*B*a)*cos(d*x+c)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d+2/7*B*cos(d*x+c)^2*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d,1],
[cos(d*x+c)^2*(A+B*cos(d*x+c))/sqrt(a+b*cos(d*x+c)),x,7,-2/15*(10*A*a*b-8*B*a^2-9*B*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*a^2*b+5*A*b^3-8*B*a^3-7*B*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*A*b-4*B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d+2/5*B*cos(d*x+c)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d,1],
[cos(d*x+c)*(A+B*cos(d*x+c))/sqrt(a+b*cos(d*x+c)),x,7,2/3*(3*A*b-2*B*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*a*b-2*B*a^2-B*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*B*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d,1],
[(A+B*cos(d*x+c))/sqrt(a+b*cos(d*x+c)),x,5,2*B*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*b-B*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],
[(A+B*cos(d*x+c))*sec(d*x+c)/sqrt(a+b*cos(d*x+c)),x,5,2*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*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))*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*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))*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*(4*A*a^2+3*A*b^2-4*B*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*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],
[cos(d*x+c)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x,8,-2/15*(40*A*a^3*b-25*A*a*b^3-48*B*a^4+24*B*a^2*b^2+9*B*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*A*a^2*b+5*A*b^3-48*B*a^3-12*B*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*(A*b-B*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*a^2*b-5*A*b^3-24*B*a^3+9*B*a*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^3/(a^2-b^2)/d-2/5*(5*A*a*b-6*B*a^2+B*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)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x,7,2/3*(6*A*a^2*b-3*A*b^3-8*B*a^3+5*B*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*A*a*b-8*B*a^2-B*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*(A*b-B*a)*sin(d*x+c)/b^2/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+2/3*B*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d,1],
[cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x,7,-2*(A*a*b-2*B*a^2+B*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*(A*b-2*B*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*(A*b-B*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))/(a+b*cos(d*x+c))^(3/2),x,6,2*(A*b-B*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*B*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*b-B*a)*sin(d*x+c)/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x,7,-2*(A*b-B*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*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*b*(A*b-B*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))*sec(d*x+c)^2/(a+b*cos(d*x+c))^(3/2),x,10,-(A*a^2-3*A*b^2+2*B*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))+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*(A*a^2-3*A*b^2+2*B*a*b)*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))*sec(d*x+c)^3/(a+b*cos(d*x+c))^(3/2),x,11,1/4*(7*A*a^2*b-15*A*b^3-4*B*a^3+12*B*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^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*(4*A*a^2+15*A*b^2-12*B*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))-1/4*b*(7*A*a^2*b-15*A*b^3-4*B*a^3+12*B*a*b^2)*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)^4*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x,9,-2/15*(80*A*a^5*b-140*A*a^3*b^3+40*A*a*b^5-128*B*a^6+212*B*a^4*b^2-55*B*a^2*b^4-9*B*b^6)*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*a^4*b-80*A*a^2*b^3-5*A*b^5-128*B*a^5+116*B*a^3*b^2+17*B*a*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^5/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+2/3*a*(A*b-B*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*a*(5*A*a^2*b-9*A*b^3-8*B*a^3+12*B*a*b^2)*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*a^4*b-65*A*a^2*b^3+5*A*b^5-64*B*a^5+98*B*a^3*b^2-14*B*a*b^4)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^4/(a^2-b^2)^2/d-2/15*(30*A*a^3*b-50*A*a*b^3-48*B*a^4+71*B*a^2*b^2-3*B*b^4)*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)^3*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x,8,2/3*(8*A*a^4*b-15*A*a^2*b^3+3*A*b^5-16*B*a^5+28*B*a^3*b^2-8*B*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*A*a^3*b-9*A*a*b^3-16*B*a^4+16*B*a^2*b^2+B*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*(A*b-B*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*A*a^2*b-7*A*b^3-6*B*a^3+10*B*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*a*b-2*B*a^2+B*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)^2*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x,7,-2/3*(2*A*a^3*b-6*A*a*b^3-8*B*a^4+15*B*a^2*b^2-3*B*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*A*a^2*b-3*A*b^3-8*B*a^3+9*B*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*(A*b-B*a)*sin(d*x+c)/b^2/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+2/3*a*(2*A*a^2*b-6*A*b^3-5*B*a^3+9*B*a*b^2)*sin(d*x+c)/b^2/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[cos(d*x+c)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x,8,-2/3*(A*a^2*b+3*A*b^3+2*B*a^3-6*B*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*(A*a*b+2*B*a^2-3*B*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*(A*b-B*a)*sin(d*x+c)/b/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+2/3*(A*a^2*b+3*A*b^3+2*B*a^3-6*B*a*b^2)*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))/(a+b*cos(d*x+c))^(5/2),x,7,2/3*(4*A*a*b-B*a^2-3*B*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*(A*b-B*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*(A*b-B*a)*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)-2/3*(4*A*a*b-B*a^2-3*B*b^2)*sin(d*x+c)/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x,10,-2/3*(7*A*a^2*b-3*A*b^3-4*B*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*(A*b-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/(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*b*(A*b-B*a)*sin(d*x+c)/a/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)+2/3*b*(7*A*a^2*b-3*A*b^3-4*B*a^3)*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))*sec(d*x+c)^2/(a+b*cos(d*x+c))^(5/2),x,11,-1/3*(3*A*a^4-26*A*a^2*b^2+15*A*b^4+14*B*a^3*b-6*B*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*A*a^2-5*A*b^2+2*B*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*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*(3*A*a^2-5*A*b^2+2*B*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*A*a^4-26*A*a^2*b^2+15*A*b^4+14*B*a^3*b-6*B*a*b^3)*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))*sec(d*x+c)^3/(a+b*cos(d*x+c))^(5/2),x,12,1/12*(33*A*a^4*b-170*A*a^2*b^3+105*A*b^5-12*B*a^5+104*B*a^3*b^2-60*B*a*b^4)*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*(27*A*a^2*b-35*A*b^3-12*B*a^3+20*B*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)))/a^3/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c))+1/4*(4*A*a^2+35*A*b^2-20*B*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^4/d/sqrt(a+b*cos(d*x+c))-1/12*b*(27*A*a^2*b-35*A*b^3-12*B*a^3+20*B*a*b^2)*sin(d*x+c)/a^3/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)-1/12*b*(33*A*a^4*b-170*A*a^2*b^3+105*A*b^5-12*B*a^5+104*B*a^3*b^2-60*B*a*b^4)*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+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x,3,2*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],
[(a*B+b*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^(3/2),x,3,2*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],
[(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x,5,2*B*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*b*B*sin(d*x+c)/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c)),1],
[(a*B+b*B*cos(d*x+c))*sec(d*x+c)/(a+b*cos(d*x+c))^(5/2),x,8,-2*b*B*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^2*B*sin(d*x+c)/a/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c)),1],
[cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x,8,2/15*(9*A*a+7*B*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+10/21*(A*b+B*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+10/21*(A*b+B*a)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*(9*A*a+7*B*b)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*(A*b+B*a)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/9*b*B*cos(d*x+c)^(7/2)*sin(d*x+c)/d,1],
[cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x,7,6/5*(A*b+B*a)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(7*A*a+5*B*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*(7*A*a+5*B*b)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*(A*b+B*a)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*b*B*cos(d*x+c)^(5/2)*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x,6,2/5*(5*A*a+3*B*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(A*b+B*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*(A*b+B*a)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*b*B*cos(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c))/sqrt(cos(d*x+c)),x,5,2*(A*b+B*a)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(3*A*a+B*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*b*B*sqrt(cos(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x,5,-2*(A*a-B*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2*(A*b+B*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2*a*A*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x,6,-2*(A*b+B*a)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(A*a+3*B*b)*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))/cos(d*x+c)^(7/2),x,7,-2/5*(3*A*a+5*B*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(A*b+B*a)*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)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x,8,2/15*(9*A*a^2+7*A*b^2+14*B*a*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+10/231*(9*b^2*B+11*a*(2*A*b+B*a))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+10/231*(9*b^2*B+11*a*(2*A*b+B*a))*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*(9*A*a^2+7*A*b^2+14*B*a*b)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/77*(9*b^2*B+11*a*(2*A*b+B*a))*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/99*b*(11*A*b+13*B*a)*cos(d*x+c)^(7/2)*sin(d*x+c)/d+2/11*b*B*cos(d*x+c)^(7/2)*(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x,7,2/15*(7*b^2*B+9*a*(2*A*b+B*a))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(7*A*a^2+5*A*b^2+10*B*a*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*(7*A*a^2+5*A*b^2+10*B*a*b)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*(7*b^2*B+9*a*(2*A*b+B*a))*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/63*b*(9*A*b+11*B*a)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/9*b*B*cos(d*x+c)^(5/2)*(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c)),x,6,2/5*(5*A*a^2+3*A*b^2+6*B*a*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(5*b^2*B+7*a*(2*A*b+B*a))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*(5*b^2*B+7*a*(2*A*b+B*a))*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/35*b*(7*A*b+9*B*a)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*b*B*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*(A+B*cos(d*x+c))/sqrt(cos(d*x+c)),x,5,2/5*(3*b^2*B+5*a*(2*A*b+B*a))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(3*A*a^2+A*b^2+2*B*a*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/15*b*(5*A*b+7*B*a)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/5*b*B*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x,5,-2*(A*a^2-A*b^2-2*B*a*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(6*A*a*b+3*B*a^2+B*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2*a^2*A*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*b^2*B*sqrt(cos(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x,5,-2*(2*A*a*b+B*a^2-B*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(A*a^2+3*A*b^2+6*B*a*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*a^2*A*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2*a*(2*A*b+B*a)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x,6,-2/5*(3*A*a^2+5*A*b^2+10*B*a*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(2*A*a*b+B*a^2+3*B*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/5*a^2*A*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/3*a*(2*A*b+B*a)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*(3*A*a^2+5*A*b^2+10*B*a*b)*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c)),x,8,2/15*(27*A*a^2*b+7*A*b^3+9*B*a^3+21*B*a*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/231*(77*A*a^3+165*A*a*b^2+165*B*a^2*b+45*B*b^3)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/231*(77*A*a^3+165*A*a*b^2+165*B*a^2*b+45*B*b^3)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*(27*A*a^2*b+7*A*b^3+9*B*a^3+21*B*a*b^2)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/77*b*(33*A*a*b+26*B*a^2+9*B*b^2)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/99*b^2*(11*A*b+15*B*a)*cos(d*x+c)^(7/2)*sin(d*x+c)/d+2/11*b*B*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))^3*(A+B*cos(d*x+c)),x,7,2/15*(15*A*a^3+27*A*a*b^2+27*B*a^2*b+7*B*b^3)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(21*A*a^2*b+5*A*b^3+7*B*a^3+15*B*a*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*(21*A*a^2*b+5*A*b^3+7*B*a^3+15*B*a*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/45*b*(27*A*a*b+22*B*a^2+7*B*b^2)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/63*b^2*(9*A*b+13*B*a)*cos(d*x+c)^(5/2)*sin(d*x+c)/d+2/9*b*B*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*(A+B*cos(d*x+c))/sqrt(cos(d*x+c)),x,6,2/5*(15*A*a^2*b+3*A*b^3+5*B*a^3+9*B*a*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/21*(21*A*a^3+21*A*a*b^2+21*B*a^2*b+5*B*b^3)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/21*b*(21*A*a*b+18*B*a^2+5*B*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/35*b^2*(7*A*b+11*B*a)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*b*B*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*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x,6,-2/5*(5*A*a^3-15*A*a*b^2-15*B*a^2*b-3*B*b^3)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(9*A*a^2*b+A*b^3+3*B*a^3+3*B*a*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d-2/3*b*(6*A*a^2-A*b^2-3*B*a*b)*sqrt(cos(d*x+c))*sin(d*x+c)/d-2/5*b^2*(5*A*a-B*b)*cos(d*x+c)^(3/2)*sin(d*x+c)/d+2*a*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))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x,6,-2*(3*A*a^2*b-A*b^3+B*a^3-3*B*a*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(A*a^3+9*A*a*b^2+9*B*a^2*b+B*b^3)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/3*a^2*(7*A*b+3*B*a)*sin(d*x+c)/d/sqrt(cos(d*x+c))-2/3*b^2*(A*a-B*b)*sqrt(cos(d*x+c))*sin(d*x+c)/d+2/3*a*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))^3*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x,6,-2/5*(3*A*a^3+15*A*a*b^2+15*B*a^2*b-5*B*b^3)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/3*(3*A*a^2*b+3*A*b^3+B*a^3+9*B*a*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d+2/15*a^2*(9*A*b+5*B*a)*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/5*a*(3*A*a^2+14*A*b^2+15*B*a*b)*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/5*a*A*(a+b*cos(d*x+c))^2*sin(d*x+c)/d/cos(d*x+c)^(5/2),1],
[cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x,7,-2/5*(5*A*a*b-5*B*a^2-3*B*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^3/d+2/3*(3*a^2+b^2)*(A*b-B*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^4/d-2*a^3*(A*b-B*a)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b^4/(a+b)/d+2/3*(A*b-B*a)*sqrt(cos(d*x+c))*sin(d*x+c)/b^2/d+2/5*B*cos(d*x+c)^(3/2)*sin(d*x+c)/b/d,1],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x,6,2*(A*b-B*a)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^2/d-2/3*(3*A*a*b-3*B*a^2-B*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^3/d+2*a^2*(A*b-B*a)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b^3/(a+b)/d+2/3*B*sqrt(cos(d*x+c))*sin(d*x+c)/b/d,1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c))/(a+b*cos(d*x+c)),x,5,2*B*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b/d+2*(A*b-B*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^2/d-2*a*(A*b-B*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))/sqrt(cos(d*x+c))/(a+b*cos(d*x+c)),x,3,2*B*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b/d+2*(A*b-B*a)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b/(a+b)/d,1],
[(A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x,5,-2*A*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d-2*(A*b-B*a)*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/a/(a+b)/d+2*A*sin(d*x+c)/a/d/sqrt(cos(d*x+c)),1],
[(A+B*cos(d*x+c))/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*b*(A*b-B*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],
[cos(d*x+c)^(5/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x,7,(3*A*a^2*b-2*A*b^3-5*B*a^3+4*B*a*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^3/(a^2-b^2)/d-1/3*(9*A*a^3*b-12*A*a*b^3-15*B*a^4+16*B*a^2*b^2+2*B*b^4)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^4/(a^2-b^2)/d+a^2*(3*A*a^2*b-5*A*b^3-5*B*a^3+7*B*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*A*a*b-5*B*a^2+2*B*b^2)*sqrt(cos(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)/d+a*(A*b-B*a)*cos(d*x+c)^(3/2)*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))/(a+b*cos(d*x+c))^2,x,6,-(A*a*b-3*B*a^2+2*B*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^2/(a^2-b^2)/d+(A*a^2*b-2*A*b^3-3*B*a^3+4*B*a*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^3/(a^2-b^2)/d-a*(A*a^2*b-3*A*b^3-3*B*a^3+5*B*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*(A*b-B*a)*sqrt(cos(d*x+c))*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))/(a+b*cos(d*x+c))^2,x,6,(A*b-B*a)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b/(a^2-b^2)/d+(A*a*b+B*a^2-2*B*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^2/(a^2-b^2)/d-(A*a^2*b+A*b^3+B*a^3-3*B*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-(A*b-B*a)*sqrt(cos(d*x+c))*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c))/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^2,x,6,-(A*b-B*a)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/(a^2-b^2)/d-(A*b-B*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b/(a^2-b^2)/d+(3*A*a^2*b-A*b^3-B*a^3-B*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*(A*b-B*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))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x,7,-(2*A*a^2-3*A*b^2+B*a*b)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/(a^2-b^2)/d+(A*b-B*a)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/(a^2-b^2)/d-(5*A*a^2*b-3*A*b^3-3*B*a^3+B*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*A*a^2-3*A*b^2+B*a*b)*sin(d*x+c)/a^2/(a^2-b^2)/d/sqrt(cos(d*x+c))+b*(A*b-B*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))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x,8,(4*A*a^2*b-5*A*b^3-2*B*a^3+3*B*a*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/(a^2-b^2)/d+1/3*(2*A*a^2-5*A*b^2+3*B*a*b)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/(a^2-b^2)/d+b*(7*A*a^2*b-5*A*b^3-5*B*a^3+3*B*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*A*a^2-5*A*b^2+3*B*a*b)*sin(d*x+c)/a^2/(a^2-b^2)/d/cos(d*x+c)^(3/2)-(4*A*a^2*b-5*A*b^3-2*B*a^3+3*B*a*b^2)*sin(d*x+c)/a^3/(a^2-b^2)/d/sqrt(cos(d*x+c))+b*(A*b-B*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)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x,7,-1/4*(3*A*a^3*b-9*A*a*b^3-15*B*a^4+29*B*a^2*b^2-8*B*b^4)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^3/(a^2-b^2)^2/d+1/4*(3*A*a^4*b-5*A*a^2*b^3+8*A*b^5-15*B*a^5+33*B*a^3*b^2-24*B*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*A*a^4*b-6*A*a^2*b^3+15*A*b^5-15*B*a^5+38*B*a^3*b^2-35*B*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*(A*b-B*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*(A*a^2*b-7*A*b^3-5*B*a^3+11*B*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],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x,7,-1/4*(A*a^2*b+5*A*b^3+3*B*a^3-9*B*a*b^2)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^2/(a^2-b^2)^2/d+1/4*(A*a^3*b-7*A*a*b^3+3*B*a^4-5*B*a^2*b^2+8*B*b^4)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^3/(a^2-b^2)^2/d-1/4*(A*a^4*b-10*A*a^2*b^3-3*A*b^5+3*B*a^5-6*B*a^3*b^2+15*B*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*(A*b-B*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*a^2*b+5*A*b^3+3*B*a^3-9*B*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],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3,x,7,1/4*(5*A*a^2*b+A*b^3-B*a^3-5*B*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*A*a^2*b+3*A*b^3+B*a^3-7*B*a*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^2/(a^2-b^2)^2/d-1/4*(3*A*a^4*b+10*A*a^2*b^3-A*b^5+B*a^5-10*B*a^3*b^2-3*B*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*(A*b-B*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*A*a^2*b+A*b^3-B*a^3-5*B*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],
[(A+B*cos(d*x+c))/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^3,x,7,-1/4*(9*A*a^2*b-3*A*b^3-5*B*a^3-B*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*A*a^2*b-A*b^3-3*B*a^3-3*B*a*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/b/(a^2-b^2)^2/d+1/4*(15*A*a^4*b-6*A*a^2*b^3+3*A*b^5-3*B*a^5-10*B*a^3*b^2+B*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*(A*b-B*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*A*a^2*b-3*A*b^3-5*B*a^3-B*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],
[(A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x,8,-1/4*(8*A*a^4-29*A*a^2*b^2+15*A*b^4+9*B*a^3*b-3*B*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*A*a^2*b-5*A*b^3-7*B*a^3+B*a*b^2)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/(a^2-b^2)^2/d-1/4*(35*A*a^4*b-38*A*a^2*b^3+15*A*b^5-15*B*a^5+6*B*a^3*b^2-3*B*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*A*a^4-29*A*a^2*b^2+15*A*b^4+9*B*a^3*b-3*B*a*b^3)*sin(d*x+c)/a^3/(a^2-b^2)^2/d/sqrt(cos(d*x+c))+1/2*b*(A*b-B*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*A*a^2*b-5*A*b^3-7*B*a^3+B*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],
[(A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^3,x,9,1/4*(24*A*a^4*b-65*A*a^2*b^3+35*A*b^5-8*B*a^5+29*B*a^3*b^2-15*B*a*b^4)*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^4/(a^2-b^2)^2/d+1/12*(8*A*a^4-61*A*a^2*b^2+35*A*b^4+33*B*a^3*b-15*B*a*b^3)*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/(a^2-b^2)^2/d+1/4*b*(63*A*a^4*b-86*A*a^2*b^3+35*A*b^5-35*B*a^5+38*B*a^3*b^2-15*B*a*b^4)*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*(8*A*a^4-61*A*a^2*b^2+35*A*b^4+33*B*a^3*b-15*B*a*b^3)*sin(d*x+c)/a^3/(a^2-b^2)^2/d/cos(d*x+c)^(3/2)-1/4*(24*A*a^4*b-65*A*a^2*b^3+35*A*b^5-8*B*a^5+29*B*a^3*b^2-15*B*a*b^4)*sin(d*x+c)/a^4/(a^2-b^2)^2/d/sqrt(cos(d*x+c))+1/2*b*(A*b-B*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*b*(13*A*a^2*b-7*A*b^3-9*B*a^3+3*B*a*b^2)*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],
[cos(d*x+c)^(5/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x,3,6/5*B*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2/5*B*cos(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[cos(d*x+c)^(3/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x,3,2/3*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,1],
[sqrt(cos(d*x+c))*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c)),x,2,2*B*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d,1],
[(a*B+b*B*cos(d*x+c))/sqrt(cos(d*x+c))/(a+b*cos(d*x+c)),x,2,2*B*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d,1],
[(a*B+b*B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x,3,-2*B*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d+2*B*sin(d*x+c)/d/sqrt(cos(d*x+c)),1],
[(a*B+b*B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x,3,2/3*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),1],
[cos(d*x+c)^(5/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x,7,-2*a*B*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^2/d+2/3*(3*a^2+b^2)*B*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^3/d-2*a^3*B*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b^3/(a+b)/d+2/3*B*sqrt(cos(d*x+c))*sin(d*x+c)/b/d,1],
[cos(d*x+c)^(3/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x,6,2*B*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b/d-2*a*B*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^2/d+2*a^2*B*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b^2/(a+b)/d,1],
[sqrt(cos(d*x+c))*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^2,x,4,2*B*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b/d-2*a*B*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/b/(a+b)/d,1],
[(a*B+b*B*cos(d*x+c))/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^2,x,2,2*B*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(a+b),sqrt(2))/(a+b)/d,1],
[(a*B+b*B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x,6,-2*B*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d-2*b*B*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],
[(a*B+b*B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x,8,2*b*B*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^2*B*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*sin(d*x+c)/a^2/d/sqrt(cos(d*x+c)),1],
[cos(d*x+c)^(3/2)*sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x,8,-1/24*(a-b)*sqrt(a+b)*(6*A*a*b-3*B*a^2+16*B*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*A*b-3*B*a+8*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^2/d+1/8*sqrt(a+b)*(2*A*a^2*b-8*A*b^3-B*a^3-4*B*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*A*a*b-3*B*a^2+16*B*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d/sqrt(cos(d*x+c))+1/4*(2*A*b-B*a)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+1/3*B*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d,1],
[sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c)),x,7,-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],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c))/sqrt(cos(d*x+c)),x,6,-(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+sqrt(a+b)*(2*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-sqrt(a+b)*(2*A*b+B*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+B*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))/cos(d*x+c)^(3/2),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/d+2*sqrt(a+b)*(A*b-a*(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)*B*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))*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x,4,2/3*(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*(a-b)*sqrt(a+b)*(A-3*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+2/3*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))/cos(d*x+c)^(7/2),x,5,2/15*(a-b)*sqrt(a+b)*(9*A*a^2-2*A*b^2+5*B*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*A*a+2*A*b-5*B*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+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))/cos(d*x+c)^(9/2),x,6,2/105*(a-b)*sqrt(a+b)*(19*A*a^2*b+8*A*b^3+63*B*a^3-14*B*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*A*b^2+a^2*(25*A-63*B)+2*a*b*(3*A-7*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+2/7*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*(25*A*a^2-4*A*b^2+7*B*a*b)*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)*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x,9,-1/192*(a-b)*sqrt(a+b)*(24*A*a^2*b+128*A*b^3-9*B*a^3+156*B*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*B-6*a^2*b*(4*A+B)-8*b^3*(16*A+9*B)-4*a*b^2*(28*A+39*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+1/64*sqrt(a+b)*(8*A*a^3*b-96*A*a*b^3-3*B*a^4-24*B*a^2*b^2-48*B*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*A*a^2*b+128*A*b^3-9*B*a^3+156*B*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*A*a*b-3*B*a^2+12*B*b^2)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+1/24*(8*A*b-3*B*a)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d+1/4*B*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d,1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c)),x,8,-1/24*(a-b)*sqrt(a+b)*(30*A*a*b+3*B*a^2+16*B*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*A*a*b+12*A*b^2+3*B*a^2+14*B*a*b+16*B*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*A*a^2*b+8*A*b^3-B*a^3+12*B*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*A*a*b+3*B*a^2+16*B*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(cos(d*x+c))+1/12*(6*A*b+7*B*a)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+1/3*b*B*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)*(A+B*cos(d*x+c))/sqrt(cos(d*x+c)),x,7,-1/4*(a-b)*sqrt(a+b)*(4*A*b+5*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/d+1/4*sqrt(a+b)*(8*A*a+4*A*b+5*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))/d-1/4*sqrt(a+b)*(12*A*a*b+3*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/d+1/4*(4*A*b+5*B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))+1/2*b*B*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)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x,7,(a-b)*sqrt(a+b)*(2*A*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-sqrt(a+b)*(2*a*(A-B)-b*(4*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-sqrt(a+b)*(2*A*b+3*B*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*A*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))-(2*A*a-B*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)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x,6,2/3*(a-b)*sqrt(a+b)*(4*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/d+2/3*sqrt(a+b)*(3*A*b^2+a^2*(A-3*B)-a*(4*A*b-6*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*b*sqrt(a+b)*B*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*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)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x,5,2/15*(a-b)*sqrt(a+b)*(9*A*a^2+3*A*b^2+20*B*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*A*a-3*A*b-5*B*a+15*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+2/5*a*A*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/15*(6*A*b+5*B*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)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x,6,2/105*(a-b)*sqrt(a+b)*(82*A*a^2*b-6*A*b^3+63*B*a^3+21*B*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*A*b^2-a^2*(25*A-63*B)+3*a*b*(19*A-7*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+2/7*a*A*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/35*(8*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*(25*A*a^2+3*A*b^2+42*B*a*b)*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))^(3/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x,7,2/315*(a-b)*sqrt(a+b)*(147*A*a^4+33*A*a^2*b^2+8*A*b^4+246*B*a^3*b-18*B*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/d+2/315*(a-b)*sqrt(a+b)*(8*A*b^3-a^3*(147*A-75*B)+3*a^2*b*(13*A-57*B)+6*a*b^2*(A-3*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+2/9*a*A*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(9/2)+2/63*(10*A*b+9*B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/315*(49*A*a^2+3*A*b^2+72*B*a*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/a/d/cos(d*x+c)^(5/2)+2/315*(88*A*a^2*b-4*A*b^3+75*B*a^3+9*B*a*b^2)*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)*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x,10,-1/1920*(a-b)*sqrt(a+b)*(150*A*a^3*b+2840*A*a*b^3-45*B*a^4+1692*B*a^2*b^2+1024*B*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*B-30*a^3*b*(5*A+B)-16*b^4*(45*A+64*B)-8*a*b^3*(355*A+193*B)-4*a^2*b^2*(295*A+423*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+1/128*sqrt(a+b)*(10*A*a^4*b-240*A*a^2*b^3-96*A*b^5-3*B*a^5-40*B*a^3*b^2-240*B*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*A*a^3*b+2840*A*a*b^3-45*B*a^4+1692*B*a^2*b^2+1024*B*b^4)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/d/sqrt(cos(d*x+c))+1/320*(50*A*a^2*b+120*A*b^3-15*B*a^3+172*B*a*b^2)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d+1/240*(50*A*a*b-15*B*a^2+64*B*b^2)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d+1/40*(10*A*b-3*B*a)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d+1/5*B*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b/d,1],
[sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c)),x,9,-1/192*(a-b)*sqrt(a+b)*(264*A*a^2*b+128*A*b^3+15*B*a^3+284*B*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*B+8*b^3*(16*A+9*B)+2*a^2*b*(132*A+59*B)+4*a*b^2*(52*A+71*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-1/64*sqrt(a+b)*(40*A*a^3*b+160*A*a*b^3-5*B*a^4+120*B*a^2*b^2+48*B*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*A*a^2*b+128*A*b^3+15*B*a^3+284*B*a*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(cos(d*x+c))+1/32*(24*A*a*b+5*B*a^2+12*B*b^2)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+1/24*(8*A*b+11*B*a)*sqrt(cos(d*x+c))*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d+1/4*b*B*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)*(A+B*cos(d*x+c))/sqrt(cos(d*x+c)),x,8,-1/24*(a-b)*sqrt(a+b)*(54*A*a*b+33*B*a^2+16*B*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*A+4*B)+a^2*(48*A+33*B)+a*(54*A*b+26*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))/d-1/8*sqrt(a+b)*(30*A*a^2*b+8*A*b^3+5*B*a^3+20*B*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*A*a*b+33*B*a^2+16*B*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))+1/4*b*(2*A*b+3*B*a)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+1/3*b*B*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)*(A+B*cos(d*x+c))/cos(d*x+c)^(3/2),x,8,1/4*(a-b)*sqrt(a+b)*(8*A*a^2-4*A*b^2-9*B*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*(A-B)-2*b^2*(2*A+B)-3*a*b*(8*A+3*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)*(20*A*a*b+15*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))/d-1/4*(8*A*a^2-4*A*b^2-9*B*a*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))-1/2*b*(4*A*a-B*b)*sqrt(cos(d*x+c))*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d+2*a*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))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(5/2),x,8,1/3*(a-b)*sqrt(a+b)*(14*A*a*b+6*B*a^2-3*B*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*A-9*B)-2*a^2*(A-3*B)-3*b^2*(6*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-b*sqrt(a+b)*(2*A*b+5*B*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*A*b+B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))-1/3*(14*A*a*b+6*B*a^2-3*B*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(cos(d*x+c))+2/3*a*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))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(7/2),x,7,2/15*(a-b)*sqrt(a+b)*(9*A*a^2+23*A*b^2+35*B*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*A*b^3-a*b^2*(23*A-45*B)+a^2*b*(17*A-35*B)-a^3*(9*A-5*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*b^2*sqrt(a+b)*B*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*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*(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)*(A+B*cos(d*x+c))/cos(d*x+c)^(9/2),x,6,2/105*(a-b)*sqrt(a+b)*(145*A*a^2*b+15*A*b^3+63*B*a^3+161*B*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*A-63*B)+15*b^2*(A-7*B)-8*a*b*(15*A-7*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+2/35*a*(10*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*(25*A*a^2+45*A*b^2+77*B*a*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(3/2)+2/7*a*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))^(5/2)*(A+B*cos(d*x+c))/cos(d*x+c)^(11/2),x,7,2/315*(a-b)*sqrt(a+b)*(147*A*a^4+279*A*a^2*b^2-10*A*b^4+435*B*a^3*b+45*B*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*A*b^3-6*a^2*b*(19*A-60*B)+3*a^3*(49*A-25*B)+15*a*b^2*(11*A-3*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+2/21*a*(4*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*(49*A*a^2+75*A*b^2+135*B*a*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(5/2)+2/315*(163*A*a^2*b+5*A*b^3+75*B*a^3+135*B*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*A*(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)*(A+B*cos(d*x+c))/cos(d*x+c)^(13/2),x,8,2/3465*(a-b)*sqrt(a+b)*(3705*A*a^4*b+255*A*a^2*b^3+40*A*b^5+1617*B*a^5+3069*B*a^3*b^2-110*B*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*A*b^4+3*a^4*(225*A-539*B)-6*a^3*b*(505*A-209*B)+15*a^2*b^2*(19*A-121*B)+10*a*b^3*(3*A-11*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+2/99*a*(14*A*b+11*B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(9/2)+2/693*(81*A*a^2+113*A*b^2+209*B*a*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/cos(d*x+c)^(7/2)+2/3465*(1145*A*a^2*b+15*A*b^3+539*B*a^3+825*B*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*A*a^4+1025*A*a^2*b^2-20*A*b^4+1793*B*a^3*b+55*B*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*A*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(11/2),1],
[(a+b*cos(d*x+c))^(5/2)*(3/2*b*B/a+B*cos(d*x+c))/cos(d*x+c)^(5/2),x,6,2*(a-b)*sqrt(a+b)*(a^2+3*b^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/d-(a-3*b)*sqrt(a+b)*(2*a^2-a*b+3*b^2)*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-b*sqrt(a+b)*(5*a+3*b^2/a)*B*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+b*B*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/cos(d*x+c)^(3/2),1],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/sqrt(a+b*cos(d*x+c)),x,7,-1/4*(a-b)*sqrt(a+b)*(4*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/b^2/d+1/4*sqrt(a+b)*(4*A*b-3*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^2/d+1/4*sqrt(a+b)*(4*A*a*b-3*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^3/d+1/4*(4*A*b-3*B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b^2/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)/b/d,1],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c))/sqrt(a+b*cos(d*x+c)),x,8,-(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/b/d+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))/b/d-sqrt(a+b)*(2*A*b-B*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+a*B*sin(d*x+c)/b/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c))+B*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c))/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),x,3,2*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)*B*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))/cos(d*x+c)^(3/2)/sqrt(a+b*cos(d*x+c)),x,3,2*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,1],
[(A+B*cos(d*x+c))/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))*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))/cos(d*x+c)^(7/2)/sqrt(a+b*cos(d*x+c)),x,5,2/15*(a-b)*sqrt(a+b)*(9*A*a^2+8*A*b^2-10*B*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*A*b^2+a^2*(9*A-5*B)-2*a*b*(A+5*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+2/5*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],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x,7,(2*A*a*b-3*B*a^2+B*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-(3*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))/b^2/sqrt(a+b)/d-sqrt(a+b)*(2*A*b-3*B*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*(A*b-B*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*a*b-3*B*a^2+B*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],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x,6,-2*(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/sqrt(a+b)/d+2*(A*b-B*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)*B*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*(A*b-B*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))/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x,4,2*(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^2/sqrt(a+b)/d+2*(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/sqrt(a+b)/d-2*(A*b-B*a)*sin(d*x+c)/(a^2-b^2)/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x,4,2*(A*a^2-2*A*b^2+B*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*A*b+a*(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/sqrt(a+b)/d+2*b*(A*b-B*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))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x,5,-2/3*(5*A*a^2*b-8*A*b^3-3*B*a^3+6*B*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*A*b+a*(A-3*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/sqrt(a+b)/d+2*b*(A*b-B*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*(A*a^2-4*A*b^2+3*B*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)^(5/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x,8,1/3*(6*A*a^3*b-14*A*a*b^3-15*B*a^4+26*B*a^2*b^2-3*B*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*a^2*b+2*A*a*b^2-12*A*b^3-15*B*a^3-5*B*a^2*b+21*B*a*b^2+3*B*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-b)/b^3/(a+b)^(3/2)/d-sqrt(a+b)*(2*A*b-5*B*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*(A*b-B*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*A*a^2*b-6*A*b^3-5*B*a^3+9*B*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*A*a^3*b-14*A*a*b^3-15*B*a^4+26*B*a^2*b^2-3*B*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],
[cos(d*x+c)^(3/2)*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x,7,2/3*(4*A*b^3+3*B*a^3-7*B*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*(A*a*b^2-3*A*b^3-3*B*a^3-B*a^2*b+6*B*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)*B*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*(A*b-B*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*A*b^3+3*B*a^3-7*B*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],
[sqrt(cos(d*x+c))*(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2),x,5,-2/3*(3*A*a^2+A*b^2-4*B*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*(3*A*a-A*b+B*a-3*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/(a-b)/(a+b)^(3/2)/d-2/3*(A*b-B*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*A*a^2+A*b^2-4*B*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],
[(A+B*cos(d*x+c))/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)*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^2*(A+B)+a*b*(3*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/sqrt(a+b)/(a^2-b^2)/d+2/3*b*(A*b-B*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*A*a^2*b-2*A*b^3-3*B*a^3-B*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],
[(A+B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x,5,2/3*(3*A*a^4-15*A*a^2*b^2+8*A*b^4+6*B*a^3*b-2*B*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*A*b^3-3*a^3*(A-B)+2*a*b^2*(3*A-B)-3*a^2*b*(3*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^3/sqrt(a+b)/(a^2-b^2)/d+2/3*b*(A*b-B*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*A*a^2*b-4*A*b^3-5*B*a^3+B*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],
[(A+B*cos(d*x+c))/cos(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x,6,-2/3*(8*A*a^4*b-28*A*a^2*b^3+16*A*b^5-3*B*a^5+15*B*a^3*b^2-8*B*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^5/(a-b)/(a+b)^(3/2)/d-2/3*(16*A*b^4-a^4*(A-3*B)+4*a*b^3*(3*A-2*B)-9*a^3*b*(A-B)-2*a^2*b^2*(8*A+3*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*b*(A*b-B*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*b*(10*A*a^2*b-6*A*b^3-7*B*a^3+3*B*a*b^2)*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*(A*a^4-13*A*a^2*b^2+8*A*b^4+8*B*a^3*b-4*B*a*b^3)*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)^(3/2)*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x,9,-(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/b/d+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))/b/d+a*sqrt(a+b)*B*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+a*B*sin(d*x+c)/b/d/sqrt(cos(d*x+c))/sqrt(a+b*cos(d*x+c))+B*sqrt(cos(d*x+c))*sin(d*x+c)/d/sqrt(a+b*cos(d*x+c)),1],
[sqrt(cos(d*x+c))*(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x,2,-2*sqrt(a+b)*B*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+b*B*cos(d*x+c))/sqrt(cos(d*x+c))/(a+b*cos(d*x+c))^(3/2),x,2,2*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,1],
[(a*B+b*B*cos(d*x+c))/cos(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),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*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],
[(1+cos(d*x+c))/cos(d*x+c)^(3/2)/sqrt(2+3*cos(d*x+c)),x,1,-cot(d*x+c)*EllipticE(sin(arcsin(sqrt(2+3*cos(d*x+c))/sqrt(5)/sqrt(cos(d*x+c)))),sqrt(5))*sqrt(-1-sec(d*x+c))*sqrt(1-sec(d*x+c))/d,1],
[(1+cos(d*x+c))/cos(d*x+c)^(3/2)/sqrt(-2+3*cos(d*x+c)),x,1,-sqrt(5)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(-2+3*cos(d*x+c))/sqrt(cos(d*x+c)))),sqrt(1/5))*sqrt(-1+sec(d*x+c))*sqrt(1+sec(d*x+c))/d,1],
[(1+cos(d*x+c))/sqrt(2-3*cos(d*x+c))/cos(d*x+c)^(3/2),x,2,sqrt(5)*sqrt(-cos(d*x+c))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(2-3*cos(d*x+c))/sqrt(-cos(d*x+c)))),sqrt(1/5))*sqrt(-1+sec(d*x+c))*sqrt(1+sec(d*x+c))/d,1],
[(1+cos(d*x+c))/sqrt(-2-3*cos(d*x+c))/cos(d*x+c)^(3/2),x,2,sqrt(-cos(d*x+c))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(-2-3*cos(d*x+c))/sqrt(5)/sqrt(-cos(d*x+c)))),sqrt(5))*sqrt(-1-sec(d*x+c))*sqrt(1-sec(d*x+c))/d,1],
[(1+cos(d*x+c))/cos(d*x+c)^(3/2)/sqrt(3+2*cos(d*x+c)),x,1,2/3*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(3+2*cos(d*x+c))/sqrt(5)/sqrt(cos(d*x+c)))),sqrt(-5))*sqrt(1-sec(d*x+c))*sqrt(1+sec(d*x+c))/d,1],
[(1+cos(d*x+c))/sqrt(3-2*cos(d*x+c))/cos(d*x+c)^(3/2),x,1,2/3*sqrt(5)*cot(d*x+c)*EllipticE(sin(arcsin(sqrt(3-2*cos(d*x+c))/sqrt(cos(d*x+c)))),sqrt(-1/5))*sqrt(1-sec(d*x+c))*sqrt(1+sec(d*x+c))/d,1],
[(1+cos(d*x+c))/cos(d*x+c)^(3/2)/sqrt(-3+2*cos(d*x+c)),x,2,-2/3*sqrt(5)*sqrt(-cos(d*x+c))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(-3+2*cos(d*x+c))/sqrt(-cos(d*x+c)))),sqrt(-1/5))*sqrt(1-sec(d*x+c))*sqrt(1+sec(d*x+c))/d,1],
[(1+cos(d*x+c))/sqrt(-3-2*cos(d*x+c))/cos(d*x+c)^(3/2),x,2,-2/3*sqrt(-cos(d*x+c))*sqrt(cos(d*x+c))*csc(d*x+c)*EllipticE(sin(arcsin(sqrt(-3-2*cos(d*x+c))/sqrt(5)/sqrt(-cos(d*x+c)))),sqrt(-5))*sqrt(1-sec(d*x+c))*sqrt(1+sec(d*x+c))/d,1],
[(c*cos(f*x+e))^m*(a+b*cos(f*x+e))^n*(A+B*cos(f*x+e)),x,0,Defer(Int)((c*cos(f*x+e))^m*(a+b*cos(f*x+e))^n*(A+B*cos(f*x+e)),x),0],
[(c*cos(f*x+e))^m*(a+b*cos(f*x+e))^4*(A+B*cos(f*x+e)),x,7,b*(A*b^3*(m^2+8*m+15)+4*a*b^2*B*(m^2+8*m+15)+2*a^3*B*(m^2+10*m+28)+a^2*A*b*(5*m^2+47*m+110))*(c*cos(f*x+e))^(1+m)*sin(f*x+e)/c/f/(2+m)/(4+m)/(5+m)+b^2*(b^2*B*(4+m)^2+2*a*A*b*(5+m)^2+a^2*B*(m^2+11*m+36))*cos(f*x+e)*(c*cos(f*x+e))^(1+m)*sin(f*x+e)/c/f/(3+m)/(4+m)/(5+m)+b*(A*b*(5+m)+a*B*(8+m))*(c*cos(f*x+e))^(1+m)*(a+b*cos(f*x+e))^2*sin(f*x+e)/c/f/(4+m)/(5+m)+b*B*(c*cos(f*x+e))^(1+m)*(a+b*cos(f*x+e))^3*sin(f*x+e)/c/f/(5+m)-(A*b^4*(m^2+4*m+3)+4*a*b^3*B*(m^2+4*m+3)+6*a^2*A*b^2*(m^2+5*m+4)+4*a^3*b*B*(m^2+5*m+4)+a^4*A*(m^2+6*m+8))*(c*cos(f*x+e))^(1+m)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],cos(f*x+e)^2)*sin(f*x+e)/c/f/(1+m)/(2+m)/(4+m)/sqrt(sin(f*x+e)^2)-(b^4*B*(m^2+6*m+8)+4*a*A*b^3*(m^2+7*m+10)+6*a^2*b^2*B*(m^2+7*m+10)+4*a^3*A*b*(m^2+8*m+15)+a^4*B*(m^2+8*m+15))*(c*cos(f*x+e))^(2+m)*hypergeom([1/2, 1+1/2*m],[2+1/2*m],cos(f*x+e)^2)*sin(f*x+e)/c^2/f/(2+m)/(3+m)/(5+m)/sqrt(sin(f*x+e)^2),1],
[(c*cos(f*x+e))^m*(a+b*cos(f*x+e))^3*(A+B*cos(f*x+e)),x,6,b*(b^2*B*(3+m)+3*a*A*b*(4+m)+2*a^2*B*(5+m))*(c*cos(f*x+e))^(1+m)*sin(f*x+e)/c/f/(2+m)/(4+m)+b^2*(A*b*(4+m)+a*B*(6+m))*cos(f*x+e)*(c*cos(f*x+e))^(1+m)*sin(f*x+e)/c/f/(3+m)/(4+m)+b*B*(c*cos(f*x+e))^(1+m)*(a+b*cos(f*x+e))^2*sin(f*x+e)/c/f/(4+m)-(a^2*(2+m)*(b*B*(1+m)+a*A*(4+m))+b*(1+m)*(b^2*B*(3+m)+3*a*A*b*(4+m)+2*a^2*B*(5+m)))*(c*cos(f*x+e))^(1+m)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],cos(f*x+e)^2)*sin(f*x+e)/c/f/(1+m)/(2+m)/(4+m)/sqrt(sin(f*x+e)^2)-(A*b^3*(2+m)+3*a*b^2*B*(2+m)+3*a^2*A*b*(3+m)+a^3*B*(3+m))*(c*cos(f*x+e))^(2+m)*hypergeom([1/2, 1+1/2*m],[2+1/2*m],cos(f*x+e)^2)*sin(f*x+e)/c^2/f/(2+m)/(3+m)/sqrt(sin(f*x+e)^2),1],
[(c*cos(f*x+e))^m*(a+b*cos(f*x+e))^2*(A+B*cos(f*x+e)),x,5,b*(A*b*(3+m)+a*B*(4+m))*(c*cos(f*x+e))^(1+m)*sin(f*x+e)/c/f/(2+m)/(3+m)+b*B*(c*cos(f*x+e))^(1+m)*(a+b*cos(f*x+e))*sin(f*x+e)/c/f/(3+m)-(A*b^2*(1+m)+2*a*b*B*(1+m)+a^2*A*(2+m))*(c*cos(f*x+e))^(1+m)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],cos(f*x+e)^2)*sin(f*x+e)/c/f/(1+m)/(2+m)/sqrt(sin(f*x+e)^2)-(b^2*B*(2+m)+a*(2*A*b+B*a)*(3+m))*(c*cos(f*x+e))^(2+m)*hypergeom([1/2, 1+1/2*m],[2+1/2*m],cos(f*x+e)^2)*sin(f*x+e)/c^2/f/(2+m)/(3+m)/sqrt(sin(f*x+e)^2),1],
[(c*cos(f*x+e))^m*(a+b*cos(f*x+e))*(A+B*cos(f*x+e)),x,5,b*B*(c*cos(f*x+e))^(1+m)*sin(f*x+e)/c/f/(2+m)-(b*B*(1+m)+a*A*(2+m))*(c*cos(f*x+e))^(1+m)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],cos(f*x+e)^2)*sin(f*x+e)/c/f/(1+m)/(2+m)/sqrt(sin(f*x+e)^2)-(A*b+B*a)*(c*cos(f*x+e))^(2+m)*hypergeom([1/2, 1+1/2*m],[2+1/2*m],cos(f*x+e)^2)*sin(f*x+e)/c^2/f/(2+m)/sqrt(sin(f*x+e)^2),1],
[(c*cos(f*x+e))^m*(A+B*cos(f*x+e))/(a+b*cos(f*x+e)),x,9,a*(A*b-B*a)*c*AppellF1(1/2,1/2-1/2*m,1,3/2,sin(f*x+e)^2,-b^2*sin(f*x+e)^2/(a^2-b^2))*(c*cos(f*x+e))^(-1+m)*(cos(f*x+e)^2)^(1/2-1/2*m)*sin(f*x+e)/b/(a^2-b^2)/f-(A*b-B*a)*AppellF1(1/2,-1/2*m,1,3/2,sin(f*x+e)^2,-b^2*sin(f*x+e)^2/(a^2-b^2))*(c*cos(f*x+e))^m*sin(f*x+e)/(a^2-b^2)/f/((cos(f*x+e)^2)^(1/2*m))-B*(c*cos(f*x+e))^(1+m)*hypergeom([1/2, 1/2+1/2*m],[3/2+1/2*m],cos(f*x+e)^2)*sin(f*x+e)/b/c/f/(1+m)/sqrt(sin(f*x+e)^2),1],
[(c*cos(f*x+e))^m*(a+b*cos(f*x+e))^(3/2)*(A+B*cos(f*x+e)),x,1,2*b*B*(c*cos(f*x+e))^(1+m)*sqrt(a+b*cos(f*x+e))*sin(f*x+e)/c/f/(5+2*m)+2*Defer(Int)((c*cos(f*x+e))^m*(1/2*a*c*(2*b*B*(1+m)+2*a*A*(5/2+m))+1/2*c*(b^2*B*(3+2*m)+a*(2*A*b+B*a)*(5+2*m))*cos(f*x+e)+1/2*b*c*(2*a*B*(3+m)+A*b*(5+2*m))*cos(f*x+e)^2)/sqrt(a+b*cos(f*x+e)),x)/c/(5+2*m),0],
[(c*cos(f*x+e))^m*sqrt(a+b*cos(f*x+e))*(A+B*cos(f*x+e)),x,0,Defer(Int)((c*cos(f*x+e))^m*sqrt(a+b*cos(f*x+e))*(A+B*cos(f*x+e)),x),0],
[(c*cos(f*x+e))^m*(A+B*cos(f*x+e))/sqrt(a+b*cos(f*x+e)),x,0,Defer(Int)((c*cos(f*x+e))^m*(A+B*cos(f*x+e))/sqrt(a+b*cos(f*x+e)),x),0],
[(c*cos(f*x+e))^m*(A+B*cos(f*x+e))/(a+b*cos(f*x+e))^(3/2),x,1,2*b*(A*b-B*a)*(c*cos(f*x+e))^(1+m)*sin(f*x+e)/a/(a^2-b^2)/c/f/sqrt(a+b*cos(f*x+e))+2*Defer(Int)((c*cos(f*x+e))^m*(1/2*c*(a*(A*a-B*b)+2*b*(A*b-B*a)*(1/2+m))-1/2*a*(A*b-B*a)*c*cos(f*x+e)-1/2*b*(A*b-B*a)*c*(3+2*m)*cos(f*x+e)^2)/sqrt(a+b*cos(f*x+e)),x)/a/(a^2-b^2)/c,0],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x,9,-2/5*a*(3*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+2/3*a*(A+B)*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)*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))*sec(d*x+c)^(5/2),x,8,-2*a*(A+B)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*a*(A+3*B)*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))*sec(d*x+c)^(3/2),x,7,-2*a*(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*a*(A+B)*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,1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sqrt(sec(d*x+c)),x,7,2*a*(A+B)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/3*a*(3*A+B)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/3*a*B*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c))/sqrt(sec(d*x+c)),x,8,2/5*a*(5*A+3*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*(A+B)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*a*B*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/3*a*(A+B)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))*(A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x,9,6/5*a*(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*a*(7*A+5*B)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/7*a*B*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/5*a*(A+B)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/21*a*(7*A+5*B)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x,9,-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)*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*(4*A+5*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/15*a^2*(7*A+5*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*A*sec(d*x+c)^(3/2)*(a^2+a^2*sec(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x,8,-4*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*(2*A+3*B)*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)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*A*sqrt(sec(d*x+c))*(a^2+a^2*sec(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x,8,4*a^2*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*(3*A+2*B)*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*(3*A-B)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*B*(a^2+a^2*sec(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))*sqrt(sec(d*x+c)),x,8,4/5*a^2*(5*A+4*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*(2*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*a^2*(5*A+7*B)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/5*B*(a^2+a^2*sec(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(3/2),1],
[(a+a*cos(d*x+c))^2*(A+B*cos(d*x+c))/sqrt(sec(d*x+c)),x,9,4/5*a^2*(4*A+3*B)*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)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/35*a^2*(7*A+9*B)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+4/21*a^2*(7*A+6*B)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/7*B*(a^2+a^2*sec(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(5/2),1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x,10,-4/5*a^3*(7*A+9*B)*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)*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*(7*A+9*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d+4/105*a^3*(41*A+42*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/7*a*A*sec(d*x+c)^(3/2)*(a+a*sec(d*x+c))^2*sin(d*x+c)/d+2/35*(11*A+7*B)*sec(d*x+c)^(3/2)*(a^3+a^3*sec(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x,9,-4/5*a^3*(9*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^3*(3*A+5*B)*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)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/5*a*A*sqrt(sec(d*x+c))*(a+a*sec(d*x+c))^2*sin(d*x+c)/d+2/15*(9*A+5*B)*sqrt(sec(d*x+c))*(a^3+a^3*sec(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x,9,-4*a^3*(A-B)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+20/3*a^3*(A+B)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+4/3*a^3*(4*A+B)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*a*B*(a+a*sec(d*x+c))^2*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/3*(A-B)*sqrt(sec(d*x+c))*(a^3+a^3*sec(d*x+c))*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x,9,4/5*a^3*(5*A+9*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^3*(5*A+3*B)*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*(5*A-6*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/5*a*B*(a+a*sec(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/15*(5*A+9*B)*(a^3+a^3*sec(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))*sqrt(sec(d*x+c)),x,9,4/5*a^3*(9*A+7*B)*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)*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)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/7*a*B*(a+a*sec(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/35*(7*A+11*B)*(a^3+a^3*sec(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(3/2),1],
[(a+a*cos(d*x+c))^3*(A+B*cos(d*x+c))/sqrt(sec(d*x+c)),x,10,4/15*a^3*(21*A+17*B)*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+11*B)*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*(24*A+23*B)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+4/21*a^3*(13*A+11*B)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/9*a*B*(a+a*sec(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(7/2)+2/63*(9*A+13*B)*(a^3+a^3*sec(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(5/2),1],
[(A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c)),x,9,3*(A-B)*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)*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)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d+1/3*(5*A-3*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d-(A-B)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*sec(d*x+c)),1],
[(A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c)),x,8,-(3*A-B)*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)*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)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d-(A-B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*sec(d*x+c)),1],
[(A+B*cos(d*x+c))*sqrt(sec(d*x+c))/(a+a*cos(d*x+c)),x,7,(A-B)*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)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d-(A-B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*sec(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),x,7,-(A-3*B)*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)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d+(A-B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*sec(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))/sec(d*x+c)^(3/2),x,8,3*(A-B)*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)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d-1/3*(3*A-5*B)*sin(d*x+c)/a/d/sqrt(sec(d*x+c))+(A-B)*sin(d*x+c)/d/sqrt(sec(d*x+c))/(a+a*sec(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))/sec(d*x+c)^(5/2),x,9,-3/5*(5*A-7*B)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/a/d+5/3*(A-B)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a/d-1/5*(5*A-7*B)*sin(d*x+c)/a/d/sec(d*x+c)^(3/2)+5/3*(A-B)*sin(d*x+c)/a/d/sqrt(sec(d*x+c))+(A-B)*sin(d*x+c)/d/sec(d*x+c)^(3/2)/(a+a*sec(d*x+c)),1],
[(A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^2,x,9,-(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)*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)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d/(1+sec(d*x+c))-1/3*(A-B)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*sec(d*x+c))^2,1],
[(A+B*cos(d*x+c))*sqrt(sec(d*x+c))/(a+a*cos(d*x+c))^2,x,8,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*(2*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-A*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d/(1+sec(d*x+c))-1/3*(A-B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*sec(d*x+c))^2,1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2/sqrt(sec(d*x+c)),x,8,-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*(A+2*B)*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+2*B)*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d/(1+sec(d*x+c))-1/3*(A-B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*sec(d*x+c))^2,1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2/sec(d*x+c)^(3/2),x,8,-(A-4*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*(2*A-5*B)*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*(2*A-5*B)*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d/(1+sec(d*x+c))+1/3*(A-B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*sec(d*x+c))^2,1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^2/sec(d*x+c)^(5/2),x,9,(4*A-7*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-5/3*(A-2*B)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^2/d-5/3*(A-2*B)*sin(d*x+c)/a^2/d/sqrt(sec(d*x+c))+1/3*(4*A-7*B)*sin(d*x+c)/a^2/d/sqrt(sec(d*x+c))/(1+sec(d*x+c))+1/3*(A-B)*sin(d*x+c)/d/sqrt(sec(d*x+c))/(a+a*sec(d*x+c))^2,1],
[(A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^3,x,10,-1/10*(49*A-9*B)*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)*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)*sqrt(sec(d*x+c))*sin(d*x+c)/a^3/d-1/5*(A-B)*sec(d*x+c)^(7/2)*sin(d*x+c)/d/(a+a*sec(d*x+c))^3-1/15*(8*A-3*B)*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d/(a+a*sec(d*x+c))^2-1/6*(13*A-3*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/(a^3+a^3*sec(d*x+c)),1],
[(A+B*cos(d*x+c))*sqrt(sec(d*x+c))/(a+a*cos(d*x+c))^3,x,9,1/10*(9*A+B)*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)*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)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/(a+a*sec(d*x+c))^3-1/15*(6*A-B)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d/(a+a*sec(d*x+c))^2-1/10*(9*A+B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a^3+a^3*sec(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3/sqrt(sec(d*x+c)),x,9,1/10*(A-B)*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)*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)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*sec(d*x+c))^3-1/15*(4*A+B)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/(a+a*sec(d*x+c))^2+1/6*(A+B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a^3+a^3*sec(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3/sec(d*x+c)^(3/2),x,9,-1/10*(A+9*B)*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)*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)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*sec(d*x+c))^3+1/15*(2*A+3*B)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/(a+a*sec(d*x+c))^2+1/6*(A+3*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a^3+a^3*sec(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3/sec(d*x+c)^(5/2),x,9,-1/10*(9*A-49*B)*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)*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)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*sec(d*x+c))^3+1/15*(3*A-8*B)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/(a+a*sec(d*x+c))^2+1/6*(3*A-13*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a^3+a^3*sec(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^3/sec(d*x+c)^(7/2),x,10,7/10*(7*A-17*B)*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)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/a^3/d-1/6*(13*A-33*B)*sin(d*x+c)/a^3/d/sqrt(sec(d*x+c))+1/5*(A-B)*sin(d*x+c)/d/sqrt(sec(d*x+c))/(a+a*sec(d*x+c))^3+1/3*(A-2*B)*sin(d*x+c)/a/d/sqrt(sec(d*x+c))/(a+a*sec(d*x+c))^2+7/30*(7*A-17*B)*sin(d*x+c)/d/sqrt(sec(d*x+c))/(a^3+a^3*sec(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(11/2),x,6,32/315*a*(8*A+9*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+16/315*a*(8*A+9*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+4/105*a*(8*A+9*B)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/63*a*(8*A+9*B)*sec(d*x+c)^(7/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/9*a*A*sec(d*x+c)^(9/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x,5,16/105*a*(6*A+7*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+8/105*a*(6*A+7*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/35*a*(6*A+7*B)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/7*a*A*sec(d*x+c)^(7/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x,4,4/15*a*(4*A+5*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*a*(4*A+5*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/5*a*A*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x,3,2/3*a*(2*A+3*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/3*a*A*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x,4,2*sqrt(a)*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))/d+2*a*A*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c)),1],
[sqrt(a+a*cos(d*x+c))*(A+B*cos(d*x+c))*sqrt(sec(d*x+c)),x,4,sqrt(a)*(2*A+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))/d+a*B*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))/sqrt(sec(d*x+c)),x,5,1/4*sqrt(a)*(4*A+3*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))/d+1/2*a*B*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/4*a*(4*A+3*B)*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))/sec(d*x+c)^(3/2),x,6,1/8*sqrt(a)*(6*A+5*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))/d+1/3*a*B*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(5/2)+1/12*a*(6*A+5*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/8*a*(6*A+5*B)*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))*sec(d*x+c)^(13/2),x,7,32/3465*a^2*(168*A+187*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+16/3465*a^2*(168*A+187*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+4/1155*a^2*(168*A+187*B)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/693*a^2*(168*A+187*B)*sec(d*x+c)^(7/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/99*a^2*(12*A+11*B)*sec(d*x+c)^(9/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/11*a*A*sqrt(a+a*cos(d*x+c))*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))*sec(d*x+c)^(11/2),x,6,16/315*a^2*(34*A+39*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+8/315*a^2*(34*A+39*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*a^2*(34*A+39*B)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/63*a^2*(10*A+9*B)*sec(d*x+c)^(7/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/9*a*A*sqrt(a+a*cos(d*x+c))*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))*sec(d*x+c)^(9/2),x,5,4/105*a^2*(52*A+63*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*a^2*(52*A+63*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/35*a^2*(8*A+7*B)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/7*a*A*sqrt(a+a*cos(d*x+c))*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))*sec(d*x+c)^(7/2),x,4,2/15*a^2*(18*A+25*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*a^2*(6*A+5*B)*sec(d*x+c)^(3/2)*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)^(5/2)*sin(d*x+c)/d,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x,5,2*a^(3/2)*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))/d+2/3*a^2*(4*A+3*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/3*a*A*sqrt(a+a*cos(d*x+c))*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))*sec(d*x+c)^(3/2),x,5,a^(3/2)*(2*A+3*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))/d-a^2*(2*A-B)*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,1],
[(a+a*cos(d*x+c))^(3/2)*(A+B*cos(d*x+c))*sqrt(sec(d*x+c)),x,5,1/4*a^(3/2)*(12*A+7*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))/d+1/4*a^2*(4*A+5*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))+1/2*a*B*sqrt(a+a*cos(d*x+c))*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))/sqrt(sec(d*x+c)),x,6,1/8*a^(3/2)*(14*A+11*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))/d+1/12*a^2*(6*A+7*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/3*a*B*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+1/8*a^2*(14*A+11*B)*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))/sec(d*x+c)^(3/2),x,7,1/64*a^(3/2)*(88*A+75*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))/d+1/24*a^2*(8*A+9*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(5/2)+1/4*a*B*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(5/2)+1/96*a^2*(88*A+75*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/64*a^2*(88*A+75*B)*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))*sec(d*x+c)^(15/2),x,8,32/45045*a^3*(4184*A+4615*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+16/45045*a^3*(4184*A+4615*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+4/15015*a^3*(4184*A+4615*B)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/9009*a^3*(4184*A+4615*B)*sec(d*x+c)^(7/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/1287*a^3*(280*A+299*B)*sec(d*x+c)^(9/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/143*a^2*(16*A+13*B)*sqrt(a+a*cos(d*x+c))*sec(d*x+c)^(11/2)*sin(d*x+c)/d+2/13*a*A*(a+a*cos(d*x+c))^(3/2)*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))*sec(d*x+c)^(13/2),x,7,16/3465*a^3*(710*A+803*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+8/3465*a^3*(710*A+803*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/1155*a^3*(710*A+803*B)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/693*a^3*(194*A+209*B)*sec(d*x+c)^(7/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/99*a^2*(14*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+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))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(11/2),x,6,4/315*a^3*(292*A+345*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/315*a^3*(292*A+345*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/315*a^3*(124*A+135*B)*sec(d*x+c)^(5/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/21*a^2*(4*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+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))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x,5,2/105*a^3*(230*A+301*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*a^3*(10*A+11*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/35*a^2*(10*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+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))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x,6,2*a^(5/2)*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))/d+2/15*a^3*(32*A+35*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/15*a^2*(8*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+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))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x,6,a^(5/2)*(2*A+5*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))/d-1/3*a^3*(14*A+3*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))+2*a^2*(2*A+B)*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,1],
[(a+a*cos(d*x+c))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x,6,1/4*a^(5/2)*(20*A+19*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))/d-1/4*a^3*(4*A-9*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))-1/2*a^2*(4*A-B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*a*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))^(5/2)*(A+B*cos(d*x+c))*sqrt(sec(d*x+c)),x,6,1/8*a^(5/2)*(38*A+25*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))/d+1/24*a^3*(54*A+49*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c))+1/4*a^2*(2*A+3*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/3*a*B*(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))^(5/2)*(A+B*cos(d*x+c))/sqrt(sec(d*x+c)),x,7,1/64*a^(5/2)*(200*A+163*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))/d+1/96*a^3*(104*A+95*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/24*a^2*(8*A+11*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+1/4*a*B*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+1/64*a^3*(200*A+163*B)*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))/sec(d*x+c)^(3/2),x,8,1/128*a^(5/2)*(326*A+283*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))/d+1/240*a^3*(170*A+157*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(5/2)+1/40*a^2*(10*A+13*B)*sqrt(a+a*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(5/2)+1/5*a*B*(a+a*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+1/192*a^3*(326*A+283*B)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/128*a^3*(326*A+283*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))*sec(d*x+c)^(11/2)/sqrt(a+a*cos(d*x+c)),x,9,-sqrt(2)*(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+2/315*(257*A-129*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))-2/315*(29*A-93*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*(19*A-3*B)*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))*sec(d*x+c)^(9/2)/sqrt(a+a*cos(d*x+c)),x,8,sqrt(2)*(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-2/105*(43*A-91*B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))+2/105*(31*A-7*B)*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))*sec(d*x+c)^(7/2)/sqrt(a+a*cos(d*x+c)),x,7,-sqrt(2)*(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+2/15*(13*A-5*B)*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))*sec(d*x+c)^(5/2)/sqrt(a+a*cos(d*x+c)),x,6,sqrt(2)*(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-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))*sec(d*x+c)^(3/2)/sqrt(a+a*cos(d*x+c)),x,5,-sqrt(2)*(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+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))*sqrt(sec(d*x+c))/sqrt(a+a*cos(d*x+c)),x,6,2*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)*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],
[(A+B*cos(d*x+c))/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),x,7,(2*A-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)*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*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c))/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2),x,8,-1/4*(4*A-7*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)*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*B*sin(d*x+c)/d/sqrt(a+a*cos(d*x+c))/sec(d*x+c)^(3/2)+1/4*(4*A-B)*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))*sec(d*x+c)^(9/2)/(a+a*cos(d*x+c))^(3/2),x,9,1/2*(19*A-15*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(2)/a^(3/2)/d-1/210*(1201*A-1029*B)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))+1/210*(397*A-273*B)*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)*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/2*(A-B)*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)*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))*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(3/2),x,8,-1/2*(15*A-11*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(2)/a^(3/2)/d+1/30*(147*A-95*B)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/30*(39*A-35*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/2*(A-B)*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)*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))*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(3/2),x,7,1/2*(11*A-7*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(2)/a^(3/2)/d-1/6*(19*A-15*B)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/sqrt(a+a*cos(d*x+c))-1/2*(A-B)*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)*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))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(3/2),x,6,-1/2*(7*A-3*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(2)/a^(3/2)/d-1/2*(A-B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)+1/2*(5*A-B)*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))*sqrt(sec(d*x+c))/(a+a*cos(d*x+c))^(3/2),x,5,1/2*(3*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(2)/a^(3/2)/d-1/2*(A-B)*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))/(a+a*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c)),x,7,2*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))/a^(3/2)/d+1/2*(A-5*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(2)/a^(3/2)/d+1/2*(A-B)*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))/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x,8,(2*A-3*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))/a^(3/2)/d-1/2*(5*A-9*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(2)/a^(3/2)/d+1/2*(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2)-1/2*(A-3*B)*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))*sec(d*x+c)^(7/2)/(a+a*cos(d*x+c))^(5/2),x,9,-1/16*(283*A-163*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(2)/a^(5/2)/d+1/240*(2671*A-1495*B)*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)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))-1/4*(A-B)*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)*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)*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))*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(5/2),x,8,1/16*(163*A-75*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(2)/a^(5/2)/d-1/48*(299*A-147*B)*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d/sqrt(a+a*cos(d*x+c))-1/4*(A-B)*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)*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)*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))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(5/2),x,7,-1/16*(75*A-19*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(2)/a^(5/2)/d-1/4*(A-B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)-1/16*(13*A-5*B)*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)*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))*sqrt(sec(d*x+c))/(a+a*cos(d*x+c))^(5/2),x,6,1/16*(19*A+5*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(2)/a^(5/2)/d-1/4*(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)/sqrt(sec(d*x+c))-1/16*(9*A-B)*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))/(a+a*cos(d*x+c))^(5/2)/sqrt(sec(d*x+c)),x,6,1/16*(5*A+3*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(2)/a^(5/2)/d+1/4*(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)/sqrt(sec(d*x+c))+1/16*(A+7*B)*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))/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x,8,2*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))/a^(5/2)/d+1/16*(3*A-43*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(2)/a^(5/2)/d+1/4*(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2)+1/16*(3*A-11*B)*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))/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x,9,(2*A-5*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))/a^(5/2)/d-1/16*(43*A-115*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(2)/a^(5/2)/d+1/4*(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2)+1/16*(7*A-15*B)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2)-1/16*(11*A-35*B)*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))*sec(d*x+c)^(5/2)/(a+a*cos(d*x+c))^(7/2),x,9,1/64*(1015*A-363*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(2)/a^(7/2)/d-1/192*(1887*A-691*B)*sqrt(sec(d*x+c))*sin(d*x+c)/a^3/d/sqrt(a+a*cos(d*x+c))-1/6*(A-B)*sec(d*x+c)^(3/2)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(7/2)-1/48*(23*A-11*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(5/2)-1/64*(109*A-41*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d/(a+a*cos(d*x+c))^(3/2)+1/192*(579*A-199*B)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^3/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+a*cos(d*x+c))^(7/2),x,8,-3/64*(121*A-21*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(2)/a^(7/2)/d-1/6*(A-B)*sqrt(sec(d*x+c))*sin(d*x+c)/d/(a+a*cos(d*x+c))^(7/2)-1/48*(19*A-7*B)*sqrt(sec(d*x+c))*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(5/2)-1/192*(199*A-43*B)*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/d/(a+a*cos(d*x+c))^(3/2)+1/192*(691*A-103*B)*sqrt(sec(d*x+c))*sin(d*x+c)/a^3/d/sqrt(a+a*cos(d*x+c)),1],
[(A+B*cos(d*x+c))*sqrt(sec(d*x+c))/(a+a*cos(d*x+c))^(7/2),x,7,1/64*(63*A+13*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(2)/a^(7/2)/d-1/6*(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(7/2)/sqrt(sec(d*x+c))-1/16*(5*A-B)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(5/2)/sqrt(sec(d*x+c))-1/192*(103*A+5*B)*sin(d*x+c)/a^2/d/(a+a*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2)/sqrt(sec(d*x+c)),x,7,1/64*(13*A+7*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(2)/a^(7/2)/d+1/6*(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(7/2)/sqrt(sec(d*x+c))+1/16*(A+3*B)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(5/2)/sqrt(sec(d*x+c))-1/192*(5*A-17*B)*sin(d*x+c)/a^2/d/(a+a*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(3/2),x,7,1/64*(7*A+5*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(2)/a^(7/2)/d+1/6*(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(3/2)+1/48*(A-13*B)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(5/2)/sqrt(sec(d*x+c))+1/192*(17*A+67*B)*sin(d*x+c)/a^2/d/(a+a*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(5/2),x,9,2*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))/a^(7/2)/d+1/64*(5*A-177*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(2)/a^(7/2)/d+1/6*(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(5/2)+1/48*(5*A-17*B)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2)+1/64*(5*A-49*B)*sin(d*x+c)/a^2/d/(a+a*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(7/2),x,10,(2*A-7*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))/a^(7/2)/d-1/64*(177*A-637*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(2)/a^(7/2)/d+1/6*(A-B)*sin(d*x+c)/d/(a+a*cos(d*x+c))^(7/2)/sec(d*x+c)^(7/2)+1/16*(3*A-7*B)*sin(d*x+c)/a/d/(a+a*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2)+1/192*(79*A-259*B)*sin(d*x+c)/a^2/d/(a+a*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2)-7/64*(7*A-27*B)*sin(d*x+c)/a^3/d/sqrt(a+a*cos(d*x+c))/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x,9,-2/5*(3*A*a+5*B*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*b+B*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*a+5*B*b)*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))*sec(d*x+c)^(5/2),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))/d+2/3*(A*a+3*B*b)*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))*sec(d*x+c)^(3/2),x,7,-2*(A*a-B*b)*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2*(A*b+B*a)*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,1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sqrt(sec(d*x+c)),x,7,2*(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))/d+2/3*(3*A*a+B*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*B*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c))/sqrt(sec(d*x+c)),x,8,2/5*(5*A*a+3*B*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*b+B*a)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*b*B*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/3*(A*b+B*a)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))*(A+B*cos(d*x+c))/sec(d*x+c)^(3/2),x,9,6/5*(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))/d+2/21*(7*A*a+5*B*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*B*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/5*(A*b+B*a)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/21*(7*A*a+5*B*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))*sec(d*x+c)^(7/2),x,9,-2/5*(3*a^2*A+5*b*(A*b+2*B*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*(2*A*a*b+B*a^2+3*B*b^2)*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^2*A+5*b*(A*b+2*B*a))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/15*a*(7*A*b+5*B*a)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*a*A*sec(d*x+c)^(3/2)*(b+a*sec(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x,8,-2*(2*A*a*b+B*a^2-B*b^2)*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^2+3*A*b^2+6*B*a*b)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/3*a*(5*A*b+3*B*a)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*a*A*sqrt(sec(d*x+c))*(b+a*sec(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x,8,-2*(a^2*A-b*(A*b+2*B*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*(6*A*a*b+3*B*a^2+B*b^2)*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*B*sin(d*x+c)/d/sqrt(sec(d*x+c))+2*a^2*A*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^2*(A+B*cos(d*x+c))*sqrt(sec(d*x+c)),x,8,2/5*(10*A*a*b+5*B*a^2+3*B*b^2)*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*a^2+A*b^2+2*B*a*b)*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*B*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/3*b*(A*b+2*B*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))/sqrt(sec(d*x+c)),x,9,2/5*(5*A*a^2+3*A*b^2+6*B*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*a*b+7*B*a^2+5*B*b^2)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/7*b^2*B*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/5*b*(A*b+2*B*a)*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)*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x,10,-2/5*(9*A*a^2*b+5*A*b^3+3*B*a^3+15*B*a*b^2)*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^3+21*A*a*b^2+21*B*a^2*b+21*B*b^3)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/5*(9*A*a^2*b+5*A*b^3+3*B*a^3+15*B*a*b^2)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/21*a*(5*A*a^2+18*A*b^2+21*B*a*b)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/35*a^2*(11*A*b+7*B*a)*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/7*a*A*sec(d*x+c)^(3/2)*(b+a*sec(d*x+c))^2*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x,9,-2/5*(3*A*a^3+15*A*a*b^2+15*B*a^2*b-5*B*b^3)*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*a^2*b+3*A*b^3+B*a^3+9*B*a*b^2)*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*a^2+14*A*b^2+15*B*a*b)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/15*a^2*(9*A*b+5*B*a)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/5*a*A*sqrt(sec(d*x+c))*(b+a*sec(d*x+c))^2*sin(d*x+c)/d,1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x,9,-2*(3*A*a^2*b-A*b^3+B*a^3-3*B*a*b^2)*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+9*A*a*b^2+9*B*a^2*b+B*b^3)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/3*a*(9*A*a*b+3*B*a^2-2*B*b^2)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*a^2*(A*a-B*b)*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/3*b*B*(b+a*sec(d*x+c))^2*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x,9,-2/5*(5*A*a^3-15*A*a*b^2-15*B*a^2*b-3*B*b^3)*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*a^2*b+A*b^3+3*B*a^3+3*B*a*b^2)*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*(5*A*b+9*B*a)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/5*a^2*(5*A*a-B*b)*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/5*b*B*(b+a*sec(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(3/2),1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))*sqrt(sec(d*x+c)),x,9,2/5*(15*A*a^2*b+3*A*b^3+5*B*a^3+9*B*a*b^2)*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*a^3+21*A*a*b^2+21*B*a^2*b+5*B*b^3)*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*(7*A*b+11*B*a)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/21*b*(21*A*a*b+18*B*a^2+5*B*b^2)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/7*b*B*(b+a*sec(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(5/2),1],
[(a+b*cos(d*x+c))^3*(A+B*cos(d*x+c))/sqrt(sec(d*x+c)),x,10,2/15*(15*A*a^3+27*A*a*b^2+27*B*a^2*b+7*B*b^3)*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*a^2*b+5*A*b^3+7*B*a^3+15*B*a*b^2)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/63*b^2*(9*A*b+13*B*a)*sin(d*x+c)/d/sec(d*x+c)^(5/2)+2/45*b*(27*A*a*b+22*B*a^2+7*B*b^2)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+2/21*(21*A*a^2*b+5*A*b^3+7*B*a^3+15*B*a*b^2)*sin(d*x+c)/d/sqrt(sec(d*x+c))+2/9*b*B*(b+a*sec(d*x+c))^2*sin(d*x+c)/d/sec(d*x+c)^(7/2),1],
[(A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x,11,2*(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*b*(A*b-B*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))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x,8,-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*(A*b-B*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/(a+b)/d+2*A*sqrt(sec(d*x+c))*sin(d*x+c)/a/d,1],
[(A+B*cos(d*x+c))*sqrt(sec(d*x+c))/(a+b*cos(d*x+c)),x,6,2*B*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-B*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/(a+b)/d,1],
[(A+B*cos(d*x+c))/(a+b*cos(d*x+c))/sqrt(sec(d*x+c)),x,8,2*B*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*b-B*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*(A*b-B*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))/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2),x,10,2*(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))/b^2/d-2/3*(3*A*a*b-3*B*a^2-B*b^2)*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^2*(A*b-B*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*B*sin(d*x+c)/b/d/sqrt(sec(d*x+c)),1],
[(A+B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^2,x,12,(4*A*a^2*b-5*A*b^3-2*B*a^3+3*B*a*b^2)*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*(2*A*a^2-5*A*b^2+3*B*a*b)*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+b*(7*A*a^2*b-5*A*b^3-5*B*a^3+3*B*a*b^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)/(a+b)^2/d-(4*A*a^2*b-5*A*b^3-2*B*a^3+3*B*a*b^2)*sqrt(sec(d*x+c))*sin(d*x+c)/a^3/(a^2-b^2)/d+1/3*(2*A*a^2-5*A*b^2+3*B*a*b)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/(a^2-b^2)/d+b*(A*b-B*a)*sec(d*x+c)^(5/2)*sin(d*x+c)/a/(a^2-b^2)/d/(b+a*sec(d*x+c)),1],
[(A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^2,x,11,-(2*A*a^2-3*A*b^2+B*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/(a^2-b^2)/d+(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/(a^2-b^2)/d-(5*A*a^2*b-3*A*b^3-3*B*a^3+B*a*b^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)/(a+b)^2/d+(2*A*a^2-3*A*b^2+B*a*b)*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/(a^2-b^2)/d+b*(A*b-B*a)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/(a^2-b^2)/d/(b+a*sec(d*x+c)),1],
[(A+B*cos(d*x+c))*sqrt(sec(d*x+c))/(a+b*cos(d*x+c))^2,x,10,-(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/(a^2-b^2)/d-(A*b-B*a)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/b/(a^2-b^2)/d+(3*A*a^2*b-A*b^3-B*a^3-B*a*b^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/(a-b)/b/(a+b)^2/d+b*(A*b-B*a)*sqrt(sec(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/(b+a*sec(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2/sqrt(sec(d*x+c)),x,10,(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))/b/(a^2-b^2)/d+(A*a*b+B*a^2-2*B*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*a^2*b+A*b^3+B*a^3-3*B*a*b^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)/b^2/(a+b)^2/d-(A*b-B*a)*sqrt(sec(d*x+c))*sin(d*x+c)/(a^2-b^2)/d/(b+a*sec(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2/sec(d*x+c)^(3/2),x,10,-(A*a*b-3*B*a^2+2*B*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^2*b-2*A*b^3-3*B*a^3+4*B*a*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*(A*a^2*b-3*A*b^3-3*B*a^3+5*B*a*b^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)/b^3/(a+b)^2/d+a*(A*b-B*a)*sqrt(sec(d*x+c))*sin(d*x+c)/b/(a^2-b^2)/d/(b+a*sec(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^2/sec(d*x+c)^(5/2),x,11,(3*A*a^2*b-2*A*b^3-5*B*a^3+4*B*a*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*(9*A*a^3*b-12*A*a*b^3-15*B*a^4+16*B*a^2*b^2+2*B*b^4)*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^2*(3*A*a^2*b-5*A*b^3-5*B*a^3+7*B*a*b^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)/b^4/(a+b)^2/d-1/3*(3*A*a*b-5*B*a^2+2*B*b^2)*sin(d*x+c)/b^2/(a^2-b^2)/d/sqrt(sec(d*x+c))+a*(A*b-B*a)*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(sec(d*x+c))/(b+a*sec(d*x+c)),1],
[(A+B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^3,x,12,-1/4*(8*A*a^4-29*A*a^2*b^2+15*A*b^4+9*B*a^3*b-3*B*a*b^3)*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*(11*A*a^2*b-5*A*b^3-7*B*a^3+B*a*b^2)*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)^2/d-1/4*(35*A*a^4*b-38*A*a^2*b^3+15*A*b^5-15*B*a^5+6*B*a^3*b^2-3*B*a*b^4)*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/(a+b)^3/d+1/4*(8*A*a^4-29*A*a^2*b^2+15*A*b^4+9*B*a^3*b-3*B*a*b^3)*sqrt(sec(d*x+c))*sin(d*x+c)/a^3/(a^2-b^2)^2/d+1/2*b*(A*b-B*a)*sec(d*x+c)^(5/2)*sin(d*x+c)/a/(a^2-b^2)/d/(b+a*sec(d*x+c))^2+1/4*b*(11*A*a^2*b-5*A*b^3-7*B*a^3+B*a*b^2)*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/(a^2-b^2)^2/d/(b+a*sec(d*x+c)),1],
[(A+B*cos(d*x+c))*sqrt(sec(d*x+c))/(a+b*cos(d*x+c))^3,x,11,-1/4*(9*A*a^2*b-3*A*b^3-5*B*a^3-B*a*b^2)*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)^2/d-1/4*(7*A*a^2*b-A*b^3-3*B*a^3-3*B*a*b^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)^2/d+1/4*(15*A*a^4*b-6*A*a^2*b^3+3*A*b^5-3*B*a^5-10*B*a^3*b^2+B*a*b^4)*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/(a+b)^3/d+1/2*b*(A*b-B*a)*sec(d*x+c)^(3/2)*sin(d*x+c)/a/(a^2-b^2)/d/(b+a*sec(d*x+c))^2+1/4*b*(9*A*a^2*b-3*A*b^3-5*B*a^3-B*a*b^2)*sqrt(sec(d*x+c))*sin(d*x+c)/a^2/(a^2-b^2)^2/d/(b+a*sec(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3/sqrt(sec(d*x+c)),x,11,1/4*(5*A*a^2*b+A*b^3-B*a^3-5*B*a*b^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)^2/d+1/4*(3*A*a^2*b+3*A*b^3+B*a^3-7*B*a*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)^2/d-1/4*(3*A*a^4*b+10*A*a^2*b^3-A*b^5+B*a^5-10*B*a^3*b^2-3*B*a*b^4)*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^2/(a+b)^3/d+1/2*b*(A*b-B*a)*sqrt(sec(d*x+c))*sin(d*x+c)/a/(a^2-b^2)/d/(b+a*sec(d*x+c))^2-1/4*(7*A*a^2*b-A*b^3-3*B*a^3-3*B*a*b^2)*sqrt(sec(d*x+c))*sin(d*x+c)/a/(a^2-b^2)^2/d/(b+a*sec(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3/sec(d*x+c)^(3/2),x,11,-1/4*(A*a^2*b+5*A*b^3+3*B*a^3-9*B*a*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)^2/d+1/4*(A*a^3*b-7*A*a*b^3+3*B*a^4-5*B*a^2*b^2+8*B*b^4)*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*a^4*b-10*A*a^2*b^3-3*A*b^5+3*B*a^5-6*B*a^3*b^2+15*B*a*b^4)*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^3/(a+b)^3/d-1/2*(A*b-B*a)*sqrt(sec(d*x+c))*sin(d*x+c)/(a^2-b^2)/d/(b+a*sec(d*x+c))^2+1/4*(3*A*a^2*b+3*A*b^3+B*a^3-7*B*a*b^2)*sqrt(sec(d*x+c))*sin(d*x+c)/b/(a^2-b^2)^2/d/(b+a*sec(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3/sec(d*x+c)^(5/2),x,11,-1/4*(3*A*a^3*b-9*A*a*b^3-15*B*a^4+29*B*a^2*b^2-8*B*b^4)*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*a^4*b-5*A*a^2*b^3+8*A*b^5-15*B*a^5+33*B*a^3*b^2-24*B*a*b^4)*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*a*(3*A*a^4*b-6*A*a^2*b^3+15*A*b^5-15*B*a^5+38*B*a^3*b^2-35*B*a*b^4)*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*(A*b-B*a)*sqrt(sec(d*x+c))*sin(d*x+c)/b/(a^2-b^2)/d/(b+a*sec(d*x+c))^2+1/4*a*(A*a^2*b-7*A*b^3-5*B*a^3+11*B*a*b^2)*sqrt(sec(d*x+c))*sin(d*x+c)/b^2/(a^2-b^2)^2/d/(b+a*sec(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^3/sec(d*x+c)^(7/2),x,12,1/4*(15*A*a^4*b-29*A*a^2*b^3+8*A*b^5-35*B*a^5+65*B*a^3*b^2-24*B*a*b^4)*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*a^5*b-99*A*a^3*b^3+72*A*a*b^5-105*B*a^6+223*B*a^4*b^2-128*B*a^2*b^4-8*B*b^6)*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^2*(15*A*a^4*b-38*A*a^2*b^3+35*A*b^5-35*B*a^5+86*B*a^3*b^2-63*B*a*b^4)*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-1/12*(15*A*a^3*b-33*A*a*b^3-35*B*a^4+61*B*a^2*b^2-8*B*b^4)*sin(d*x+c)/b^3/(a^2-b^2)^2/d/sqrt(sec(d*x+c))+1/2*a*(A*b-B*a)*sin(d*x+c)/b/(a^2-b^2)/d/sqrt(sec(d*x+c))/(b+a*sec(d*x+c))^2+1/4*a*(3*A*a^2*b-9*A*b^3-7*B*a^3+13*B*a*b^2)*sin(d*x+c)/b^2/(a^2-b^2)^2/d/sqrt(sec(d*x+c))/(b+a*sec(d*x+c)),1],
[(a*B+b*B*cos(d*x+c))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c)),x,4,2/3*B*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/3*B*sec(d*x+c)^(3/2)*sin(d*x+c)/d,1],
[(a*B+b*B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c)),x,4,-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*B*sqrt(sec(d*x+c))*sin(d*x+c)/d,1],
[(a*B+b*B*cos(d*x+c))*sqrt(sec(d*x+c))/(a+b*cos(d*x+c)),x,3,2*B*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d,1],
[(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))/sqrt(sec(d*x+c)),x,3,2*B*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d,1],
[(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))/sec(d*x+c)^(3/2),x,4,2/3*B*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))*sqrt(sec(d*x+c))/d+2/3*B*sin(d*x+c)/d/sqrt(sec(d*x+c)),1],
[(a*B+b*B*cos(d*x+c))/(a+b*cos(d*x+c))/sec(d*x+c)^(5/2),x,4,6/5*B*sqrt(cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))*sqrt(sec(d*x+c))/d+2/5*B*sin(d*x+c)/d/sec(d*x+c)^(3/2),1],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x,7,2/105*(a-b)*sqrt(a+b)*(19*A*a^2*b+8*A*b^3+63*B*a^3-14*B*a*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^4/d/sqrt(sec(d*x+c))+2/105*(a-b)*sqrt(a+b)*(8*A*b^2+a^2*(25*A-63*B)+2*a*b*(3*A-7*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))+2/105*(25*A*a^2-4*A*b^2+7*B*a*b)*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))*sec(d*x+c)^(7/2),x,6,2/15*(a-b)*sqrt(a+b)*(9*A*a^2-2*A*b^2+5*B*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))-2/15*(a-b)*sqrt(a+b)*(9*A*a+2*A*b-5*B*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+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))*sec(d*x+c)^(5/2),x,5,2/3*(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*(a-b)*sqrt(a+b)*(A-3*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))+2/3*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))*sec(d*x+c)^(3/2),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/d/sqrt(sec(d*x+c))+2*sqrt(a+b)*(A*b-a*(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)*B*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],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c))*sqrt(sec(d*x+c)),x,7,-(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],
[sqrt(a+b*cos(d*x+c))*(A+B*cos(d*x+c))/sqrt(sec(d*x+c)),x,8,-1/4*(a-b)*sqrt(a+b)*(4*A*b+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/b/d/sqrt(sec(d*x+c))+1/4*sqrt(a+b)*(4*A*b+(a+2*b)*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/d/sqrt(sec(d*x+c))-1/4*sqrt(a+b)*(4*A*a*b-B*a^2+4*B*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*B*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/4*(4*A*b+B*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))/sec(d*x+c)^(3/2),x,9,-1/24*(a-b)*sqrt(a+b)*(6*A*a*b-3*B*a^2+16*B*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/d/sqrt(sec(d*x+c))+1/24*sqrt(a+b)*(a+2*b)*(6*A*b-3*B*a+8*B*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*a^2*b-8*A*b^3-B*a^3-4*B*a*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))+1/4*(2*A*b-B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/3*B*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/24*(6*A*a*b-3*B*a^2+16*B*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))^(3/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(11/2),x,8,2/315*(a-b)*sqrt(a+b)*(147*A*a^4+33*A*a^2*b^2+8*A*b^4+246*B*a^3*b-18*B*a*b^3)*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-a^3*(147*A-75*B)+3*a^2*b*(13*A-57*B)+6*a*b^2*(A-3*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))+2/315*(88*A*a^2*b-4*A*b^3+75*B*a^3+9*B*a*b^2)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d+2/315*(49*A*a^2+3*A*b^2+72*B*a*b)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d+2/63*(10*A*b+9*B*a)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/9*a*A*sqrt(a+b*cos(d*x+c))*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))*sec(d*x+c)^(9/2),x,7,2/105*(a-b)*sqrt(a+b)*(82*A*a^2*b-6*A*b^3+63*B*a^3+21*B*a*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^3/d/sqrt(sec(d*x+c))-2/105*(a-b)*sqrt(a+b)*(6*A*b^2-a^2*(25*A-63*B)+3*a*b*(19*A-7*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*(25*A*a^2+3*A*b^2+42*B*a*b)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d+2/35*(8*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*sqrt(a+b*cos(d*x+c))*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))*sec(d*x+c)^(7/2),x,6,2/15*(a-b)*sqrt(a+b)*(9*A*a^2+3*A*b^2+20*B*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))-2/15*(a-b)*sqrt(a+b)*(9*A*a-3*A*b-5*B*a+15*B*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))+2/15*(6*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*sqrt(a+b*cos(d*x+c))*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))*sec(d*x+c)^(5/2),x,7,2/3*(a-b)*sqrt(a+b)*(4*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/d/sqrt(sec(d*x+c))+2/3*sqrt(a+b)*(3*A*b^2+a^2*(A-3*B)-a*(4*A*b-6*B*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*b*sqrt(a+b)*B*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*A*sqrt(a+b*cos(d*x+c))*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))*sec(d*x+c)^(3/2),x,8,(a-b)*sqrt(a+b)*(2*A*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*(A-B)-b*(4*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+3*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))/d/sqrt(sec(d*x+c))+2*a*A*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d-(2*A*a-B*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))^(3/2)*(A+B*cos(d*x+c))*sqrt(sec(d*x+c)),x,8,-1/4*(a-b)*sqrt(a+b)*(4*A*b+5*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/d/sqrt(sec(d*x+c))+1/4*sqrt(a+b)*(8*A*a+4*A*b+5*B*a+2*B*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)*(12*A*a*b+3*B*a^2+4*B*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*B*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/4*(4*A*b+5*B*a)*sqrt(a+b*cos(d*x+c))*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))/sqrt(sec(d*x+c)),x,9,-1/24*(a-b)*sqrt(a+b)*(30*A*a*b+3*B*a^2+16*B*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)*(30*A*a*b+12*A*b^2+3*B*a^2+14*B*a*b+16*B*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*sqrt(a+b)*(6*A*a^2*b+8*A*b^3-B*a^3+12*B*a*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))+1/3*b*B*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sec(d*x+c)^(3/2)+1/12*(6*A*b+7*B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/24*(30*A*a*b+3*B*a^2+16*B*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))/sec(d*x+c)^(3/2),x,10,-1/192*(a-b)*sqrt(a+b)*(24*A*a^2*b+128*A*b^3-9*B*a^3+156*B*a*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/d/sqrt(sec(d*x+c))-1/192*sqrt(a+b)*(9*a^3*B-6*a^2*b*(4*A+B)-8*b^3*(16*A+9*B)-4*a*b^2*(28*A+39*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))+1/64*sqrt(a+b)*(8*A*a^3*b-96*A*a*b^3-3*B*a^4-24*B*a^2*b^2-48*B*b^4)*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*(8*A*a*b-3*B*a^2+12*B*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/24*(8*A*b-3*B*a)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/4*B*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/192*(24*A*a^2*b+128*A*b^3-9*B*a^3+156*B*a*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+B*cos(d*x+c))*sec(d*x+c)^(13/2),x,9,2/3465*(a-b)*sqrt(a+b)*(3705*A*a^4*b+255*A*a^2*b^3+40*A*b^5+1617*B*a^5+3069*B*a^3*b^2-110*B*a*b^4)*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+3*a^4*(225*A-539*B)-6*a^3*b*(505*A-209*B)+15*a^2*b^2*(19*A-121*B)+10*a*b^3*(3*A-11*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))+2/3465*(675*A*a^4+1025*A*a^2*b^2-20*A*b^4+1793*B*a^3*b+55*B*a*b^3)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a^2/d+2/3465*(1145*A*a^2*b+15*A*b^3+539*B*a^3+825*B*a*b^2)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/a/d+2/693*(81*A*a^2+113*A*b^2+209*B*a*b)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(7/2)*sin(d*x+c)/d+2/99*a*(14*A*b+11*B*a)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(9/2)*sin(d*x+c)/d+2/11*a*A*(a+b*cos(d*x+c))^(3/2)*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))*sec(d*x+c)^(11/2),x,8,2/315*(a-b)*sqrt(a+b)*(147*A*a^4+279*A*a^2*b^2-10*A*b^4+435*B*a^3*b+45*B*a*b^3)*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^3-6*a^2*b*(19*A-60*B)+3*a^3*(49*A-25*B)+15*a*b^2*(11*A-3*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))+2/315*(163*A*a^2*b+5*A*b^3+75*B*a^3+135*B*a*b^2)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/a/d+2/315*(49*A*a^2+75*A*b^2+135*B*a*b)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(5/2)*sin(d*x+c)/d+2/21*a*(4*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*(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))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(9/2),x,7,2/105*(a-b)*sqrt(a+b)*(145*A*a^2*b+15*A*b^3+63*B*a^3+161*B*a*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^2/d/sqrt(sec(d*x+c))+2/105*(a-b)*sqrt(a+b)*(a^2*(25*A-63*B)+15*b^2*(A-7*B)-8*a*b*(15*A-7*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))+2/105*(25*A*a^2+45*A*b^2+77*B*a*b)*sqrt(a+b*cos(d*x+c))*sec(d*x+c)^(3/2)*sin(d*x+c)/d+2/35*a*(10*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*(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))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(7/2),x,8,2/15*(a-b)*sqrt(a+b)*(9*A*a^2+23*A*b^2+35*B*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/d/sqrt(sec(d*x+c))+2/15*sqrt(a+b)*(15*A*b^3-a*b^2*(23*A-45*B)+a^2*b*(17*A-35*B)-a^3*(9*A-5*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*b^2*sqrt(a+b)*B*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*a*(8*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*(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))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(5/2),x,9,1/3*(a-b)*sqrt(a+b)*(14*A*a*b+6*B*a^2-3*B*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/d/sqrt(sec(d*x+c))-1/3*sqrt(a+b)*(2*a*b*(7*A-9*B)-2*a^2*(A-3*B)-3*b^2*(6*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))-b*sqrt(a+b)*(2*A*b+5*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))/d/sqrt(sec(d*x+c))+2*a*(2*A*b+B*a)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d-1/3*(14*A*a*b+6*B*a^2-3*B*b^2)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2/3*a*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))^(5/2)*(A+B*cos(d*x+c))*sec(d*x+c)^(3/2),x,9,1/4*(a-b)*sqrt(a+b)*(8*A*a^2-4*A*b^2-9*B*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/d/sqrt(sec(d*x+c))-1/4*sqrt(a+b)*(8*a^2*(A-B)-2*b^2*(2*A+B)-3*a*b*(8*A+3*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)*(20*A*a*b+15*B*a^2+4*B*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*(4*A*a-B*b)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))-1/4*(8*A*a^2-4*A*b^2-9*B*a*b)*sqrt(a+b*cos(d*x+c))*sqrt(sec(d*x+c))*sin(d*x+c)/d+2*a*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))^(5/2)*(A+B*cos(d*x+c))*sqrt(sec(d*x+c)),x,9,-1/24*(a-b)*sqrt(a+b)*(54*A*a*b+33*B*a^2+16*B*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/d/sqrt(sec(d*x+c))+1/24*sqrt(a+b)*(4*b^2*(3*A+4*B)+a^2*(48*A+33*B)+a*(54*A*b+26*B*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))-1/8*sqrt(a+b)*(30*A*a^2*b+8*A*b^3+5*B*a^3+20*B*a*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))+1/4*b*(2*A*b+3*B*a)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/3*b*B*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/24*(54*A*a*b+33*B*a^2+16*B*b^2)*sqrt(a+b*cos(d*x+c))*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))/sqrt(sec(d*x+c)),x,10,-1/192*(a-b)*sqrt(a+b)*(264*A*a^2*b+128*A*b^3+15*B*a^3+284*B*a*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))+1/192*sqrt(a+b)*(15*a^3*B+8*b^3*(16*A+9*B)+2*a^2*b*(132*A+59*B)+4*a*b^2*(52*A+71*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/d/sqrt(sec(d*x+c))-1/64*sqrt(a+b)*(40*A*a^3*b+160*A*a*b^3-5*B*a^4+120*B*a^2*b^2+48*B*b^4)*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*b*B*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sec(d*x+c)^(3/2)+1/32*(24*A*a*b+5*B*a^2+12*B*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/24*(8*A*b+11*B*a)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/d/sqrt(sec(d*x+c))+1/192*(264*A*a^2*b+128*A*b^3+15*B*a^3+284*B*a*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+B*cos(d*x+c))/sec(d*x+c)^(3/2),x,11,-1/1920*(a-b)*sqrt(a+b)*(150*A*a^3*b+2840*A*a*b^3-45*B*a^4+1692*B*a^2*b^2+1024*B*b^4)*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*B-30*a^3*b*(5*A+B)-16*b^4*(45*A+64*B)-8*a*b^3*(355*A+193*B)-4*a^2*b^2*(295*A+423*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))+1/128*sqrt(a+b)*(10*A*a^4*b-240*A*a^2*b^3-96*A*b^5-3*B*a^5-40*B*a^3*b^2-240*B*a*b^4)*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*a^2*b+120*A*b^3-15*B*a^3+172*B*a*b^2)*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/240*(50*A*a*b-15*B*a^2+64*B*b^2)*(a+b*cos(d*x+c))^(3/2)*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/40*(10*A*b-3*B*a)*(a+b*cos(d*x+c))^(5/2)*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/5*B*(a+b*cos(d*x+c))^(7/2)*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/1920*(150*A*a^3*b+2840*A*a*b^3-45*B*a^4+1692*B*a^2*b^2+1024*B*b^4)*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))*sec(d*x+c)^(7/2)/sqrt(a+b*cos(d*x+c)),x,6,2/15*(a-b)*sqrt(a+b)*(9*A*a^2+8*A*b^2-10*B*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^4/d/sqrt(sec(d*x+c))-2/15*sqrt(a+b)*(8*A*b^2+a^2*(9*A-5*B)-2*a*b*(A+5*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))-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))*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))*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))*sec(d*x+c)^(3/2)/sqrt(a+b*cos(d*x+c)),x,4,2*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)),1],
[(A+B*cos(d*x+c))*sqrt(sec(d*x+c))/sqrt(a+b*cos(d*x+c)),x,4,2*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)*B*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))/sqrt(a+b*cos(d*x+c))/sqrt(sec(d*x+c)),x,9,-(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/b/d/sqrt(sec(d*x+c))+sqrt(a+b)*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/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^2/d/sqrt(sec(d*x+c))+B*sin(d*x+c)/d/sqrt(a+b*cos(d*x+c))/sqrt(sec(d*x+c))+a*B*sqrt(sec(d*x+c))*sin(d*x+c)/b/d/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c))/sqrt(a+b*cos(d*x+c))/sec(d*x+c)^(3/2),x,8,-1/4*(a-b)*sqrt(a+b)*(4*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/b^2/d/sqrt(sec(d*x+c))+1/4*sqrt(a+b)*(4*A*b-3*B*a+2*B*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))+1/4*sqrt(a+b)*(4*A*a*b-3*B*a^2-4*B*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*B*sqrt(a+b*cos(d*x+c))*sin(d*x+c)/b/d/sqrt(sec(d*x+c))+1/4*(4*A*b-3*B*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))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(3/2),x,6,-2/3*(5*A*a^2*b-8*A*b^3-3*B*a^3+6*B*a*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^4/sqrt(a+b)/d/sqrt(sec(d*x+c))+2/3*(a+2*b)*(4*A*b+a*(A-3*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/sqrt(a+b)/d/sqrt(sec(d*x+c))+2*b*(A*b-B*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*(A*a^2-4*A*b^2+3*B*a*b)*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))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x,5,2*(A*a^2-2*A*b^2+B*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/sqrt(a+b)/d/sqrt(sec(d*x+c))-2*(2*A*b+a*(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/sqrt(a+b)/d/sqrt(sec(d*x+c))+2*b*(A*b-B*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))*sqrt(sec(d*x+c))/(a+b*cos(d*x+c))^(3/2),x,5,2*(A*b-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/sqrt(a+b)/d/sqrt(sec(d*x+c))+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))/a/sqrt(a+b)/d/sqrt(sec(d*x+c))-2*(A*b-B*a)*sqrt(sec(d*x+c))*sin(d*x+c)/(a^2-b^2)/d/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c)),x,7,-2*(A*b-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/b/sqrt(a+b)/d/sqrt(sec(d*x+c))+2*(A*b-B*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)*B*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*(A*b-B*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))/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x,8,(2*A*a*b-3*B*a^2+B*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-(3*a+b)*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/sqrt(a+b)/d/sqrt(sec(d*x+c))-sqrt(a+b)*(2*A*b-3*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^3/d/sqrt(sec(d*x+c))+2*a*(A*b-B*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*a*b-3*B*a^2+B*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))*sec(d*x+c)^(5/2)/(a+b*cos(d*x+c))^(5/2),x,7,-2/3*(8*A*a^4*b-28*A*a^2*b^3+16*A*b^5-3*B*a^5+15*B*a^3*b^2-8*B*a*b^4)*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/(a-b)/(a+b)^(3/2)/d/sqrt(sec(d*x+c))-2/3*(16*A*b^4-a^4*(A-3*B)+4*a*b^3*(3*A-2*B)-9*a^3*b*(A-B)-2*a^2*b^2*(8*A+3*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*b*(A*b-B*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*b*(10*A*a^2*b-6*A*b^3-7*B*a^3+3*B*a*b^2)*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*(A*a^4-13*A*a^2*b^2+8*A*b^4+8*B*a^3*b-4*B*a*b^3)*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))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(5/2),x,6,2/3*(3*A*a^4-15*A*a^2*b^2+8*A*b^4+6*B*a^3*b-2*B*a*b^3)*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/(a-b)/(a+b)^(3/2)/d/sqrt(sec(d*x+c))+2/3*(8*A*b^3-3*a^3*(A-B)+2*a*b^2*(3*A-B)-3*a^2*b*(3*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^3/sqrt(a+b)/(a^2-b^2)/d/sqrt(sec(d*x+c))+2/3*b*(A*b-B*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*b*(8*A*a^2*b-4*A*b^3-5*B*a^3+B*a*b^2)*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))*sqrt(sec(d*x+c))/(a+b*cos(d*x+c))^(5/2),x,6,2/3*(6*A*a^2*b-2*A*b^3-3*B*a^3-B*a*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^3/(a-b)/(a+b)^(3/2)/d/sqrt(sec(d*x+c))-2/3*(2*A*b^2-3*a^2*(A+B)+a*b*(3*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/sqrt(a+b)/(a^2-b^2)/d/sqrt(sec(d*x+c))+2/3*b*(A*b-B*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*(6*A*a^2*b-2*A*b^3-3*B*a^3-B*a*b^2)*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+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2)/sqrt(sec(d*x+c)),x,6,-2/3*(3*A*a^2+A*b^2-4*B*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/(a-b)/(a+b)^(3/2)/d/sqrt(sec(d*x+c))+2/3*(a*(3*A+B)-b*(A+3*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/(a-b)/(a+b)^(3/2)/d/sqrt(sec(d*x+c))-2/3*(A*b-B*a)*sin(d*x+c)/(a^2-b^2)/d/(a+b*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c))+2/3*(3*A*a^2+A*b^2-4*B*a*b)*sqrt(sec(d*x+c))*sin(d*x+c)/(a^2-b^2)^2/d/sqrt(a+b*cos(d*x+c)),1],
[(A+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(3/2),x,8,2/3*(4*A*b^3+3*B*a^3-7*B*a*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/(a-b)/b^2/(a+b)^(3/2)/d/sqrt(sec(d*x+c))-2/3*(3*A*b^3+3*a^3*B+a^2*b*B-a*b^2*(A+6*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/(a-b)/b^2/(a+b)^(3/2)/d/sqrt(sec(d*x+c))-2*sqrt(a+b)*B*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*(A*b-B*a)*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*(4*A*b^3+3*B*a^3-7*B*a*b^2)*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+B*cos(d*x+c))/(a+b*cos(d*x+c))^(5/2)/sec(d*x+c)^(5/2),x,9,1/3*(6*A*a^3*b-14*A*a*b^3-15*B*a^4+26*B*a^2*b^2-3*B*b^4)*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*(3*b^3*(4*A-B)+15*a^3*B-a*b^2*(2*A+21*B)-a^2*(6*A*b-5*B*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-b)/b^3/(a+b)^(3/2)/d/sqrt(sec(d*x+c))-sqrt(a+b)*(2*A*b-5*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^4/d/sqrt(sec(d*x+c))+2/3*a*(A*b-B*a)*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*a*(2*A*a^2*b-6*A*b^3-5*B*a^3+9*B*a*b^2)*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*(6*A*a^3*b-14*A*a*b^3-15*B*a^4+26*B*a^2*b^2-3*B*b^4)*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],
[(B*a+b*B*cos(d*x+c))*sec(d*x+c)^(3/2)/(a+b*cos(d*x+c))^(3/2),x,5,2*(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^2/d/sqrt(sec(d*x+c))-2*sqrt(a+b)*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)),1],
[(B*a+b*B*cos(d*x+c))*sqrt(sec(d*x+c))/(a+b*cos(d*x+c))^(3/2),x,3,2*sqrt(a+b)*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)),1],
[(B*a+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2)/sqrt(sec(d*x+c)),x,3,-2*sqrt(a+b)*B*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],
[(B*a+b*B*cos(d*x+c))/(a+b*cos(d*x+c))^(3/2)/sec(d*x+c)^(3/2),x,10,-(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/b/d/sqrt(sec(d*x+c))+sqrt(a+b)*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/d/sqrt(sec(d*x+c))+a*sqrt(a+b)*B*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))+B*sin(d*x+c)/d/sqrt(a+b*cos(d*x+c))/sqrt(sec(d*x+c))+a*B*sqrt(sec(d*x+c))*sin(d*x+c)/b/d/sqrt(a+b*cos(d*x+c)),1],
[(a+b*cos(f*x+e))^n*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x,1,(c*cos(f*x+e))^m*(c*sec(f*x+e))^m*Defer(Int)((a+b*cos(f*x+e))^n*(A+B*cos(f*x+e))/((c*cos(f*x+e))^m),x),0],
[(a+b*cos(f*x+e))^4*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x,10,-c^6*(4*a^3*A*b*(m^2-8*m+15)+a^4*B*(m^2-8*m+15)+4*a*A*b^3*(m^2-7*m+10)+6*a^2*b^2*B*(m^2-7*m+10)+b^4*B*(m^2-6*m+8))*hypergeom([1/2, 3-1/2*m],[4-1/2*m],cos(f*x+e)^2)*(c*sec(f*x+e))^(-6+m)*sin(f*x+e)/f/(2-m)/(4-m)/(6-m)/sqrt(sin(f*x+e)^2)-c^5*(a^4*A*(m^2-6*m+8)+6*a^2*A*b^2*(m^2-5*m+4)+4*a^3*b*B*(m^2-5*m+4)+A*b^4*(m^2-4*m+3)+4*a*b^3*B*(m^2-4*m+3))*hypergeom([1/2, 5/2-1/2*m],[7/2-1/2*m],cos(f*x+e)^2)*(c*sec(f*x+e))^(-5+m)*sin(f*x+e)/f/(1-m)/(3-m)/(5-m)/sqrt(sin(f*x+e)^2)-a*c^5*(4*a^2*A*b*(m^2-4*m+3)+a^3*B*(m^2-4*m+3)+2*A*b^3*(m^2-2*m+4)+a*b^2*B*(5*m^2-13*m+8))*(c*sec(f*x+e))^(-5+m)*tan(f*x+e)/f/(1-m)/(2-m)/(4-m)-a^2*c^5*(2*a*b*B*(1-m)^2+a^2*A*(2-m)^2+A*b^2*(m^2-m+6))*sec(f*x+e)*(c*sec(f*x+e))^(-5+m)*tan(f*x+e)/f/(1-m)/(2-m)/(3-m)-a*c^5*(a*B*(1-m)-A*b*(2+m))*(c*sec(f*x+e))^(-5+m)*(b+a*sec(f*x+e))^2*tan(f*x+e)/f/(1-m)/(2-m)-a*A*c^5*(c*sec(f*x+e))^(-5+m)*(b+a*sec(f*x+e))^3*tan(f*x+e)/f/(1-m),1],
[(a+b*cos(f*x+e))^3*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x,9,-c^5*(a^3*A*(m^2-6*m+8)+3*a*A*b^2*(m^2-5*m+4)+3*a^2*b*B*(m^2-5*m+4)+b^3*B*(m^2-4*m+3))*hypergeom([1/2, 5/2-1/2*m],[7/2-1/2*m],cos(f*x+e)^2)*(c*sec(f*x+e))^(-5+m)*sin(f*x+e)/f/(1-m)/(3-m)/(5-m)/sqrt(sin(f*x+e)^2)-c^4*(A*b^3*(2-m)+3*a*b^2*B*(2-m)+3*a^2*A*b*(3-m)+a^3*B*(3-m))*hypergeom([1/2, 2-1/2*m],[3-1/2*m],cos(f*x+e)^2)*(c*sec(f*x+e))^(-4+m)*sin(f*x+e)/f/(2-m)/(4-m)/sqrt(sin(f*x+e)^2)-a*c^4*(3*a*b*B*(1-m)+a^2*A*(2-m)-2*A*b^2*m)*(c*sec(f*x+e))^(-4+m)*tan(f*x+e)/f/(1-m)/(3-m)-a^2*c^4*(a*B*(1-m)-A*b*(1+m))*sec(f*x+e)*(c*sec(f*x+e))^(-4+m)*tan(f*x+e)/f/(1-m)/(2-m)-a*A*c^4*(c*sec(f*x+e))^(-4+m)*(b+a*sec(f*x+e))^2*tan(f*x+e)/f/(1-m),1],
[(a+b*cos(f*x+e))^2*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x,8,-c^4*(b^2*B*(2-m)+2*a*A*b*(3-m)+a^2*B*(3-m))*hypergeom([1/2, 2-1/2*m],[3-1/2*m],cos(f*x+e)^2)*(c*sec(f*x+e))^(-4+m)*sin(f*x+e)/f/(2-m)/(4-m)/sqrt(sin(f*x+e)^2)-c^3*(A*b^2*(1-m)+2*a*b*B*(1-m)+a^2*A*(2-m))*hypergeom([1/2, 3/2-1/2*m],[5/2-1/2*m],cos(f*x+e)^2)*(c*sec(f*x+e))^(-3+m)*sin(f*x+e)/f/(1-m)/(3-m)/sqrt(sin(f*x+e)^2)-a*c^3*(a*B*(1-m)-A*b*m)*(c*sec(f*x+e))^(-3+m)*tan(f*x+e)/f/(1-m)/(2-m)-a*A*c^3*(c*sec(f*x+e))^(-3+m)*(b+a*sec(f*x+e))*tan(f*x+e)/f/(1-m),1],
[(a+b*cos(f*x+e))*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x,7,-c^3*(b*B*(1-m)+a*A*(2-m))*hypergeom([1/2, 3/2-1/2*m],[5/2-1/2*m],cos(f*x+e)^2)*(c*sec(f*x+e))^(-3+m)*sin(f*x+e)/f/(1-m)/(3-m)/sqrt(sin(f*x+e)^2)-(A*b+B*a)*c^2*hypergeom([1/2, 1-1/2*m],[2-1/2*m],cos(f*x+e)^2)*(c*sec(f*x+e))^(-2+m)*sin(f*x+e)/f/(2-m)/sqrt(sin(f*x+e)^2)-a*A*c^2*(c*sec(f*x+e))^(-2+m)*tan(f*x+e)/f/(1-m),1],
[(A+B*cos(f*x+e))*(c*sec(f*x+e))^m/(a+b*cos(f*x+e)),x,12,-(A*b-B*a)*AppellF1(1/2,1/2*m,1,3/2,sin(f*x+e)^2,-b^2*sin(f*x+e)^2/(a^2-b^2))*cos(f*x+e)*(cos(f*x+e)^2)^(1/2*m)*(c*sec(f*x+e))^(1+m)*sin(f*x+e)/(a^2-b^2)/c/f+a*(A*b-B*a)*AppellF1(1/2,1/2+1/2*m,1,3/2,sin(f*x+e)^2,-b^2*sin(f*x+e)^2/(a^2-b^2))*(cos(f*x+e)^2)^(1/2+1/2*m)*(c*sec(f*x+e))^(1+m)*sin(f*x+e)/b/(a^2-b^2)/c/f-B*c*hypergeom([1/2, 1/2-1/2*m],[3/2-1/2*m],cos(f*x+e)^2)*(c*sec(f*x+e))^(-1+m)*sin(f*x+e)/b/f/(1-m)/sqrt(sin(f*x+e)^2),1],
[(a+b*cos(f*x+e))^(3/2)*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x,2,2*b*B*cos(f*x+e)*sqrt(a+b*cos(f*x+e))*(c*sec(f*x+e))^m*sin(f*x+e)/f/(5-2*m)+2*(c*cos(f*x+e))^m*(c*sec(f*x+e))^m*Defer(Int)((1/2*a*c*(2*b*B*(1-m)+2*a*A*(5/2-m))+1/2*c*(b^2*B*(3-2*m)+a*(2*A*b+B*a)*(5-2*m))*cos(f*x+e)+1/2*b*c*(A*b*(5-2*m)+2*a*B*(3-m))*cos(f*x+e)^2)/((c*cos(f*x+e))^m)/sqrt(a+b*cos(f*x+e)),x)/c/(5-2*m),0],
[sqrt(a+b*cos(f*x+e))*(A+B*cos(f*x+e))*(c*sec(f*x+e))^m,x,1,(c*cos(f*x+e))^m*(c*sec(f*x+e))^m*Defer(Int)(sqrt(a+b*cos(f*x+e))*(A+B*cos(f*x+e))/((c*cos(f*x+e))^m),x),0],
[(A+B*cos(f*x+e))*(c*sec(f*x+e))^m/sqrt(a+b*cos(f*x+e)),x,1,(c*cos(f*x+e))^m*(c*sec(f*x+e))^m*Defer(Int)((A+B*cos(f*x+e))/((c*cos(f*x+e))^m)/sqrt(a+b*cos(f*x+e)),x),0],
[(A+B*cos(f*x+e))*(c*sec(f*x+e))^m/(a+b*cos(f*x+e))^(3/2),x,2,2*b*(A*b-B*a)*cos(f*x+e)*(c*sec(f*x+e))^m*sin(f*x+e)/a/(a^2-b^2)/f/sqrt(a+b*cos(f*x+e))+2*(c*cos(f*x+e))^m*(c*sec(f*x+e))^m*Defer(Int)((1/2*c*(a^2*A+A*b^2*(1-2*m)-2*a*b*B*(1-m))-1/2*a*(A*b-B*a)*c*cos(f*x+e)-1/2*b*(A*b-B*a)*c*(3-2*m)*cos(f*x+e)^2)/((c*cos(f*x+e))^m)/sqrt(a+b*cos(f*x+e)),x)/a/(a^2-b^2)/c,0]]: