lst:=[[cos(d*x+c)^7*(a+a*sin(d*x+c)),x,3,8/5*(a+a*sin(d*x+c))^5/a^4/d-2*(a+a*sin(d*x+c))^6/a^5/d+6/7*(a+a*sin(d*x+c))^7/a^6/d-1/8*(a+a*sin(d*x+c))^8/a^7/d,1],
[cos(d*x+c)^6*(a+a*sin(d*x+c)),x,5,5/16*a*x-1/7*a*cos(d*x+c)^7/d+5/16*a*cos(d*x+c)*sin(d*x+c)/d+5/24*a*cos(d*x+c)^3*sin(d*x+c)/d+1/6*a*cos(d*x+c)^5*sin(d*x+c)/d,1],
[cos(d*x+c)^5*(a+a*sin(d*x+c)),x,3,(a+a*sin(d*x+c))^4/a^3/d-4/5*(a+a*sin(d*x+c))^5/a^4/d+1/6*(a+a*sin(d*x+c))^6/a^5/d,1],
[cos(d*x+c)^4*(a+a*sin(d*x+c)),x,4,3/8*a*x-1/5*a*cos(d*x+c)^5/d+3/8*a*cos(d*x+c)*sin(d*x+c)/d+1/4*a*cos(d*x+c)^3*sin(d*x+c)/d,1],
[cos(d*x+c)^3*(a+a*sin(d*x+c)),x,3,2/3*(a+a*sin(d*x+c))^3/a^2/d-1/4*(a+a*sin(d*x+c))^4/a^3/d,1],
[cos(d*x+c)^2*(a+a*sin(d*x+c)),x,3,1/2*a*x-1/3*a*cos(d*x+c)^3/d+1/2*a*cos(d*x+c)*sin(d*x+c)/d,1],
[cos(d*x+c)*(a+a*sin(d*x+c)),x,2,1/2*(a+a*sin(d*x+c))^2/a/d,1],
[sec(d*x+c)*(a+a*sin(d*x+c)),x,2,-a*ln(1-sin(d*x+c))/d,1],
[sec(d*x+c)^2*(a+a*sin(d*x+c)),x,3,a*sec(d*x+c)/d+a*tan(d*x+c)/d,1],
[sec(d*x+c)^3*(a+a*sin(d*x+c)),x,4,1/2*a*arctanh(sin(d*x+c))/d+1/2*a^3/d/(a^2-a^2*sin(d*x+c)),1],
[sec(d*x+c)^4*(a+a*sin(d*x+c)),x,3,1/3*a*sec(d*x+c)^3/d+a*tan(d*x+c)/d+1/3*a*tan(d*x+c)^3/d,1],
[sec(d*x+c)^5*(a+a*sin(d*x+c)),x,4,3/8*a*arctanh(sin(d*x+c))/d+1/8*a^5/d/(a^2-a^2*sin(d*x+c))^2+1/4*a^5/d/(a^4-a^4*sin(d*x+c))-1/8*a^5/d/(a^4+a^4*sin(d*x+c)),1],
[cos(d*x+c)^6*(a+a*sin(d*x+c))^2,x,6,45/128*a^2*x-9/56*a^2*cos(d*x+c)^7/d+45/128*a^2*cos(d*x+c)*sin(d*x+c)/d+15/64*a^2*cos(d*x+c)^3*sin(d*x+c)/d+3/16*a^2*cos(d*x+c)^5*sin(d*x+c)/d-1/8*cos(d*x+c)^7*(a^2+a^2*sin(d*x+c))/d,1],
[cos(d*x+c)^5*(a+a*sin(d*x+c))^2,x,3,4/5*(a+a*sin(d*x+c))^5/a^3/d-2/3*(a+a*sin(d*x+c))^6/a^4/d+1/7*(a+a*sin(d*x+c))^7/a^5/d,1],
[cos(d*x+c)^4*(a+a*sin(d*x+c))^2,x,5,7/16*a^2*x-7/30*a^2*cos(d*x+c)^5/d+7/16*a^2*cos(d*x+c)*sin(d*x+c)/d+7/24*a^2*cos(d*x+c)^3*sin(d*x+c)/d-1/6*cos(d*x+c)^5*(a^2+a^2*sin(d*x+c))/d,1],
[cos(d*x+c)^3*(a+a*sin(d*x+c))^2,x,3,1/2*(a+a*sin(d*x+c))^4/a^2/d-1/5*(a+a*sin(d*x+c))^5/a^3/d,1],
[cos(d*x+c)^2*(a+a*sin(d*x+c))^2,x,4,5/8*a^2*x-5/12*a^2*cos(d*x+c)^3/d+5/8*a^2*cos(d*x+c)*sin(d*x+c)/d-1/4*cos(d*x+c)^3*(a^2+a^2*sin(d*x+c))/d,1],
[cos(d*x+c)*(a+a*sin(d*x+c))^2,x,2,1/3*(a+a*sin(d*x+c))^3/a/d,1],
[sec(d*x+c)*(a+a*sin(d*x+c))^2,x,3,-2*a^2*ln(1-sin(d*x+c))/d-a^2*sin(d*x+c)/d,1],
[sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x,3,-a^2*x+2*a^4*cos(d*x+c)/d/(a^2-a^2*sin(d*x+c)),1],
[sec(d*x+c)^3*(a+a*sin(d*x+c))^2,x,2,a^3/d/(a-a*sin(d*x+c)),1],
[sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x,3,1/3*a^4*cos(d*x+c)/d/(a-a*sin(d*x+c))^2+1/3*a^4*cos(d*x+c)/d/(a^2-a^2*sin(d*x+c)),1],
[sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x,4,1/4*a^2*arctanh(sin(d*x+c))/d+1/4*a^4/d/(a-a*sin(d*x+c))^2+1/4*a^5/d/(a^3-a^3*sin(d*x+c)),1],
[sec(d*x+c)^6*(a+a*sin(d*x+c))^2,x,3,2/5*sec(d*x+c)^5*(a^2+a^2*sin(d*x+c))/d+3/5*a^2*tan(d*x+c)/d+1/5*a^2*tan(d*x+c)^3/d,1],
[sec(d*x+c)^7*(a+a*sin(d*x+c))^2,x,4,1/4*a^2*arctanh(sin(d*x+c))/d+1/12*a^5/d/(a-a*sin(d*x+c))^3+1/8*a^4/d/(a-a*sin(d*x+c))^2+3/16*a^7/d/(a^5-a^5*sin(d*x+c))-1/16*a^7/d/(a^5+a^5*sin(d*x+c)),1],
[sec(d*x+c)^8*(a+a*sin(d*x+c))^2,x,3,2/7*sec(d*x+c)^7*(a^2+a^2*sin(d*x+c))/d+5/7*a^2*tan(d*x+c)/d+10/21*a^2*tan(d*x+c)^3/d+1/7*a^2*tan(d*x+c)^5/d,1],
[cos(d*x+c)^6*(a+a*sin(d*x+c))^3,x,7,55/128*a^3*x-11/56*a^3*cos(d*x+c)^7/d+55/128*a^3*cos(d*x+c)*sin(d*x+c)/d+55/192*a^3*cos(d*x+c)^3*sin(d*x+c)/d+11/48*a^3*cos(d*x+c)^5*sin(d*x+c)/d-1/9*a*cos(d*x+c)^7*(a+a*sin(d*x+c))^2/d-11/72*cos(d*x+c)^7*(a^3+a^3*sin(d*x+c))/d,1],
[cos(d*x+c)^5*(a+a*sin(d*x+c))^3,x,3,2/3*(a+a*sin(d*x+c))^6/a^3/d-4/7*(a+a*sin(d*x+c))^7/a^4/d+1/8*(a+a*sin(d*x+c))^8/a^5/d,1],
[cos(d*x+c)^4*(a+a*sin(d*x+c))^3,x,6,9/16*a^3*x-3/10*a^3*cos(d*x+c)^5/d+9/16*a^3*cos(d*x+c)*sin(d*x+c)/d+3/8*a^3*cos(d*x+c)^3*sin(d*x+c)/d-1/7*a*cos(d*x+c)^5*(a+a*sin(d*x+c))^2/d-3/14*cos(d*x+c)^5*(a^3+a^3*sin(d*x+c))/d,1],
[cos(d*x+c)^3*(a+a*sin(d*x+c))^3,x,3,2/5*(a+a*sin(d*x+c))^5/a^2/d-1/6*(a+a*sin(d*x+c))^6/a^3/d,1],
[cos(d*x+c)^2*(a+a*sin(d*x+c))^3,x,5,7/8*a^3*x-7/12*a^3*cos(d*x+c)^3/d+7/8*a^3*cos(d*x+c)*sin(d*x+c)/d-1/5*a*cos(d*x+c)^3*(a+a*sin(d*x+c))^2/d-7/20*cos(d*x+c)^3*(a^3+a^3*sin(d*x+c))/d,1],
[cos(d*x+c)*(a+a*sin(d*x+c))^3,x,2,1/4*(a+a*sin(d*x+c))^4/a/d,1],
[sec(d*x+c)*(a+a*sin(d*x+c))^3,x,3,-4*a^3*ln(1-sin(d*x+c))/d-3*a^3*sin(d*x+c)/d-1/2*a^3*sin(d*x+c)^2/d,1],
[sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x,4,-3*a^3*x+3*a^3*cos(d*x+c)/d+2*a^5*cos(d*x+c)^3/d/(a-a*sin(d*x+c))^2,1],
[sec(d*x+c)^3*(a+a*sin(d*x+c))^3,x,3,a^3*ln(1-sin(d*x+c))/d+2*a^3/d/(1-sin(d*x+c)),1],
[sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x,2,1/3*a^6*cos(d*x+c)^3/d/(a-a*sin(d*x+c))^3,1],
[sec(d*x+c)^5*(a+a*sin(d*x+c))^3,x,2,1/2*a^5/d/(a-a*sin(d*x+c))^2,1],
[sec(d*x+c)^6*(a+a*sin(d*x+c))^3,x,4,1/5*a^6*cos(d*x+c)/d/(a-a*sin(d*x+c))^3+2/15*a^5*cos(d*x+c)/d/(a-a*sin(d*x+c))^2+2/15*a^6*cos(d*x+c)/d/(a^3-a^3*sin(d*x+c)),1],
[sec(d*x+c)^7*(a+a*sin(d*x+c))^3,x,4,1/8*a^3*arctanh(sin(d*x+c))/d+1/6*a^6/d/(a-a*sin(d*x+c))^3+1/8*a^7/d/(a^2-a^2*sin(d*x+c))^2+1/8*a^7/d/(a^4-a^4*sin(d*x+c)),1],
[sec(d*x+c)^8*(a+a*sin(d*x+c))^3,x,4,3/35*a^3*sec(d*x+c)^5/d+2/7*a*sec(d*x+c)^7*(a+a*sin(d*x+c))^2/d+3/7*a^3*tan(d*x+c)/d+2/7*a^3*tan(d*x+c)^3/d+3/35*a^3*tan(d*x+c)^5/d,1],
[cos(d*x+c)^5*(a+a*sin(d*x+c))^8,x,3,4/11*(a+a*sin(d*x+c))^11/a^3/d-1/3*(a+a*sin(d*x+c))^12/a^4/d+1/13*(a+a*sin(d*x+c))^13/a^5/d,1],
[cos(d*x+c)^4*(a+a*sin(d*x+c))^8,x,11,4199/1024*a^8*x-4199/1920*a^8*cos(d*x+c)^5/d+4199/1024*a^8*cos(d*x+c)*sin(d*x+c)/d+4199/1536*a^8*cos(d*x+c)^3*sin(d*x+c)/d-323/1320*a^3*cos(d*x+c)^5*(a+a*sin(d*x+c))^5/d-19/132*a^2*cos(d*x+c)^5*(a+a*sin(d*x+c))^6/d-1/12*a*cos(d*x+c)^5*(a+a*sin(d*x+c))^7/d-4199/6336*a^2*cos(d*x+c)^5*(a^2+a^2*sin(d*x+c))^3/d-323/792*cos(d*x+c)^5*(a^2+a^2*sin(d*x+c))^4/d-4199/4032*cos(d*x+c)^5*(a^4+a^4*sin(d*x+c))^2/d-4199/2688*cos(d*x+c)^5*(a^8+a^8*sin(d*x+c))/d,1],
[cos(d*x+c)^3*(a+a*sin(d*x+c))^8,x,3,1/5*(a+a*sin(d*x+c))^10/a^2/d-1/11*(a+a*sin(d*x+c))^11/a^3/d,1],
[cos(d*x+c)^2*(a+a*sin(d*x+c))^8,x,10,2431/256*a^8*x-2431/384*a^8*cos(d*x+c)^3/d+2431/256*a^8*cos(d*x+c)*sin(d*x+c)/d-17/48*a^3*cos(d*x+c)^3*(a+a*sin(d*x+c))^5/d-17/90*a^2*cos(d*x+c)^3*(a+a*sin(d*x+c))^6/d-1/10*a*cos(d*x+c)^3*(a+a*sin(d*x+c))^7/d-2431/2016*a^2*cos(d*x+c)^3*(a^2+a^2*sin(d*x+c))^3/d-221/336*cos(d*x+c)^3*(a^2+a^2*sin(d*x+c))^4/d-2431/1120*cos(d*x+c)^3*(a^4+a^4*sin(d*x+c))^2/d-2431/640*cos(d*x+c)^3*(a^8+a^8*sin(d*x+c))/d,1],
[cos(d*x+c)*(a+a*sin(d*x+c))^8,x,2,1/9*(a+a*sin(d*x+c))^9/a/d,1],
[sec(d*x+c)*(a+a*sin(d*x+c))^8,x,3,-128*a^8*ln(1-sin(d*x+c))/d-64*a^8*sin(d*x+c)/d-16/3*a^5*(a+a*sin(d*x+c))^3/d-4/5*a^3*(a+a*sin(d*x+c))^5/d-1/3*a^2*(a+a*sin(d*x+c))^6/d-1/7*a*(a+a*sin(d*x+c))^7/d-2*(a^2+a^2*sin(d*x+c))^4/d-16*(a^4+a^4*sin(d*x+c))^2/d,1],
[sec(d*x+c)^2*(a+a*sin(d*x+c))^8,x,9,-3003/16*a^8*x+1001/10*a^8*cos(d*x+c)^5/d-3003/16*a^8*cos(d*x+c)*sin(d*x+c)/d-1001/8*a^8*cos(d*x+c)^3*sin(d*x+c)/d+2*a^15*cos(d*x+c)^13/d/(a-a*sin(d*x+c))^7+26*a^13*cos(d*x+c)^11/d/(a-a*sin(d*x+c))^5+286/3*a^14*cos(d*x+c)^9/d/(a^2-a^2*sin(d*x+c))^3+143/2*a^16*cos(d*x+c)^7/d/(a^8-a^8*sin(d*x+c)),1],
[sec(d*x+c)^3*(a+a*sin(d*x+c))^8,x,3,192*a^8*ln(1-sin(d*x+c))/d+129*a^8*sin(d*x+c)/d+36*a^8*sin(d*x+c)^2/d+10*a^8*sin(d*x+c)^3/d+2*a^8*sin(d*x+c)^4/d+1/5*a^8*sin(d*x+c)^5/d+64*a^9/d/(a-a*sin(d*x+c)),1],
[sec(d*x+c)^4*(a+a*sin(d*x+c))^8,x,8,1155/8*a^8*x-385/4*a^8*cos(d*x+c)^3/d+1155/8*a^8*cos(d*x+c)*sin(d*x+c)/d+2/3*a^15*cos(d*x+c)^11/d/(a-a*sin(d*x+c))^7-22/3*a^13*cos(d*x+c)^9/d/(a-a*sin(d*x+c))^5-66*a^14*cos(d*x+c)^7/d/(a^2-a^2*sin(d*x+c))^3-231/4*a^16*cos(d*x+c)^5/d/(a^8-a^8*sin(d*x+c)),1],
[sec(d*x+c)^5*(a+a*sin(d*x+c))^8,x,3,-80*a^8*ln(1-sin(d*x+c))/d-31*a^8*sin(d*x+c)/d-4*a^8*sin(d*x+c)^2/d-1/3*a^8*sin(d*x+c)^3/d+16*a^10/d/(a-a*sin(d*x+c))^2-80*a^9/d/(a-a*sin(d*x+c)),1],
[cos(d*x+c)^6/(a+a*sin(d*x+c)),x,4,3/8*x/a+1/5*cos(d*x+c)^5/a/d+3/8*cos(d*x+c)*sin(d*x+c)/a/d+1/4*cos(d*x+c)^3*sin(d*x+c)/a/d,1],
[cos(d*x+c)^5/(a+a*sin(d*x+c)),x,3,-2/3*(a-a*sin(d*x+c))^3/a^4/d+1/4*(a-a*sin(d*x+c))^4/a^5/d,1],
[cos(d*x+c)^4/(a+a*sin(d*x+c)),x,3,1/2*x/a+1/3*cos(d*x+c)^3/a/d+1/2*cos(d*x+c)*sin(d*x+c)/a/d,1],
[cos(d*x+c)^3/(a+a*sin(d*x+c)),x,2,-1/2*(a-a*sin(d*x+c))^2/a^3/d,1],
[cos(d*x+c)^2/(a+a*sin(d*x+c)),x,2,x/a+cos(d*x+c)/a/d,1],
[cos(d*x+c)/(a+a*sin(d*x+c)),x,2,ln(1+sin(d*x+c))/a/d,1],
[sec(d*x+c)/(a+a*sin(d*x+c)),x,4,1/2*arctanh(sin(d*x+c))/a/d-1/2/d/(a+a*sin(d*x+c)),1],
[sec(d*x+c)^2/(a+a*sin(d*x+c)),x,3,-1/3*sec(d*x+c)/d/(a+a*sin(d*x+c))+2/3*tan(d*x+c)/a/d,1],
[sec(d*x+c)^3/(a+a*sin(d*x+c)),x,4,3/8*arctanh(sin(d*x+c))/a/d+1/8/d/(a-a*sin(d*x+c))-1/4/d/(a+a*sin(d*x+c))-1/8*a^3/d/(a^2+a^2*sin(d*x+c))^2,1],
[sec(d*x+c)^4/(a+a*sin(d*x+c)),x,3,-1/5*sec(d*x+c)^3/d/(a+a*sin(d*x+c))+4/5*tan(d*x+c)/a/d+4/15*tan(d*x+c)^3/a/d,1],
[sec(d*x+c)^5/(a+a*sin(d*x+c)),x,4,5/16*arctanh(sin(d*x+c))/a/d+1/8/d/(a-a*sin(d*x+c))-3/16/d/(a+a*sin(d*x+c))-1/24*a^5/d/(a^2+a^2*sin(d*x+c))^3+1/32*a^5/d/(a^3-a^3*sin(d*x+c))^2-3/32*a^5/d/(a^3+a^3*sin(d*x+c))^2,1],
[cos(d*x+c)^8/(a+a*sin(d*x+c))^2,x,5,7/16*x/a^2+7/30*cos(d*x+c)^5/a^2/d+7/16*cos(d*x+c)*sin(d*x+c)/a^2/d+7/24*cos(d*x+c)^3*sin(d*x+c)/a^2/d+1/6*cos(d*x+c)^7/d/(a^2+a^2*sin(d*x+c)),1],
[cos(d*x+c)^7/(a+a*sin(d*x+c))^2,x,3,-1/2*(a-a*sin(d*x+c))^4/a^6/d+1/5*(a-a*sin(d*x+c))^5/a^7/d,1],
[cos(d*x+c)^6/(a+a*sin(d*x+c))^2,x,4,5/8*x/a^2+5/12*cos(d*x+c)^3/a^2/d+5/8*cos(d*x+c)*sin(d*x+c)/a^2/d+1/4*cos(d*x+c)^5/d/(a^2+a^2*sin(d*x+c)),1],
[cos(d*x+c)^5/(a+a*sin(d*x+c))^2,x,2,-1/3*(a-a*sin(d*x+c))^3/a^5/d,1],
[cos(d*x+c)^4/(a+a*sin(d*x+c))^2,x,3,3/2*x/a^2+3/2*cos(d*x+c)/a^2/d+1/2*cos(d*x+c)^3/d/(a^2+a^2*sin(d*x+c)),1],
[cos(d*x+c)^3/(a+a*sin(d*x+c))^2,x,3,2*ln(1+sin(d*x+c))/a^2/d-sin(d*x+c)/a^2/d,1],
[cos(d*x+c)^2/(a+a*sin(d*x+c))^2,x,2,-x/a^2-2*cos(d*x+c)/d/(a^2+a^2*sin(d*x+c)),1],
[cos(d*x+c)/(a+a*sin(d*x+c))^2,x,2,-1/d/(a^2+a^2*sin(d*x+c)),1],
[sec(d*x+c)/(a+a*sin(d*x+c))^2,x,4,1/4*arctanh(sin(d*x+c))/a^2/d-1/4/d/(a+a*sin(d*x+c))^2-1/4/d/(a^2+a^2*sin(d*x+c)),1],
[sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x,4,-1/5*sec(d*x+c)/d/(a+a*sin(d*x+c))^2-1/5*sec(d*x+c)/d/(a^2+a^2*sin(d*x+c))+2/5*tan(d*x+c)/a^2/d,1],
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[sec(d*x+c)^6/(a+a*sin(d*x+c))^(3/2),x,9,-3003/8192*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/sqrt(2)/a^(3/2)/d-3003/8192*cos(d*x+c)/d/(a+a*sin(d*x+c))^(3/2)-1001/5120*sec(d*x+c)/d/(a+a*sin(d*x+c))^(3/2)-143/960*sec(d*x+c)^3/d/(a+a*sin(d*x+c))^(3/2)-1/8*sec(d*x+c)^5/d/(a+a*sin(d*x+c))^(3/2)+1001/2048*sec(d*x+c)/a/d/sqrt(a+a*sin(d*x+c))+143/640*sec(d*x+c)^3/a/d/sqrt(a+a*sin(d*x+c))+13/80*sec(d*x+c)^5/a/d/sqrt(a+a*sin(d*x+c)),1],
[cos(d*x+c)^10/(a+a*sin(d*x+c))^(5/2),x,3,-64/2145*a^3*cos(d*x+c)^11/d/(a+a*sin(d*x+c))^(11/2)-16/195*a^2*cos(d*x+c)^11/d/(a+a*sin(d*x+c))^(9/2)-2/15*a*cos(d*x+c)^11/d/(a+a*sin(d*x+c))^(7/2),1],
[cos(d*x+c)^9/(a+a*sin(d*x+c))^(5/2),x,3,32/5*(a+a*sin(d*x+c))^(5/2)/a^5/d-64/7*(a+a*sin(d*x+c))^(7/2)/a^6/d+16/3*(a+a*sin(d*x+c))^(9/2)/a^7/d-16/11*(a+a*sin(d*x+c))^(11/2)/a^8/d+2/13*(a+a*sin(d*x+c))^(13/2)/a^9/d,1],
[cos(d*x+c)^8/(a+a*sin(d*x+c))^(5/2),x,2,-8/99*a^2*cos(d*x+c)^9/d/(a+a*sin(d*x+c))^(9/2)-2/11*a*cos(d*x+c)^9/d/(a+a*sin(d*x+c))^(7/2),1],
[cos(d*x+c)^7/(a+a*sin(d*x+c))^(5/2),x,3,16/3*(a+a*sin(d*x+c))^(3/2)/a^4/d-24/5*(a+a*sin(d*x+c))^(5/2)/a^5/d+12/7*(a+a*sin(d*x+c))^(7/2)/a^6/d-2/9*(a+a*sin(d*x+c))^(9/2)/a^7/d,1],
[cos(d*x+c)^6/(a+a*sin(d*x+c))^(5/2),x,1,-2/7*a*cos(d*x+c)^7/d/(a+a*sin(d*x+c))^(7/2),1],
[cos(d*x+c)^5/(a+a*sin(d*x+c))^(5/2),x,3,8*sqrt(a+a*sin(d*x+c))/a^3/d-8/3*(a+a*sin(d*x+c))^(3/2)/a^4/d+2/5*(a+a*sin(d*x+c))^(5/2)/a^5/d,1],
[cos(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x,4,-4*sqrt(2)*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/a^(5/2)/d+2/3*cos(d*x+c)^3/a/d/(a+a*sin(d*x+c))^(3/2)+4*cos(d*x+c)/a^2/d/sqrt(a+a*sin(d*x+c)),1],
[cos(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x,3,-4/a^2/d/sqrt(a+a*sin(d*x+c))-2*sqrt(a+a*sin(d*x+c))/a^3/d,1],
[cos(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x,3,arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/sqrt(2)/a^(5/2)/d-cos(d*x+c)/a/d/(a+a*sin(d*x+c))^(3/2),1],
[cos(d*x+c)/(a+a*sin(d*x+c))^(5/2),x,2,-2/3/a/d/(a+a*sin(d*x+c))^(3/2),1],
[sec(d*x+c)/(a+a*sin(d*x+c))^(5/2),x,6,1/4*arctanh(sqrt(a+a*sin(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(5/2)/d-1/5/d/(a+a*sin(d*x+c))^(5/2)-1/6/a/d/(a+a*sin(d*x+c))^(3/2)-1/4/a^2/d/sqrt(a+a*sin(d*x+c)),1],
[sec(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x,6,-35/128*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/sqrt(2)/a^(5/2)/d-1/6*sec(d*x+c)/d/(a+a*sin(d*x+c))^(5/2)-35/128*cos(d*x+c)/a/d/(a+a*sin(d*x+c))^(3/2)-7/48*sec(d*x+c)/a/d/(a+a*sin(d*x+c))^(3/2)+35/96*sec(d*x+c)/a^2/d/sqrt(a+a*sin(d*x+c)),1],
[sec(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x,8,9/32*arctanh(sqrt(a+a*sin(d*x+c))/sqrt(2)/sqrt(a))/sqrt(2)/a^(5/2)/d-1/7*sec(d*x+c)^2/d/(a+a*sin(d*x+c))^(5/2)-3/16/a/d/(a+a*sin(d*x+c))^(3/2)-9/70*sec(d*x+c)^2/a/d/(a+a*sin(d*x+c))^(3/2)-9/32/a^2/d/sqrt(a+a*sin(d*x+c))+9/40*sec(d*x+c)^2/a^2/d/sqrt(a+a*sin(d*x+c)),1],
[sec(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x,8,-1155/4096*arctanh(sqrt(a)*cos(d*x+c)/sqrt(2)/sqrt(a+a*sin(d*x+c)))/sqrt(2)/a^(5/2)/d-1/8*sec(d*x+c)^3/d/(a+a*sin(d*x+c))^(5/2)-1155/4096*cos(d*x+c)/a/d/(a+a*sin(d*x+c))^(3/2)-77/512*sec(d*x+c)/a/d/(a+a*sin(d*x+c))^(3/2)-11/96*sec(d*x+c)^3/a/d/(a+a*sin(d*x+c))^(3/2)+385/1024*sec(d*x+c)/a^2/d/sqrt(a+a*sin(d*x+c))+11/64*sec(d*x+c)^3/a^2/d/sqrt(a+a*sin(d*x+c)),1],
[(e*cos(d*x+c))^(7/2)*(a+a*sin(d*x+c)),x,5,-2/9*a*(e*cos(d*x+c))^(9/2)/d/e+10/21*a*e^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))+10/21*a*e^3*sqrt(e*cos(d*x+c))*sin(d*x+c)/d+2/7*a*e*(e*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[(e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c)),x,4,-2/7*a*(e*cos(d*x+c))^(7/2)/d/e+6/5*a*e^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/sqrt(cos(d*x+c))+2/5*a*e*(e*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[(e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c)),x,4,-2/5*a*(e*cos(d*x+c))^(5/2)/d/e+2/3*a*e^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))+2/3*a*e*sqrt(e*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(e*cos(d*x+c))*(a+a*sin(d*x+c)),x,3,-2/3*a*(e*cos(d*x+c))^(3/2)/d/e+2*a*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/sqrt(cos(d*x+c)),1],
[(a+a*sin(d*x+c))/sqrt(e*cos(d*x+c)),x,3,-2*a*sqrt(e*cos(d*x+c))/d/e+2*a*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c)),1],
[(a+a*sin(d*x+c))/(e*cos(d*x+c))^(3/2),x,4,2*a/d/e/sqrt(e*cos(d*x+c))-2*a*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^2/sqrt(cos(d*x+c))+2*a*sin(d*x+c)/d/e/sqrt(e*cos(d*x+c)),1],
[(a+a*sin(d*x+c))/(e*cos(d*x+c))^(5/2),x,4,2/3*a/d/e/(e*cos(d*x+c))^(3/2)+2/3*a*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/e^2/sqrt(e*cos(d*x+c))+2/3*a*sin(d*x+c)/d/e/(e*cos(d*x+c))^(3/2),1],
[(a+a*sin(d*x+c))/(e*cos(d*x+c))^(7/2),x,5,2/5*a/d/e/(e*cos(d*x+c))^(5/2)-6/5*a*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^4/sqrt(cos(d*x+c))+2/5*a*sin(d*x+c)/d/e/(e*cos(d*x+c))^(5/2)+6/5*a*sin(d*x+c)/d/e^3/sqrt(e*cos(d*x+c)),1],
[(e*cos(d*x+c))^(7/2)*(a+a*sin(d*x+c))^2,x,6,-26/99*a^2*(e*cos(d*x+c))^(9/2)/d/e+130/231*a^2*e^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))+130/231*a^2*e^3*sqrt(e*cos(d*x+c))*sin(d*x+c)/d+26/77*a^2*e*(e*cos(d*x+c))^(5/2)*sin(d*x+c)/d-2/11*(e*cos(d*x+c))^(9/2)*(a^2+a^2*sin(d*x+c))/d/e,1],
[(e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^2,x,5,-22/63*a^2*(e*cos(d*x+c))^(7/2)/d/e+22/15*a^2*e^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/sqrt(cos(d*x+c))+22/45*a^2*e*(e*cos(d*x+c))^(3/2)*sin(d*x+c)/d-2/9*(e*cos(d*x+c))^(7/2)*(a^2+a^2*sin(d*x+c))/d/e,1],
[(e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^2,x,5,-18/35*a^2*(e*cos(d*x+c))^(5/2)/d/e+6/7*a^2*e^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))+6/7*a^2*e*sqrt(e*cos(d*x+c))*sin(d*x+c)/d-2/7*(e*cos(d*x+c))^(5/2)*(a^2+a^2*sin(d*x+c))/d/e,1],
[sqrt(e*cos(d*x+c))*(a+a*sin(d*x+c))^2,x,4,-14/15*a^2*(e*cos(d*x+c))^(3/2)/d/e+14/5*a^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/sqrt(cos(d*x+c))-2/5*(e*cos(d*x+c))^(3/2)*(a^2+a^2*sin(d*x+c))/d/e,1],
[(a+a*sin(d*x+c))^2/sqrt(e*cos(d*x+c)),x,4,-10/3*a^2*sqrt(e*cos(d*x+c))/d/e+10/3*a^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))-2/3*sqrt(e*cos(d*x+c))*(a^2+a^2*sin(d*x+c))/d/e,1],
[(a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(3/2),x,4,-6*a^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^2/sqrt(cos(d*x+c))+4*a^4*(e*cos(d*x+c))^(3/2)/d/e^3/(a^2-a^2*sin(d*x+c)),1],
[(a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(5/2),x,4,-2/3*a^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/e^2/sqrt(e*cos(d*x+c))+4/3*a^4*sqrt(e*cos(d*x+c))/d/e^3/(a^2-a^2*sin(d*x+c)),1],
[(a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(7/2),x,5,-2/5*a^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^4/sqrt(cos(d*x+c))+2/5*a^4*(e*cos(d*x+c))^(3/2)/d/e^5/(a-a*sin(d*x+c))^2+2/5*a^4*(e*cos(d*x+c))^(3/2)/d/e^5/(a^2-a^2*sin(d*x+c)),1],
[(a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(9/2),x,4,2/7*a^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/e^4/sqrt(e*cos(d*x+c))+2/7*a^2*sin(d*x+c)/d/e^3/(e*cos(d*x+c))^(3/2)+4/7*(a^2+a^2*sin(d*x+c))/d/e/(e*cos(d*x+c))^(7/2),1],
[(a+a*sin(d*x+c))^2/(e*cos(d*x+c))^(11/2),x,5,-2/3*a^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^6/sqrt(cos(d*x+c))+2/9*a^2*sin(d*x+c)/d/e^3/(e*cos(d*x+c))^(5/2)+2/3*a^2*sin(d*x+c)/d/e^5/sqrt(e*cos(d*x+c))+4/9*(a^2+a^2*sin(d*x+c))/d/e/(e*cos(d*x+c))^(9/2),1],
[(e*cos(d*x+c))^(7/2)*(a+a*sin(d*x+c))^3,x,7,-34/99*a^3*(e*cos(d*x+c))^(9/2)/d/e+170/231*a^3*e^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))+170/231*a^3*e^3*sqrt(e*cos(d*x+c))*sin(d*x+c)/d+34/77*a^3*e*(e*cos(d*x+c))^(5/2)*sin(d*x+c)/d-2/13*a*(e*cos(d*x+c))^(9/2)*(a+a*sin(d*x+c))^2/d/e-34/143*(e*cos(d*x+c))^(9/2)*(a^3+a^3*sin(d*x+c))/d/e,1],
[(e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^3,x,6,-10/21*a^3*(e*cos(d*x+c))^(7/2)/d/e+2*a^3*e^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/sqrt(cos(d*x+c))+2/3*a^3*e*(e*cos(d*x+c))^(3/2)*sin(d*x+c)/d-2/11*a*(e*cos(d*x+c))^(7/2)*(a+a*sin(d*x+c))^2/d/e-10/33*(e*cos(d*x+c))^(7/2)*(a^3+a^3*sin(d*x+c))/d/e,1],
[(e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^3,x,6,-26/35*a^3*(e*cos(d*x+c))^(5/2)/d/e+26/21*a^3*e^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))+26/21*a^3*e*sqrt(e*cos(d*x+c))*sin(d*x+c)/d-2/9*a*(e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^2/d/e-26/63*(e*cos(d*x+c))^(5/2)*(a^3+a^3*sin(d*x+c))/d/e,1],
[sqrt(e*cos(d*x+c))*(a+a*sin(d*x+c))^3,x,5,-22/15*a^3*(e*cos(d*x+c))^(3/2)/d/e+22/5*a^3*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/sqrt(cos(d*x+c))-2/7*a*(e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^2/d/e-22/35*(e*cos(d*x+c))^(3/2)*(a^3+a^3*sin(d*x+c))/d/e,1],
[(a+a*sin(d*x+c))^3/sqrt(e*cos(d*x+c)),x,5,-6*a^3*sqrt(e*cos(d*x+c))/d/e+6*a^3*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))-2/5*a*sqrt(e*cos(d*x+c))*(a+a*sin(d*x+c))^2/d/e-6/5*sqrt(e*cos(d*x+c))*(a^3+a^3*sin(d*x+c))/d/e,1],
[(a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(3/2),x,5,14/3*a^3*(e*cos(d*x+c))^(3/2)/d/e^3-14*a^3*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^2/sqrt(cos(d*x+c))+4*a^5*(e*cos(d*x+c))^(7/2)/d/e^5/(a-a*sin(d*x+c))^2,1],
[(a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(5/2),x,5,10/3*a^3*sqrt(e*cos(d*x+c))/d/e^3-10/3*a^3*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/e^2/sqrt(e*cos(d*x+c))+4/3*a^5*(e*cos(d*x+c))^(5/2)/d/e^5/(a-a*sin(d*x+c))^2,1],
[(a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(7/2),x,5,6/5*a^3*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^4/sqrt(cos(d*x+c))+4/5*a^5*(e*cos(d*x+c))^(3/2)/d/e^5/(a-a*sin(d*x+c))^2-6/5*a^6*(e*cos(d*x+c))^(3/2)/d/e^5/(a^3-a^3*sin(d*x+c)),1],
[(a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(9/2),x,5,-2/21*a^3*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/e^4/sqrt(e*cos(d*x+c))+4/7*a^5*sqrt(e*cos(d*x+c))/d/e^5/(a-a*sin(d*x+c))^2-2/21*a^6*sqrt(e*cos(d*x+c))/d/e^5/(a^3-a^3*sin(d*x+c)),1],
[(a+a*sin(d*x+c))^3/(e*cos(d*x+c))^(11/2),x,6,-2/15*a^3*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^6/sqrt(cos(d*x+c))+2/9*a^6*(e*cos(d*x+c))^(3/2)/d/e^7/(a-a*sin(d*x+c))^3+2/15*a^5*(e*cos(d*x+c))^(3/2)/d/e^7/(a-a*sin(d*x+c))^2+2/15*a^6*(e*cos(d*x+c))^(3/2)/d/e^7/(a^3-a^3*sin(d*x+c)),1],
[(e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^4,x,7,-442/385*a^4*(e*cos(d*x+c))^(5/2)/d/e+442/231*a^4*e^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))+442/231*a^4*e*sqrt(e*cos(d*x+c))*sin(d*x+c)/d-2/11*a*(e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^3/d/e-34/99*(e*cos(d*x+c))^(5/2)*(a^2+a^2*sin(d*x+c))^2/d/e-442/693*(e*cos(d*x+c))^(5/2)*(a^4+a^4*sin(d*x+c))/d/e,1],
[sqrt(e*cos(d*x+c))*(a+a*sin(d*x+c))^4,x,6,-22/9*a^4*(e*cos(d*x+c))^(3/2)/d/e+22/3*a^4*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/sqrt(cos(d*x+c))-2/9*a*(e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^3/d/e-10/21*(e*cos(d*x+c))^(3/2)*(a^2+a^2*sin(d*x+c))^2/d/e-22/21*(e*cos(d*x+c))^(3/2)*(a^4+a^4*sin(d*x+c))/d/e,1],
[(a+a*sin(d*x+c))^4/sqrt(e*cos(d*x+c)),x,6,-78/7*a^4*sqrt(e*cos(d*x+c))/d/e+78/7*a^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))-2/7*a*sqrt(e*cos(d*x+c))*(a+a*sin(d*x+c))^3/d/e-26/35*sqrt(e*cos(d*x+c))*(a^2+a^2*sin(d*x+c))^2/d/e-78/35*sqrt(e*cos(d*x+c))*(a^4+a^4*sin(d*x+c))/d/e,1],
[(a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(3/2),x,6,-154/5*a^4*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^2/sqrt(cos(d*x+c))-154/15*a^4*(e*cos(d*x+c))^(3/2)*sin(d*x+c)/d/e^3+4*a^7*(e*cos(d*x+c))^(11/2)/d/e^7/(a-a*sin(d*x+c))^3+44/3*a^8*(e*cos(d*x+c))^(7/2)/d/e^5/(a^4-a^4*sin(d*x+c)),1],
[(a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(5/2),x,6,-10*a^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/e^2/sqrt(e*cos(d*x+c))-10*a^4*sqrt(e*cos(d*x+c))*sin(d*x+c)/d/e^3+4/3*a^7*(e*cos(d*x+c))^(9/2)/d/e^7/(a-a*sin(d*x+c))^3+12*a^8*(e*cos(d*x+c))^(5/2)/d/e^5/(a^4-a^4*sin(d*x+c)),1],
[(a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(7/2),x,5,42/5*a^4*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^4/sqrt(cos(d*x+c))+4/5*a^7*(e*cos(d*x+c))^(7/2)/d/e^7/(a-a*sin(d*x+c))^3-28/5*a^8*(e*cos(d*x+c))^(3/2)/d/e^5/(a^4-a^4*sin(d*x+c)),1],
[(a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(9/2),x,5,10/21*a^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/e^4/sqrt(e*cos(d*x+c))+4/7*a^7*(e*cos(d*x+c))^(5/2)/d/e^7/(a-a*sin(d*x+c))^3-20/21*a^8*sqrt(e*cos(d*x+c))/d/e^5/(a^4-a^4*sin(d*x+c)),1],
[(a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(11/2),x,6,2/15*a^4*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^6/sqrt(cos(d*x+c))+4/9*a^7*(e*cos(d*x+c))^(3/2)/d/e^7/(a-a*sin(d*x+c))^3-2/15*a^8*(e*cos(d*x+c))^(3/2)/d/e^7/(a^2-a^2*sin(d*x+c))^2-2/15*a^8*(e*cos(d*x+c))^(3/2)/d/e^7/(a^4-a^4*sin(d*x+c)),1],
[(a+a*sin(d*x+c))^4/(e*cos(d*x+c))^(13/2),x,6,-2/77*a^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/e^6/sqrt(e*cos(d*x+c))+4/11*a^7*sqrt(e*cos(d*x+c))/d/e^7/(a-a*sin(d*x+c))^3-2/77*a^8*sqrt(e*cos(d*x+c))/d/e^7/(a^2-a^2*sin(d*x+c))^2-2/77*a^8*sqrt(e*cos(d*x+c))/d/e^7/(a^4-a^4*sin(d*x+c)),1],
[(e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c)),x,5,2/9*e*(e*cos(d*x+c))^(9/2)/a/d+10/21*e^6*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d/sqrt(e*cos(d*x+c))+10/21*e^5*sqrt(e*cos(d*x+c))*sin(d*x+c)/a/d+2/7*e^3*(e*cos(d*x+c))^(5/2)*sin(d*x+c)/a/d,1],
[(e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c)),x,4,2/7*e*(e*cos(d*x+c))^(7/2)/a/d+6/5*e^4*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d/sqrt(cos(d*x+c))+2/5*e^3*(e*cos(d*x+c))^(3/2)*sin(d*x+c)/a/d,1],
[(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c)),x,4,2/5*e*(e*cos(d*x+c))^(5/2)/a/d+2/3*e^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d/sqrt(e*cos(d*x+c))+2/3*e^3*sqrt(e*cos(d*x+c))*sin(d*x+c)/a/d,1],
[(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c)),x,3,2/3*e*(e*cos(d*x+c))^(3/2)/a/d+2*e^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d/sqrt(cos(d*x+c)),1],
[(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c)),x,3,2*e*sqrt(e*cos(d*x+c))/a/d+2*e^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d/sqrt(e*cos(d*x+c)),1],
[sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c)),x,3,-2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d/sqrt(cos(d*x+c))-2*(e*cos(d*x+c))^(3/2)/d/e/(a+a*sin(d*x+c)),1],
[1/sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c)),x,3,2/3*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d/sqrt(e*cos(d*x+c))-2/3*sqrt(e*cos(d*x+c))/d/e/(a+a*sin(d*x+c)),1],
[1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c)),x,4,-6/5*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d/e^2/sqrt(cos(d*x+c))+6/5*sin(d*x+c)/a/d/e/sqrt(e*cos(d*x+c))-2/5/d/e/sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c)),1],
[1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c)),x,4,10/21*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a/d/e^2/sqrt(e*cos(d*x+c))+10/21*sin(d*x+c)/a/d/e/(e*cos(d*x+c))^(3/2)-2/7/d/e/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c)),1],
[1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c)),x,5,-14/15*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a/d/e^4/sqrt(cos(d*x+c))+14/45*sin(d*x+c)/a/d/e/(e*cos(d*x+c))^(5/2)+14/15*sin(d*x+c)/a/d/e^3/sqrt(e*cos(d*x+c))-2/9/d/e/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c)),1],
[(e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c))^2,x,5,6/7*e^6*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d/sqrt(e*cos(d*x+c))+6/7*e^5*sqrt(e*cos(d*x+c))*sin(d*x+c)/a^2/d+18/35*e^3*(e*cos(d*x+c))^(5/2)*sin(d*x+c)/a^2/d+4/5*e*(e*cos(d*x+c))^(9/2)/d/(a^2+a^2*sin(d*x+c)),1],
[(e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^2,x,4,14/5*e^4*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d/sqrt(cos(d*x+c))+14/15*e^3*(e*cos(d*x+c))^(3/2)*sin(d*x+c)/a^2/d+4/3*e*(e*cos(d*x+c))^(7/2)/d/(a^2+a^2*sin(d*x+c)),1],
[(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^2,x,4,10/3*e^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d/sqrt(e*cos(d*x+c))+10/3*e^3*sqrt(e*cos(d*x+c))*sin(d*x+c)/a^2/d+4*e*(e*cos(d*x+c))^(5/2)/d/(a^2+a^2*sin(d*x+c)),1],
[(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^2,x,3,-6*e^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d/sqrt(cos(d*x+c))-4*e*(e*cos(d*x+c))^(3/2)/d/(a^2+a^2*sin(d*x+c)),1],
[(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^2,x,3,-2/3*e^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d/sqrt(e*cos(d*x+c))-4/3*e*sqrt(e*cos(d*x+c))/d/(a^2+a^2*sin(d*x+c)),1],
[sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c))^2,x,4,-2/5*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d/sqrt(cos(d*x+c))-2/5*(e*cos(d*x+c))^(3/2)/d/e/(a+a*sin(d*x+c))^2-2/5*(e*cos(d*x+c))^(3/2)/d/e/(a^2+a^2*sin(d*x+c)),1],
[1/sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c))^2,x,4,2/7*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d/sqrt(e*cos(d*x+c))-2/7*sqrt(e*cos(d*x+c))/d/e/(a+a*sin(d*x+c))^2-2/7*sqrt(e*cos(d*x+c))/d/e/(a^2+a^2*sin(d*x+c)),1],
[1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^2,x,5,-2/3*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d/e^2/sqrt(cos(d*x+c))+2/3*sin(d*x+c)/a^2/d/e/sqrt(e*cos(d*x+c))-2/9/d/e/sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c))^2-2/9/d/e/sqrt(e*cos(d*x+c))/(a^2+a^2*sin(d*x+c)),1],
[1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^2,x,5,10/33*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^2/d/e^2/sqrt(e*cos(d*x+c))+10/33*sin(d*x+c)/a^2/d/e/(e*cos(d*x+c))^(3/2)-2/11/d/e/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^2-2/11/d/e/(e*cos(d*x+c))^(3/2)/(a^2+a^2*sin(d*x+c)),1],
[1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^2,x,6,-42/65*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^2/d/e^4/sqrt(cos(d*x+c))+14/65*sin(d*x+c)/a^2/d/e/(e*cos(d*x+c))^(5/2)+42/65*sin(d*x+c)/a^2/d/e^3/sqrt(e*cos(d*x+c))-2/13/d/e/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^2-2/13/d/e/(e*cos(d*x+c))^(5/2)/(a^2+a^2*sin(d*x+c)),1],
[(e*cos(d*x+c))^(15/2)/(a+a*sin(d*x+c))^3,x,6,26/45*e^3*(e*cos(d*x+c))^(9/2)/a^3/d+26/21*e^8*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d/sqrt(e*cos(d*x+c))+26/21*e^7*sqrt(e*cos(d*x+c))*sin(d*x+c)/a^3/d+26/35*e^5*(e*cos(d*x+c))^(5/2)*sin(d*x+c)/a^3/d+4/5*e*(e*cos(d*x+c))^(13/2)/a/d/(a+a*sin(d*x+c))^2,1],
[(e*cos(d*x+c))^(13/2)/(a+a*sin(d*x+c))^3,x,5,22/21*e^3*(e*cos(d*x+c))^(7/2)/a^3/d+22/5*e^6*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d/sqrt(cos(d*x+c))+22/15*e^5*(e*cos(d*x+c))^(3/2)*sin(d*x+c)/a^3/d+4/3*e*(e*cos(d*x+c))^(11/2)/a/d/(a+a*sin(d*x+c))^2,1],
[(e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c))^3,x,5,18/5*e^3*(e*cos(d*x+c))^(5/2)/a^3/d+6*e^6*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d/sqrt(e*cos(d*x+c))+6*e^5*sqrt(e*cos(d*x+c))*sin(d*x+c)/a^3/d+4*e*(e*cos(d*x+c))^(9/2)/a/d/(a+a*sin(d*x+c))^2,1],
[(e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^3,x,4,-14/3*e^3*(e*cos(d*x+c))^(3/2)/a^3/d-14*e^4*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d/sqrt(cos(d*x+c))-4*e*(e*cos(d*x+c))^(7/2)/a/d/(a+a*sin(d*x+c))^2,1],
[(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^3,x,4,-10/3*e^3*sqrt(e*cos(d*x+c))/a^3/d-10/3*e^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d/sqrt(e*cos(d*x+c))-4/3*e*(e*cos(d*x+c))^(5/2)/a/d/(a+a*sin(d*x+c))^2,1],
[(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^3,x,4,6/5*e^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d/sqrt(cos(d*x+c))-4/5*e*(e*cos(d*x+c))^(3/2)/a/d/(a+a*sin(d*x+c))^2+6/5*e*(e*cos(d*x+c))^(3/2)/d/(a^3+a^3*sin(d*x+c)),1],
[(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^3,x,4,-2/21*e^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d/sqrt(e*cos(d*x+c))-4/7*e*sqrt(e*cos(d*x+c))/a/d/(a+a*sin(d*x+c))^2+2/21*e*sqrt(e*cos(d*x+c))/d/(a^3+a^3*sin(d*x+c)),1],
[sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c))^3,x,5,-2/15*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d/sqrt(cos(d*x+c))-2/9*(e*cos(d*x+c))^(3/2)/d/e/(a+a*sin(d*x+c))^3-2/15*(e*cos(d*x+c))^(3/2)/a/d/e/(a+a*sin(d*x+c))^2-2/15*(e*cos(d*x+c))^(3/2)/d/e/(a^3+a^3*sin(d*x+c)),1],
[1/sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c))^3,x,5,10/77*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^3/d/sqrt(e*cos(d*x+c))-2/11*sqrt(e*cos(d*x+c))/d/e/(a+a*sin(d*x+c))^3-10/77*sqrt(e*cos(d*x+c))/a/d/e/(a+a*sin(d*x+c))^2-10/77*sqrt(e*cos(d*x+c))/d/e/(a^3+a^3*sin(d*x+c)),1],
[1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^3,x,6,-14/39*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^3/d/e^2/sqrt(cos(d*x+c))+14/39*sin(d*x+c)/a^3/d/e/sqrt(e*cos(d*x+c))-2/13/d/e/sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c))^3-14/117/a/d/e/sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c))^2-14/117/d/e/sqrt(e*cos(d*x+c))/(a^3+a^3*sin(d*x+c)),1],
[(e*cos(d*x+c))^(15/2)/(a+a*sin(d*x+c))^4,x,6,78/7*e^8*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^4/d/sqrt(e*cos(d*x+c))+78/7*e^7*sqrt(e*cos(d*x+c))*sin(d*x+c)/a^4/d+234/35*e^5*(e*cos(d*x+c))^(5/2)*sin(d*x+c)/a^4/d+4*e*(e*cos(d*x+c))^(13/2)/a/d/(a+a*sin(d*x+c))^3+52/5*e^3*(e*cos(d*x+c))^(9/2)/d/(a^4+a^4*sin(d*x+c)),1],
[(e*cos(d*x+c))^(13/2)/(a+a*sin(d*x+c))^4,x,5,-154/5*e^6*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^4/d/sqrt(cos(d*x+c))-154/15*e^5*(e*cos(d*x+c))^(3/2)*sin(d*x+c)/a^4/d-4*e*(e*cos(d*x+c))^(11/2)/a/d/(a+a*sin(d*x+c))^3-44/3*e^3*(e*cos(d*x+c))^(7/2)/d/(a^4+a^4*sin(d*x+c)),1],
[(e*cos(d*x+c))^(11/2)/(a+a*sin(d*x+c))^4,x,5,-10*e^6*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^4/d/sqrt(e*cos(d*x+c))-10*e^5*sqrt(e*cos(d*x+c))*sin(d*x+c)/a^4/d-4/3*e*(e*cos(d*x+c))^(9/2)/a/d/(a+a*sin(d*x+c))^3-12*e^3*(e*cos(d*x+c))^(5/2)/d/(a^4+a^4*sin(d*x+c)),1],
[(e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^4,x,4,42/5*e^4*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^4/d/sqrt(cos(d*x+c))-4/5*e*(e*cos(d*x+c))^(7/2)/a/d/(a+a*sin(d*x+c))^3+28/5*e^3*(e*cos(d*x+c))^(3/2)/d/(a^4+a^4*sin(d*x+c)),1],
[(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^4,x,4,10/21*e^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^4/d/sqrt(e*cos(d*x+c))-4/7*e*(e*cos(d*x+c))^(5/2)/a/d/(a+a*sin(d*x+c))^3+20/21*e^3*sqrt(e*cos(d*x+c))/d/(a^4+a^4*sin(d*x+c)),1],
[(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^4,x,5,2/15*e^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^4/d/sqrt(cos(d*x+c))-4/9*e*(e*cos(d*x+c))^(3/2)/a/d/(a+a*sin(d*x+c))^3+2/15*e*(e*cos(d*x+c))^(3/2)/d/(a^2+a^2*sin(d*x+c))^2+2/15*e*(e*cos(d*x+c))^(3/2)/d/(a^4+a^4*sin(d*x+c)),1],
[(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^4,x,5,-2/77*e^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^4/d/sqrt(e*cos(d*x+c))-4/11*e*sqrt(e*cos(d*x+c))/a/d/(a+a*sin(d*x+c))^3+2/77*e*sqrt(e*cos(d*x+c))/d/(a^2+a^2*sin(d*x+c))^2+2/77*e*sqrt(e*cos(d*x+c))/d/(a^4+a^4*sin(d*x+c)),1],
[sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c))^4,x,6,-2/39*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^4/d/sqrt(cos(d*x+c))-2/13*(e*cos(d*x+c))^(3/2)/d/e/(a+a*sin(d*x+c))^4-10/117*(e*cos(d*x+c))^(3/2)/a/d/e/(a+a*sin(d*x+c))^3-2/39*(e*cos(d*x+c))^(3/2)/d/e/(a^2+a^2*sin(d*x+c))^2-2/39*(e*cos(d*x+c))^(3/2)/d/e/(a^4+a^4*sin(d*x+c)),1],
[1/sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c))^4,x,6,2/33*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/a^4/d/sqrt(e*cos(d*x+c))-2/15*sqrt(e*cos(d*x+c))/d/e/(a+a*sin(d*x+c))^4-14/165*sqrt(e*cos(d*x+c))/a/d/e/(a+a*sin(d*x+c))^3-2/33*sqrt(e*cos(d*x+c))/d/e/(a^2+a^2*sin(d*x+c))^2-2/33*sqrt(e*cos(d*x+c))/d/e/(a^4+a^4*sin(d*x+c)),1],
[1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^4,x,7,-42/221*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/a^4/d/e^2/sqrt(cos(d*x+c))+42/221*sin(d*x+c)/a^4/d/e/sqrt(e*cos(d*x+c))-2/17/d/e/sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c))^4-18/221/a/d/e/sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c))^3-14/221/d/e/sqrt(e*cos(d*x+c))/(a^2+a^2*sin(d*x+c))^2-14/221/d/e/sqrt(e*cos(d*x+c))/(a^4+a^4*sin(d*x+c)),1],
[(e*cos(d*x+c))^(3/2)*sqrt(a+a*sin(d*x+c)),x,8,-1/2*a*(e*cos(d*x+c))^(5/2)/d/e/sqrt(a+a*sin(d*x+c))+3/4*e*sqrt(e*cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d-3/4*e^(3/2)*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(1+cos(d*x+c)+sin(d*x+c))+3/4*e^(3/2)*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(1+cos(d*x+c)+sin(d*x+c)),1],
[sqrt(e*cos(d*x+c))*sqrt(a+a*sin(d*x+c)),x,7,-a*(e*cos(d*x+c))^(3/2)/d/e/sqrt(a+a*sin(d*x+c))+sqrt(e)*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(1+cos(d*x+c)+sin(d*x+c))+sqrt(e)*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(1+cos(d*x+c)+sin(d*x+c)),1],
[sqrt(a+a*sin(d*x+c))/sqrt(e*cos(d*x+c)),x,6,-2*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/sqrt(e)/(1+cos(d*x+c)+sin(d*x+c))+2*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/sqrt(e)/(1+cos(d*x+c)+sin(d*x+c)),1],
[sqrt(a+a*sin(d*x+c))/(e*cos(d*x+c))^(3/2),x,1,2*sqrt(a+a*sin(d*x+c))/d/e/sqrt(e*cos(d*x+c)),1],
[sqrt(a+a*sin(d*x+c))/(e*cos(d*x+c))^(5/2),x,2,-2*sqrt(a+a*sin(d*x+c))/d/e/(e*cos(d*x+c))^(3/2)+4/3*(a+a*sin(d*x+c))^(3/2)/a/d/e/(e*cos(d*x+c))^(3/2),1],
[sqrt(a+a*sin(d*x+c))/(e*cos(d*x+c))^(7/2),x,3,-2/3*sqrt(a+a*sin(d*x+c))/d/e/(e*cos(d*x+c))^(5/2)+8/3*(a+a*sin(d*x+c))^(3/2)/a/d/e/(e*cos(d*x+c))^(5/2)-16/15*(a+a*sin(d*x+c))^(5/2)/a^2/d/e/(e*cos(d*x+c))^(5/2),1],
[sqrt(a+a*sin(d*x+c))/(e*cos(d*x+c))^(9/2),x,4,-2/5*sqrt(a+a*sin(d*x+c))/d/e/(e*cos(d*x+c))^(7/2)-12/5*(a+a*sin(d*x+c))^(3/2)/a/d/e/(e*cos(d*x+c))^(7/2)+16/5*(a+a*sin(d*x+c))^(5/2)/a^2/d/e/(e*cos(d*x+c))^(7/2)-32/35*(a+a*sin(d*x+c))^(7/2)/a^3/d/e/(e*cos(d*x+c))^(7/2),1],
[(e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^(3/2),x,10,-15/32*a^3*(e*cos(d*x+c))^(7/2)/d/e/(a+a*sin(d*x+c))^(3/2)+15/64*a^2*e*(e*cos(d*x+c))^(3/2)/d/sqrt(a+a*sin(d*x+c))-3/8*a^2*(e*cos(d*x+c))^(7/2)/d/e/sqrt(a+a*sin(d*x+c))-1/4*a*(e*cos(d*x+c))^(7/2)*sqrt(a+a*sin(d*x+c))/d/e+45/64*a*e^(5/2)*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(1+cos(d*x+c)+sin(d*x+c))+45/64*a*e^(5/2)*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(1+cos(d*x+c)+sin(d*x+c)),1],
[(e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^(3/2),x,9,-7/12*a^2*(e*cos(d*x+c))^(5/2)/d/e/sqrt(a+a*sin(d*x+c))+7/8*a*e*sqrt(e*cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d-1/3*a*(e*cos(d*x+c))^(5/2)*sqrt(a+a*sin(d*x+c))/d/e-7/8*a*e^(3/2)*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(1+cos(d*x+c)+sin(d*x+c))+7/8*a*e^(3/2)*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(1+cos(d*x+c)+sin(d*x+c)),1],
[sqrt(e*cos(d*x+c))*(a+a*sin(d*x+c))^(3/2),x,8,-5/4*a^2*(e*cos(d*x+c))^(3/2)/d/e/sqrt(a+a*sin(d*x+c))-1/2*a*(e*cos(d*x+c))^(3/2)*sqrt(a+a*sin(d*x+c))/d/e+5/4*a*sqrt(e)*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(1+cos(d*x+c)+sin(d*x+c))+5/4*a*sqrt(e)*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(1+cos(d*x+c)+sin(d*x+c)),1],
[(a+a*sin(d*x+c))^(3/2)/sqrt(e*cos(d*x+c)),x,7,-a*sqrt(e*cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/e-3*a*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/sqrt(e)/(1+cos(d*x+c)+sin(d*x+c))+3*a*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/sqrt(e)/(1+cos(d*x+c)+sin(d*x+c)),1],
[(a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(3/2),x,7,4*a*sqrt(a+a*sin(d*x+c))/d/e/sqrt(e*cos(d*x+c))-2*a^2*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/e^(3/2)/(a+a*cos(d*x+c)+a*sin(d*x+c))-2*a^2*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/e^(3/2)/(a+a*cos(d*x+c)+a*sin(d*x+c)),1],
[(a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(5/2),x,1,2/3*(a+a*sin(d*x+c))^(3/2)/d/e/(e*cos(d*x+c))^(3/2),1],
[(a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(7/2),x,2,2*(a+a*sin(d*x+c))^(3/2)/d/e/(e*cos(d*x+c))^(5/2)-4/5*(a+a*sin(d*x+c))^(5/2)/a/d/e/(e*cos(d*x+c))^(5/2),1],
[(a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(9/2),x,3,-2*(a+a*sin(d*x+c))^(3/2)/d/e/(e*cos(d*x+c))^(7/2)+8/3*(a+a*sin(d*x+c))^(5/2)/a/d/e/(e*cos(d*x+c))^(7/2)-16/21*(a+a*sin(d*x+c))^(7/2)/a^2/d/e/(e*cos(d*x+c))^(7/2),1],
[(a+a*sin(d*x+c))^(3/2)/(e*cos(d*x+c))^(11/2),x,4,-2/3*(a+a*sin(d*x+c))^(3/2)/d/e/(e*cos(d*x+c))^(9/2)+4*(a+a*sin(d*x+c))^(5/2)/a/d/e/(e*cos(d*x+c))^(9/2)-16/5*(a+a*sin(d*x+c))^(7/2)/a^2/d/e/(e*cos(d*x+c))^(9/2)+32/45*(a+a*sin(d*x+c))^(9/2)/a^3/d/e/(e*cos(d*x+c))^(9/2),1],
[(e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^(5/2),x,10,-77/96*a^3*(e*cos(d*x+c))^(5/2)/d/e/sqrt(a+a*sin(d*x+c))+77/64*a^2*e*sqrt(e*cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d-11/24*a^2*(e*cos(d*x+c))^(5/2)*sqrt(a+a*sin(d*x+c))/d/e-77/64*a^2*e^(3/2)*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(1+cos(d*x+c)+sin(d*x+c))+77/64*a^2*e^(3/2)*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(1+cos(d*x+c)+sin(d*x+c))-1/4*a*(e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^(3/2)/d/e,1],
[sqrt(e*cos(d*x+c))*(a+a*sin(d*x+c))^(5/2),x,9,-15/8*a^3*(e*cos(d*x+c))^(3/2)/d/e/sqrt(a+a*sin(d*x+c))-3/4*a^2*(e*cos(d*x+c))^(3/2)*sqrt(a+a*sin(d*x+c))/d/e+15/8*a^2*sqrt(e)*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(1+cos(d*x+c)+sin(d*x+c))+15/8*a^2*sqrt(e)*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(1+cos(d*x+c)+sin(d*x+c))-1/3*a*(e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^(3/2)/d/e,1],
[(a+a*sin(d*x+c))^(5/2)/sqrt(e*cos(d*x+c)),x,8,-7/4*a^2*sqrt(e*cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/e-21/4*a^2*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/sqrt(e)/(1+cos(d*x+c)+sin(d*x+c))+21/4*a^2*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/sqrt(e)/(1+cos(d*x+c)+sin(d*x+c))-1/2*a*sqrt(e*cos(d*x+c))*(a+a*sin(d*x+c))^(3/2)/d/e,1],
[(a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(3/2),x,8,5*a^3*(e*cos(d*x+c))^(3/2)/d/e^3/sqrt(a+a*sin(d*x+c))-5*a^2*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/e^(3/2)/(1+cos(d*x+c)+sin(d*x+c))-5*a^2*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/e^(3/2)/(1+cos(d*x+c)+sin(d*x+c))+4*a*(a+a*sin(d*x+c))^(3/2)/d/e/sqrt(e*cos(d*x+c)),1],
[(a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(5/2),x,7,2*a^2*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/e^(5/2)/(1+cos(d*x+c)+sin(d*x+c))-2*a^2*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/e^(5/2)/(1+cos(d*x+c)+sin(d*x+c))+4/3*a*(a+a*sin(d*x+c))^(3/2)/d/e/(e*cos(d*x+c))^(3/2),1],
[(a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(7/2),x,1,2/5*(a+a*sin(d*x+c))^(5/2)/d/e/(e*cos(d*x+c))^(5/2),1],
[(a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(9/2),x,2,2/3*(a+a*sin(d*x+c))^(5/2)/d/e/(e*cos(d*x+c))^(7/2)-4/21*(a+a*sin(d*x+c))^(7/2)/a/d/e/(e*cos(d*x+c))^(7/2),1],
[(a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(11/2),x,3,2*(a+a*sin(d*x+c))^(5/2)/d/e/(e*cos(d*x+c))^(9/2)-8/5*(a+a*sin(d*x+c))^(7/2)/a/d/e/(e*cos(d*x+c))^(9/2)+16/45*(a+a*sin(d*x+c))^(9/2)/a^2/d/e/(e*cos(d*x+c))^(9/2),1],
[(a+a*sin(d*x+c))^(5/2)/(e*cos(d*x+c))^(13/2),x,4,-2*(a+a*sin(d*x+c))^(5/2)/d/e/(e*cos(d*x+c))^(11/2)+4*(a+a*sin(d*x+c))^(7/2)/a/d/e/(e*cos(d*x+c))^(11/2)-16/7*(a+a*sin(d*x+c))^(9/2)/a^2/d/e/(e*cos(d*x+c))^(11/2)+32/77*(a+a*sin(d*x+c))^(11/2)/a^3/d/e/(e*cos(d*x+c))^(11/2),1],
[(e*cos(d*x+c))^(5/2)/sqrt(a+a*sin(d*x+c)),x,8,-1/2*a*(e*cos(d*x+c))^(7/2)/d/e/(a+a*sin(d*x+c))^(3/2)+1/4*e*(e*cos(d*x+c))^(3/2)/d/sqrt(a+a*sin(d*x+c))+3/4*e^(5/2)*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(a+a*cos(d*x+c)+a*sin(d*x+c))+3/4*e^(5/2)*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(a+a*cos(d*x+c)+a*sin(d*x+c)),1],
[(e*cos(d*x+c))^(3/2)/sqrt(a+a*sin(d*x+c)),x,7,e*sqrt(e*cos(d*x+c))*sqrt(a+a*sin(d*x+c))/a/d-e^(3/2)*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/a/d/(1+cos(d*x+c)+sin(d*x+c))+e^(3/2)*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/a/d/(1+cos(d*x+c)+sin(d*x+c)),1],
[sqrt(e*cos(d*x+c))/sqrt(a+a*sin(d*x+c)),x,6,2*sqrt(e)*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(a+a*cos(d*x+c)+a*sin(d*x+c))+2*sqrt(e)*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(a+a*cos(d*x+c)+a*sin(d*x+c)),1],
[1/sqrt(e*cos(d*x+c))/sqrt(a+a*sin(d*x+c)),x,1,-2*sqrt(e*cos(d*x+c))/d/e/sqrt(a+a*sin(d*x+c)),1],
[1/(e*cos(d*x+c))^(3/2)/sqrt(a+a*sin(d*x+c)),x,2,-2/3/d/e/sqrt(e*cos(d*x+c))/sqrt(a+a*sin(d*x+c))+4/3*sqrt(a+a*sin(d*x+c))/a/d/e/sqrt(e*cos(d*x+c)),1],
[1/(e*cos(d*x+c))^(5/2)/sqrt(a+a*sin(d*x+c)),x,3,-2/5/d/e/(e*cos(d*x+c))^(3/2)/sqrt(a+a*sin(d*x+c))-8/5*sqrt(a+a*sin(d*x+c))/a/d/e/(e*cos(d*x+c))^(3/2)+16/15*(a+a*sin(d*x+c))^(3/2)/a^2/d/e/(e*cos(d*x+c))^(3/2),1],
[1/(e*cos(d*x+c))^(7/2)/sqrt(a+a*sin(d*x+c)),x,4,-2/7/d/e/(e*cos(d*x+c))^(5/2)/sqrt(a+a*sin(d*x+c))-4/7*sqrt(a+a*sin(d*x+c))/a/d/e/(e*cos(d*x+c))^(5/2)+16/7*(a+a*sin(d*x+c))^(3/2)/a^2/d/e/(e*cos(d*x+c))^(5/2)-32/35*(a+a*sin(d*x+c))^(5/2)/a^3/d/e/(e*cos(d*x+c))^(5/2),1],
[(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(3/2),x,8,1/2*e*(e*cos(d*x+c))^(5/2)/a/d/sqrt(a+a*sin(d*x+c))+5/4*e^3*sqrt(e*cos(d*x+c))*sqrt(a+a*sin(d*x+c))/a^2/d-5/4*e^(7/2)*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/a^2/d/(1+cos(d*x+c)+sin(d*x+c))+5/4*e^(7/2)*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/a^2/d/(1+cos(d*x+c)+sin(d*x+c)),1],
[(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(3/2),x,7,e*(e*cos(d*x+c))^(3/2)/a/d/sqrt(a+a*sin(d*x+c))+3*e^(5/2)*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(a^2+a^2*cos(d*x+c)+a^2*sin(d*x+c))+3*e^(5/2)*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(a^2+a^2*cos(d*x+c)+a^2*sin(d*x+c)),1],
[(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(3/2),x,8,-2*(e*cos(d*x+c))^(5/2)/d/e/(a+a*sin(d*x+c))^(3/2)-2*e*sqrt(e*cos(d*x+c))*sqrt(a+a*sin(d*x+c))/a^2/d+2*e^(3/2)*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/a^2/d/(1+cos(d*x+c)+sin(d*x+c))-2*e^(3/2)*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/a^2/d/(1+cos(d*x+c)+sin(d*x+c)),1],
[sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c))^(3/2),x,1,-2/3*(e*cos(d*x+c))^(3/2)/d/e/(a+a*sin(d*x+c))^(3/2),1],
[1/sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c))^(3/2),x,2,-2/5*sqrt(e*cos(d*x+c))/d/e/(a+a*sin(d*x+c))^(3/2)-4/5*sqrt(e*cos(d*x+c))/a/d/e/sqrt(a+a*sin(d*x+c)),1],
[1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(3/2),x,3,-2/7/d/e/sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c))^(3/2)-8/21/a/d/e/sqrt(e*cos(d*x+c))/sqrt(a+a*sin(d*x+c))+16/21*sqrt(a+a*sin(d*x+c))/a^2/d/e/sqrt(e*cos(d*x+c)),1],
[1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(3/2),x,4,-2/9/d/e/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(3/2)-4/15/a/d/e/(e*cos(d*x+c))^(3/2)/sqrt(a+a*sin(d*x+c))-16/15*sqrt(a+a*sin(d*x+c))/a^2/d/e/(e*cos(d*x+c))^(3/2)+32/45*(a+a*sin(d*x+c))^(3/2)/a^3/d/e/(e*cos(d*x+c))^(3/2),1],
[1/(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(3/2),x,5,-2/11/d/e/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(3/2)-16/77/a/d/e/(e*cos(d*x+c))^(5/2)/sqrt(a+a*sin(d*x+c))-32/77*sqrt(a+a*sin(d*x+c))/a^2/d/e/(e*cos(d*x+c))^(5/2)+128/77*(a+a*sin(d*x+c))^(3/2)/a^3/d/e/(e*cos(d*x+c))^(5/2)-256/385*(a+a*sin(d*x+c))^(5/2)/a^4/d/e/(e*cos(d*x+c))^(5/2),1],
[(e*cos(d*x+c))^(9/2)/(a+a*sin(d*x+c))^(5/2),x,9,1/2*e*(e*cos(d*x+c))^(7/2)/a/d/(a+a*sin(d*x+c))^(3/2)+7/4*e^3*(e*cos(d*x+c))^(3/2)/a^2/d/sqrt(a+a*sin(d*x+c))+21/4*e^(9/2)*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(a^3+a^3*cos(d*x+c)+a^3*sin(d*x+c))+21/4*e^(9/2)*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(a^3+a^3*cos(d*x+c)+a^3*sin(d*x+c)),1],
[(e*cos(d*x+c))^(7/2)/(a+a*sin(d*x+c))^(5/2),x,8,-4*e*(e*cos(d*x+c))^(5/2)/a/d/(a+a*sin(d*x+c))^(3/2)-5*e^3*sqrt(e*cos(d*x+c))*sqrt(a+a*sin(d*x+c))/a^3/d+5*e^(7/2)*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/a^3/d/(1+cos(d*x+c)+sin(d*x+c))-5*e^(7/2)*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/a^3/d/(1+cos(d*x+c)+sin(d*x+c)),1],
[(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(5/2),x,7,-4/3*e*(e*cos(d*x+c))^(3/2)/a/d/(a+a*sin(d*x+c))^(3/2)-2*e^(5/2)*arcsinh(sqrt(e*cos(d*x+c))/sqrt(e))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(a^3+a^3*cos(d*x+c)+a^3*sin(d*x+c))-2*e^(5/2)*arctan(sqrt(e)*sin(d*x+c)/sqrt(e*cos(d*x+c))/sqrt(1+cos(d*x+c)))*sqrt(1+cos(d*x+c))*sqrt(a+a*sin(d*x+c))/d/(a^3+a^3*cos(d*x+c)+a^3*sin(d*x+c)),1],
[(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(5/2),x,1,-2/5*(e*cos(d*x+c))^(5/2)/d/e/(a+a*sin(d*x+c))^(5/2),1],
[sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c))^(5/2),x,2,-2/7*(e*cos(d*x+c))^(3/2)/d/e/(a+a*sin(d*x+c))^(5/2)-4/21*(e*cos(d*x+c))^(3/2)/a/d/e/(a+a*sin(d*x+c))^(3/2),1],
[1/sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c))^(5/2),x,3,-2/9*sqrt(e*cos(d*x+c))/d/e/(a+a*sin(d*x+c))^(5/2)-8/45*sqrt(e*cos(d*x+c))/a/d/e/(a+a*sin(d*x+c))^(3/2)-16/45*sqrt(e*cos(d*x+c))/a^2/d/e/sqrt(a+a*sin(d*x+c)),1],
[1/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(5/2),x,4,-2/11/d/e/sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c))^(5/2)-12/77/a/d/e/sqrt(e*cos(d*x+c))/(a+a*sin(d*x+c))^(3/2)-16/77/a^2/d/e/sqrt(e*cos(d*x+c))/sqrt(a+a*sin(d*x+c))+32/77*sqrt(a+a*sin(d*x+c))/a^3/d/e/sqrt(e*cos(d*x+c)),1],
[1/(e*cos(d*x+c))^(5/2)/(a+a*sin(d*x+c))^(5/2),x,5,-2/13/d/e/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(5/2)-16/117/a/d/e/(e*cos(d*x+c))^(3/2)/(a+a*sin(d*x+c))^(3/2)-32/195/a^2/d/e/(e*cos(d*x+c))^(3/2)/sqrt(a+a*sin(d*x+c))-128/195*sqrt(a+a*sin(d*x+c))/a^3/d/e/(e*cos(d*x+c))^(3/2)+256/585*(a+a*sin(d*x+c))^(3/2)/a^4/d/e/(e*cos(d*x+c))^(3/2),1],
[(e*cos(d*x+c))^(7/3)/sqrt(a+a*sin(d*x+c)),x,2,-3/5*2^(1/6)*(e*cos(d*x+c))^(10/3)*hypergeom([-1/6, 5/3],[8/3],1/2-1/2*sin(d*x+c))/d/e/(1+sin(d*x+c))^(7/6)/sqrt(a+a*sin(d*x+c)),1],
[(e*cos(d*x+c))^(5/3)/sqrt(a+a*sin(d*x+c)),x,2,-3/8*(e*cos(d*x+c))^(8/3)*hypergeom([1/6, 4/3],[7/3],1/2-1/2*sin(d*x+c))*2^(5/6)/d/e/(1+sin(d*x+c))^(5/6)/sqrt(a+a*sin(d*x+c)),1],
[(e*cos(d*x+c))^(2/3)/sqrt(a+a*sin(d*x+c)),x,2,-3/5*2^(1/3)*(e*cos(d*x+c))^(5/3)*hypergeom([2/3, 5/6],[11/6],1/2-1/2*sin(d*x+c))/d/e/(1+sin(d*x+c))^(1/3)/sqrt(a+a*sin(d*x+c)),1],
[(e*cos(d*x+c))^(1/3)/sqrt(a+a*sin(d*x+c)),x,2,-3/4*(e*cos(d*x+c))^(4/3)*hypergeom([2/3, 5/6],[5/3],1/2-1/2*sin(d*x+c))*2^(1/6)/d/e/(1+sin(d*x+c))^(1/6)/sqrt(a+a*sin(d*x+c)),1],
[1/(e*cos(d*x+c))^(1/3)/sqrt(a+a*sin(d*x+c)),x,2,-3/4*(e*cos(d*x+c))^(2/3)*hypergeom([1/3, 7/6],[4/3],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(1/6)*2^(5/6)/d/e/sqrt(a+a*sin(d*x+c)),1],
[1/(e*cos(d*x+c))^(4/3)/sqrt(a+a*sin(d*x+c)),x,2,3/2*hypergeom([-1/6, 5/3],[5/6],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(2/3)*2^(1/3)/d/e/(e*cos(d*x+c))^(1/3)/sqrt(a+a*sin(d*x+c)),1],
[(e*cos(d*x+c))^p*(a+a*sin(d*x+c))^3,x,1,-2^(7/2+1/2*p)*a^3*(e*cos(d*x+c))^(p+1)*hypergeom([-5/2-1/2*p, 1/2*p+1/2],[3/2+1/2*p],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-1/2-1/2*p)/d/e/(p+1),1],
[(e*cos(d*x+c))^p*(a+a*sin(d*x+c))^2,x,1,-2^(5/2+1/2*p)*a^2*(e*cos(d*x+c))^(p+1)*hypergeom([-3/2-1/2*p, 1/2*p+1/2],[3/2+1/2*p],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-1/2-1/2*p)/d/e/(p+1),1],
[(e*cos(d*x+c))^p*(a+a*sin(d*x+c)),x,1,-2^(3/2+1/2*p)*a*(e*cos(d*x+c))^(p+1)*hypergeom([-1/2-1/2*p, 1/2*p+1/2],[3/2+1/2*p],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-1/2-1/2*p)/d/e/(p+1),1],
[(e*cos(d*x+c))^p/(a+a*sin(d*x+c)),x,1,-2^(-1/2+1/2*p)*(e*cos(d*x+c))^(p+1)*hypergeom([3/2-1/2*p, 1/2*p+1/2],[3/2+1/2*p],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-1/2-1/2*p)/a/d/e/(p+1),1],
[(e*cos(d*x+c))^p/(a+a*sin(d*x+c))^2,x,1,-2^(-3/2+1/2*p)*(e*cos(d*x+c))^(p+1)*hypergeom([5/2-1/2*p, 1/2*p+1/2],[3/2+1/2*p],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-1/2-1/2*p)/a^2/d/e/(p+1),1],
[(e*cos(d*x+c))^p/(a+a*sin(d*x+c))^3,x,1,-2^(-5/2+1/2*p)*(e*cos(d*x+c))^(p+1)*hypergeom([7/2-1/2*p, 1/2*p+1/2],[3/2+1/2*p],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-1/2-1/2*p)/a^3/d/e/(p+1),1],
[(e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(5/2),x,2,-2^(3+1/2*p)*(e*cos(d*x+c))^(p+1)*hypergeom([-2-1/2*p, 1/2*p+1/2],[3/2+1/2*p],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-3-1/2*p)*(a+a*sin(d*x+c))^(5/2)/d/e/(p+1),1],
[(e*cos(d*x+c))^p*(a+a*sin(d*x+c))^(3/2),x,2,-2^(2+1/2*p)*(e*cos(d*x+c))^(p+1)*hypergeom([-1-1/2*p, 1/2*p+1/2],[3/2+1/2*p],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-2-1/2*p)*(a+a*sin(d*x+c))^(3/2)/d/e/(p+1),1],
[(e*cos(d*x+c))^p*sqrt(a+a*sin(d*x+c)),x,2,-2^(1+1/2*p)*(e*cos(d*x+c))^(p+1)*hypergeom([-1/2*p, 1/2*p+1/2],[3/2+1/2*p],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-1-1/2*p)*sqrt(a+a*sin(d*x+c))/d/e/(p+1),1],
[(e*cos(d*x+c))^p/sqrt(a+a*sin(d*x+c)),x,2,-2^(1/2*p)*(e*cos(d*x+c))^(p+1)*hypergeom([1-1/2*p, 1/2*p+1/2],[3/2+1/2*p],1/2-1/2*sin(d*x+c))/d/e/(p+1)/((1+sin(d*x+c))^(1/2*p))/sqrt(a+a*sin(d*x+c)),1],
[(e*cos(d*x+c))^p/(a+a*sin(d*x+c))^(3/2),x,2,-2^(-1+1/2*p)*(e*cos(d*x+c))^(p+1)*hypergeom([2-1/2*p, 1/2*p+1/2],[3/2+1/2*p],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(1-1/2*p)/d/e/(p+1)/(a+a*sin(d*x+c))^(3/2),1],
[(e*cos(d*x+c))^p/(a+a*sin(d*x+c))^(5/2),x,2,-2^(-2+1/2*p)*(e*cos(d*x+c))^(p+1)*hypergeom([3-1/2*p, 1/2*p+1/2],[3/2+1/2*p],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(2-1/2*p)/d/e/(p+1)/(a+a*sin(d*x+c))^(5/2),1],
[(e*cos(d*x+c))^p*(a+a*sin(d*x+c))^m,x,2,-2^(1/2+m+1/2*p)*(e*cos(d*x+c))^(p+1)*hypergeom([1/2-m-1/2*p, 1/2*p+1/2],[3/2+1/2*p],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-1/2-m-1/2*p)*(a+a*sin(d*x+c))^m/d/e/(p+1),1],
[cos(d*x+c)^7*(a+a*sin(d*x+c))^m,x,3,8*(a+a*sin(d*x+c))^(4+m)/a^4/d/(4+m)-12*(a+a*sin(d*x+c))^(5+m)/a^5/d/(5+m)+6*(a+a*sin(d*x+c))^(6+m)/a^6/d/(6+m)-(a+a*sin(d*x+c))^(7+m)/a^7/d/(7+m),1],
[cos(d*x+c)^5*(a+a*sin(d*x+c))^m,x,3,4*(a+a*sin(d*x+c))^(3+m)/a^3/d/(3+m)-4*(a+a*sin(d*x+c))^(4+m)/a^4/d/(4+m)+(a+a*sin(d*x+c))^(5+m)/a^5/d/(5+m),1],
[cos(d*x+c)^3*(a+a*sin(d*x+c))^m,x,3,2*(a+a*sin(d*x+c))^(2+m)/a^2/d/(2+m)-(a+a*sin(d*x+c))^(3+m)/a^3/d/(3+m),1],
[cos(d*x+c)*(a+a*sin(d*x+c))^m,x,2,(a+a*sin(d*x+c))^(1+m)/a/d/(1+m),1],
[sec(d*x+c)*(a+a*sin(d*x+c))^m,x,2,1/2*hypergeom([1, m],[1+m],1/2+1/2*sin(d*x+c))*(a+a*sin(d*x+c))^m/d/m,1],
[sec(d*x+c)^3*(a+a*sin(d*x+c))^m,x,2,-1/4*a*hypergeom([2, -1+m],[m],1/2+1/2*sin(d*x+c))*(a+a*sin(d*x+c))^(-1+m)/d/(1-m),1],
[sec(d*x+c)^5*(a+a*sin(d*x+c))^m,x,2,-1/8*a^2*hypergeom([3, -2+m],[-1+m],1/2+1/2*sin(d*x+c))*(a+a*sin(d*x+c))^(-2+m)/d/(2-m),1],
[cos(d*x+c)^4*(a+a*sin(d*x+c))^m,x,2,-1/5*2^(5/2+m)*cos(d*x+c)^5*hypergeom([5/2, -3/2-m],[7/2],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-5/2-m)*(a+a*sin(d*x+c))^m/d,1],
[cos(d*x+c)^2*(a+a*sin(d*x+c))^m,x,2,-1/3*2^(3/2+m)*cos(d*x+c)^3*hypergeom([3/2, -1/2-m],[5/2],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-3/2-m)*(a+a*sin(d*x+c))^m/d,1],
[sec(d*x+c)^2*(a+a*sin(d*x+c))^m,x,2,2^(-1/2+m)*hypergeom([-1/2, 3/2-m],[1/2],1/2-1/2*sin(d*x+c))*sec(d*x+c)*(1+sin(d*x+c))^(1/2-m)*(a+a*sin(d*x+c))^m/d,1],
[sec(d*x+c)^4*(a+a*sin(d*x+c))^m,x,2,1/3*2^(-3/2+m)*hypergeom([-3/2, 5/2-m],[-1/2],1/2-1/2*sin(d*x+c))*sec(d*x+c)^3*(1+sin(d*x+c))^(3/2-m)*(a+a*sin(d*x+c))^m/d,1],
[(e*cos(d*x+c))^(5/2)*(a+a*sin(d*x+c))^m,x,2,-1/7*2^(11/4+m)*(e*cos(d*x+c))^(7/2)*hypergeom([7/4, -3/4-m],[11/4],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-7/4-m)*(a+a*sin(d*x+c))^m/d/e,1],
[(e*cos(d*x+c))^(3/2)*(a+a*sin(d*x+c))^m,x,2,-1/5*2^(9/4+m)*(e*cos(d*x+c))^(5/2)*hypergeom([5/4, -1/4-m],[9/4],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-5/4-m)*(a+a*sin(d*x+c))^m/d/e,1],
[sqrt(e*cos(d*x+c))*(a+a*sin(d*x+c))^m,x,2,-1/3*2^(7/4+m)*(e*cos(d*x+c))^(3/2)*hypergeom([3/4, 1/4-m],[7/4],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-3/4-m)*(a+a*sin(d*x+c))^m/d/e,1],
[(a+a*sin(d*x+c))^m/sqrt(e*cos(d*x+c)),x,2,-2^(5/4+m)*sqrt(e*cos(d*x+c))*hypergeom([1/4, 3/4-m],[5/4],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-1/4-m)*(a+a*sin(d*x+c))^m/d/e,1],
[(a+a*sin(d*x+c))^m/(e*cos(d*x+c))^(3/2),x,2,2^(3/4+m)*hypergeom([-1/4, 5/4-m],[3/4],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(1/4-m)*(a+a*sin(d*x+c))^m/d/e/sqrt(e*cos(d*x+c)),1],
[(a+a*sin(d*x+c))^m/(e*cos(d*x+c))^(5/2),x,2,1/3*2^(1/4+m)*hypergeom([-3/4, 7/4-m],[1/4],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(3/4-m)*(a+a*sin(d*x+c))^m/d/e/(e*cos(d*x+c))^(3/2),1],
[(e*cos(d*x+c))^(-4-m)*(a+a*sin(d*x+c))^m,x,4,-(e*cos(d*x+c))^(-3-m)*(a+a*sin(d*x+c))^m/d/e/(3-m)-3*(e*cos(d*x+c))^(-3-m)*(a+a*sin(d*x+c))^(1+m)/a/d/e/(1-m)/(3-m)+6*(e*cos(d*x+c))^(-3-m)*(a+a*sin(d*x+c))^(2+m)/a^2/d/e/(3-m)/(-m^2+1)-6*(e*cos(d*x+c))^(-3-m)*(a+a*sin(d*x+c))^(3+m)/a^3/d/e/(m^4-10*m^2+9),1],
[(e*cos(d*x+c))^(-3-m)*(a+a*sin(d*x+c))^m,x,3,-(e*cos(d*x+c))^(-2-m)*(a+a*sin(d*x+c))^m/d/e/(2-m)+2*(e*cos(d*x+c))^(-2-m)*(a+a*sin(d*x+c))^(1+m)/a/d/e/(2-m)/m-2*(e*cos(d*x+c))^(-2-m)*(a+a*sin(d*x+c))^(2+m)/a^2/d/e/m/(-m^2+4),1],
[(e*cos(d*x+c))^(-2-m)*(a+a*sin(d*x+c))^m,x,2,-(e*cos(d*x+c))^(-1-m)*(a+a*sin(d*x+c))^m/d/e/(1-m)+(e*cos(d*x+c))^(-1-m)*(a+a*sin(d*x+c))^(1+m)/a/d/e/(-m^2+1),1],
[(e*cos(d*x+c))^(-1-m)*(a+a*sin(d*x+c))^m,x,1,(a+a*sin(d*x+c))^m/d/e/m/((e*cos(d*x+c))^m),1],
[(a+a*sin(d*x+c))^m/((e*cos(d*x+c))^m),x,2,-2^(1/2+1/2*m)*(e*cos(d*x+c))^(1-m)*hypergeom([1/2-1/2*m, 1/2-1/2*m],[3/2-1/2*m],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-1/2-1/2*m)*(a+a*sin(d*x+c))^m/d/e/(1-m),1],
[(e*cos(d*x+c))^(1-m)*(a+a*sin(d*x+c))^m,x,2,-2^(1+1/2*m)*(e*cos(d*x+c))^(2-m)*hypergeom([1-1/2*m, -1/2*m],[2-1/2*m],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-1-1/2*m)*(a+a*sin(d*x+c))^m/d/e/(2-m),1],
[(e*cos(d*x+c))^(2-m)*(a+a*sin(d*x+c))^m,x,2,-2^(3/2+1/2*m)*(e*cos(d*x+c))^(3-m)*hypergeom([-1/2-1/2*m, 3/2-1/2*m],[5/2-1/2*m],1/2-1/2*sin(d*x+c))*(1+sin(d*x+c))^(-3/2-1/2*m)*(a+a*sin(d*x+c))^m/d/e/(3-m),1],
[(e*cos(d*x+c))^(5-2*m)*(a+a*sin(d*x+c))^m,x,3,-8*a^3*(e*cos(d*x+c))^(6-2*m)*(a+a*sin(d*x+c))^(-3+m)/d/e/(5-m)/(m^2-7*m+12)-4*a^2*(e*cos(d*x+c))^(6-2*m)*(a+a*sin(d*x+c))^(-2+m)/d/e/(m^2-9*m+20)-a*(e*cos(d*x+c))^(6-2*m)*(a+a*sin(d*x+c))^(-1+m)/d/e/(5-m),1],
[(e*cos(d*x+c))^(3-2*m)*(a+a*sin(d*x+c))^m,x,2,-2*a^2*(e*cos(d*x+c))^(4-2*m)*(a+a*sin(d*x+c))^(-2+m)/d/e/(m^2-5*m+6)-a*(e*cos(d*x+c))^(4-2*m)*(a+a*sin(d*x+c))^(-1+m)/d/e/(3-m),1],
[(e*cos(d*x+c))^(1-2*m)*(a+a*sin(d*x+c))^m,x,1,-a*(e*cos(d*x+c))^(2-2*m)*(a+a*sin(d*x+c))^(-1+m)/d/e/(1-m),1],
[(e*cos(d*x+c))^(-1-2*m)*(a+a*sin(d*x+c))^m,x,2,1/2*hypergeom([1, -m],[1-m],1/2-1/2*sin(d*x+c))*(a+a*sin(d*x+c))^m/d/e/m/((e*cos(d*x+c))^(2*m)),1],
[(e*cos(d*x+c))^(-3-2*m)*(a+a*sin(d*x+c))^m,x,2,1/4*hypergeom([2, -1-m],[-m],1/2-1/2*sin(d*x+c))*(a+a*sin(d*x+c))^(1+m)/a/d/e/(1+m)/((e*cos(d*x+c))^(2+2*m)),1],
[(e*cos(d*x+c))^(4-2*m)*(a+a*sin(d*x+c))^m,x,2,-4*sqrt(2)*(e*cos(d*x+c))^(5-2*m)*hypergeom([-3/2, 5/2-m],[7/2-m],1/2-1/2*sin(d*x+c))*(a+a*sin(d*x+c))^m/d/e/(5-2*m)/(1+sin(d*x+c))^(5/2),1],
[(e*cos(d*x+c))^(2-2*m)*(a+a*sin(d*x+c))^m,x,2,-2*sqrt(2)*(e*cos(d*x+c))^(3-2*m)*hypergeom([-1/2, 3/2-m],[5/2-m],1/2-1/2*sin(d*x+c))*(a+a*sin(d*x+c))^m/d/e/(3-2*m)/(1+sin(d*x+c))^(3/2),1],
[(a+a*sin(d*x+c))^m/((e*cos(d*x+c))^(2*m)),x,2,-sqrt(2)*(e*cos(d*x+c))^(1-2*m)*hypergeom([1/2, 1/2-m],[3/2-m],1/2-1/2*sin(d*x+c))*(a+a*sin(d*x+c))^m/d/e/(1-2*m)/sqrt(1+sin(d*x+c)),1],
[(e*cos(d*x+c))^(-2-2*m)*(a+a*sin(d*x+c))^m,x,2,(e*cos(d*x+c))^(-1-2*m)*hypergeom([3/2, -1/2-m],[1/2-m],1/2-1/2*sin(d*x+c))*sqrt(1+sin(d*x+c))*(a+a*sin(d*x+c))^m/sqrt(2)/d/e/(1+2*m),1],
[cos(d*x+c)^5*(a+b*sin(d*x+c)),x,4,-1/6*b*cos(d*x+c)^6/d+a*sin(d*x+c)/d-2/3*a*sin(d*x+c)^3/d+1/5*a*sin(d*x+c)^5/d,1],
[cos(d*x+c)^3*(a+b*sin(d*x+c)),x,3,-1/4*b*cos(d*x+c)^4/d+a*sin(d*x+c)/d-1/3*a*sin(d*x+c)^3/d,1],
[cos(d*x+c)*(a+b*sin(d*x+c)),x,2,1/2*(a+b*sin(d*x+c))^2/b/d,1],
[sec(d*x+c)*(a+b*sin(d*x+c)),x,4,-1/2*(a+b)*ln(1-sin(d*x+c))/d+1/2*(a-b)*ln(1+sin(d*x+c))/d,1],
[sec(d*x+c)^3*(a+b*sin(d*x+c)),x,3,1/2*a*arctanh(sin(d*x+c))/d+1/2*sec(d*x+c)^2*(b+a*sin(d*x+c))/d,1],
[sec(d*x+c)^5*(a+b*sin(d*x+c)),x,4,3/8*a*arctanh(sin(d*x+c))/d+1/4*sec(d*x+c)^4*(b+a*sin(d*x+c))/d+3/8*a*sec(d*x+c)*tan(d*x+c)/d,1],
[cos(d*x+c)^4*(a+b*sin(d*x+c)),x,4,3/8*a*x-1/5*b*cos(d*x+c)^5/d+3/8*a*cos(d*x+c)*sin(d*x+c)/d+1/4*a*cos(d*x+c)^3*sin(d*x+c)/d,1],
[cos(d*x+c)^2*(a+b*sin(d*x+c)),x,3,1/2*a*x-1/3*b*cos(d*x+c)^3/d+1/2*a*cos(d*x+c)*sin(d*x+c)/d,1],
[sec(d*x+c)^2*(a+b*sin(d*x+c)),x,3,b*sec(d*x+c)/d+a*tan(d*x+c)/d,1],
[sec(d*x+c)^4*(a+b*sin(d*x+c)),x,3,1/3*b*sec(d*x+c)^3/d+a*tan(d*x+c)/d+1/3*a*tan(d*x+c)^3/d,1],
[sec(d*x+c)^6*(a+b*sin(d*x+c)),x,3,1/5*b*sec(d*x+c)^5/d+a*tan(d*x+c)/d+2/3*a*tan(d*x+c)^3/d+1/5*a*tan(d*x+c)^5/d,1],
[cos(d*x+c)^5*(a+b*sin(d*x+c))^2,x,3,-1/3*a*b*cos(d*x+c)^6/d+a^2*sin(d*x+c)/d-1/3*(2*a^2-b^2)*sin(d*x+c)^3/d+1/5*(a^2-2*b^2)*sin(d*x+c)^5/d+1/7*b^2*sin(d*x+c)^7/d,1],
[cos(d*x+c)^3*(a+b*sin(d*x+c))^2,x,3,-1/3*(a^2-b^2)*(a+b*sin(d*x+c))^3/b^3/d+1/2*a*(a+b*sin(d*x+c))^4/b^3/d-1/5*(a+b*sin(d*x+c))^5/b^3/d,1],
[cos(d*x+c)*(a+b*sin(d*x+c))^2,x,2,1/3*(a+b*sin(d*x+c))^3/b/d,1],
[sec(d*x+c)*(a+b*sin(d*x+c))^2,x,3,-1/2*(a+b)^2*ln(1-sin(d*x+c))/d+1/2*(a-b)^2*ln(1+sin(d*x+c))/d-b^2*sin(d*x+c)/d,1],
[sec(d*x+c)^3*(a+b*sin(d*x+c))^2,x,3,1/2*(a^2-b^2)*arctanh(sin(d*x+c))/d+1/2*sec(d*x+c)^2*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))/d,1],
[sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x,5,1/8*(3*a^2-b^2)*arctanh(sin(d*x+c))/d+1/16*(a+b)*(3*a+b)/d/(1-sin(d*x+c))-1/16*(a-b)*(3*a-b)/d/(1+sin(d*x+c))+1/4*sec(d*x+c)^3*(a+b*sin(d*x+c))^2*tan(d*x+c)/d,1],
[cos(d*x+c)^6*(a+b*sin(d*x+c))^2,x,6,5/128*(8*a^2+b^2)*x-9/56*a*b*cos(d*x+c)^7/d+5/128*(8*a^2+b^2)*cos(d*x+c)*sin(d*x+c)/d+5/192*(8*a^2+b^2)*cos(d*x+c)^3*sin(d*x+c)/d+1/48*(8*a^2+b^2)*cos(d*x+c)^5*sin(d*x+c)/d-1/8*b*cos(d*x+c)^7*(a+b*sin(d*x+c))/d,1],
[cos(d*x+c)^4*(a+b*sin(d*x+c))^2,x,5,1/16*(6*a^2+b^2)*x-7/30*a*b*cos(d*x+c)^5/d+1/16*(6*a^2+b^2)*cos(d*x+c)*sin(d*x+c)/d+1/24*(6*a^2+b^2)*cos(d*x+c)^3*sin(d*x+c)/d-1/6*b*cos(d*x+c)^5*(a+b*sin(d*x+c))/d,1],
[cos(d*x+c)^2*(a+b*sin(d*x+c))^2,x,4,1/8*(4*a^2+b^2)*x-5/12*a*b*cos(d*x+c)^3/d+1/8*(4*a^2+b^2)*cos(d*x+c)*sin(d*x+c)/d-1/4*b*cos(d*x+c)^3*(a+b*sin(d*x+c))/d,1],
[sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x,3,-b^2*x+a*b*cos(d*x+c)/d+sec(d*x+c)*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))/d,1],
[sec(d*x+c)^4*(a+b*sin(d*x+c))^2,x,4,1/3*a*b*sec(d*x+c)/d+1/3*sec(d*x+c)^3*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))/d+1/3*(2*a^2-b^2)*tan(d*x+c)/d,1],
[sec(d*x+c)^6*(a+b*sin(d*x+c))^2,x,4,1/5*a*b*sec(d*x+c)^3/d+1/5*sec(d*x+c)^5*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))/d+1/5*(4*a^2-b^2)*tan(d*x+c)/d+1/15*(4*a^2-b^2)*tan(d*x+c)^3/d,1],
[sec(d*x+c)^8*(a+b*sin(d*x+c))^2,x,4,1/7*a*b*sec(d*x+c)^5/d+1/7*sec(d*x+c)^7*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))/d+1/7*(6*a^2-b^2)*tan(d*x+c)/d+2/21*(6*a^2-b^2)*tan(d*x+c)^3/d+1/35*(6*a^2-b^2)*tan(d*x+c)^5/d,1],
[cos(d*x+c)^5*(a+b*sin(d*x+c))^3,x,3,1/4*(a^2-b^2)^2*(a+b*sin(d*x+c))^4/b^5/d-4/5*a*(a^2-b^2)*(a+b*sin(d*x+c))^5/b^5/d+1/3*(3*a^2-b^2)*(a+b*sin(d*x+c))^6/b^5/d-4/7*a*(a+b*sin(d*x+c))^7/b^5/d+1/8*(a+b*sin(d*x+c))^8/b^5/d,1],
[cos(d*x+c)^3*(a+b*sin(d*x+c))^3,x,3,-1/4*(a^2-b^2)*(a+b*sin(d*x+c))^4/b^3/d+2/5*a*(a+b*sin(d*x+c))^5/b^3/d-1/6*(a+b*sin(d*x+c))^6/b^3/d,1],
[cos(d*x+c)*(a+b*sin(d*x+c))^3,x,2,1/4*(a+b*sin(d*x+c))^4/b/d,1],
[sec(d*x+c)*(a+b*sin(d*x+c))^3,x,3,-1/2*(a+b)^3*ln(1-sin(d*x+c))/d+1/2*(a-b)^3*ln(1+sin(d*x+c))/d-3*a*b^2*sin(d*x+c)/d-1/2*b^3*sin(d*x+c)^2/d,1],
[sec(d*x+c)^3*(a+b*sin(d*x+c))^3,x,3,-1/4*(a-2*b)*(a+b)^2*ln(1-sin(d*x+c))/d+1/4*(a-b)^2*(a+2*b)*ln(1+sin(d*x+c))/d+1/4*(a+b)^3/d/(1-sin(d*x+c))-1/4*(a-b)^3/d/(1+sin(d*x+c)),1],
[sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x,4,3/8*a*(a^2-b^2)*arctanh(sin(d*x+c))/d+3/8*a*sec(d*x+c)^2*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))/d+1/4*sec(d*x+c)^3*(a+b*sin(d*x+c))^3*tan(d*x+c)/d,1],
[cos(d*x+c)^4*(a+b*sin(d*x+c))^3,x,6,3/16*a*(2*a^2+b^2)*x-1/70*b*(17*a^2+4*b^2)*cos(d*x+c)^5/d+3/16*a*(2*a^2+b^2)*cos(d*x+c)*sin(d*x+c)/d+1/8*a*(2*a^2+b^2)*cos(d*x+c)^3*sin(d*x+c)/d-3/14*a*b*cos(d*x+c)^5*(a+b*sin(d*x+c))/d-1/7*b*cos(d*x+c)^5*(a+b*sin(d*x+c))^2/d,1],
[cos(d*x+c)^2*(a+b*sin(d*x+c))^3,x,5,1/8*a*(4*a^2+3*b^2)*x-1/60*b*(27*a^2+8*b^2)*cos(d*x+c)^3/d+1/8*a*(4*a^2+3*b^2)*cos(d*x+c)*sin(d*x+c)/d-7/20*a*b*cos(d*x+c)^3*(a+b*sin(d*x+c))/d-1/5*b*cos(d*x+c)^3*(a+b*sin(d*x+c))^2/d,1],
[sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x,2,-3*a*b^2*x+2*b*(a^2+b^2)*cos(d*x+c)/d+a*b^2*cos(d*x+c)*sin(d*x+c)/d+sec(d*x+c)*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^2/d,1],
[sec(d*x+c)^4*(a+b*sin(d*x+c))^3,x,5,2/3*b*(a^2-b^2)*sec(d*x+c)/d+1/3*sec(d*x+c)^3*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^2/d+2/3*a*(a^2-b^2)*tan(d*x+c)/d,1],
[sec(d*x+c)^6*(a+b*sin(d*x+c))^3,x,5,2/15*b*(2*a^2-b^2)*sec(d*x+c)/d+1/5*sec(d*x+c)^5*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^2/d+2/15*sec(d*x+c)^3*(a+b*sin(d*x+c))*(a*b+(2*a^2-b^2)*sin(d*x+c))/d+2/15*a*(4*a^2-3*b^2)*tan(d*x+c)/d,1],
[sec(d*x+c)^8*(a+b*sin(d*x+c))^3,x,5,2/35*b*(3*a^2-b^2)*sec(d*x+c)^3/d+1/7*sec(d*x+c)^7*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^2/d+2/35*sec(d*x+c)^5*(a+b*sin(d*x+c))*(2*a*b+(3*a^2-b^2)*sin(d*x+c))/d+12/35*a*(2*a^2-b^2)*tan(d*x+c)/d+4/35*a*(2*a^2-b^2)*tan(d*x+c)^3/d,1],
[sec(d*x+c)^10*(a+b*sin(d*x+c))^3,x,5,2/63*b*(4*a^2-b^2)*sec(d*x+c)^5/d+1/9*sec(d*x+c)^9*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^2/d+2/63*sec(d*x+c)^7*(a+b*sin(d*x+c))*(3*a*b+(4*a^2-b^2)*sin(d*x+c))/d+2/21*a*(8*a^2-3*b^2)*tan(d*x+c)/d+4/63*a*(8*a^2-3*b^2)*tan(d*x+c)^3/d+2/105*a*(8*a^2-3*b^2)*tan(d*x+c)^5/d,1],
[cos(d*x+c)^5*(a+b*sin(d*x+c))^8,x,3,1/9*(a^2-b^2)^2*(a+b*sin(d*x+c))^9/b^5/d-2/5*a*(a^2-b^2)*(a+b*sin(d*x+c))^10/b^5/d+2/11*(3*a^2-b^2)*(a+b*sin(d*x+c))^11/b^5/d-1/3*a*(a+b*sin(d*x+c))^12/b^5/d+1/13*(a+b*sin(d*x+c))^13/b^5/d,1],
[cos(d*x+c)^3*(a+b*sin(d*x+c))^8,x,3,-1/9*(a^2-b^2)*(a+b*sin(d*x+c))^9/b^3/d+1/5*a*(a+b*sin(d*x+c))^10/b^3/d-1/11*(a+b*sin(d*x+c))^11/b^3/d,1],
[cos(d*x+c)*(a+b*sin(d*x+c))^8,x,2,1/9*(a+b*sin(d*x+c))^9/b/d,1],
[sec(d*x+c)*(a+b*sin(d*x+c))^8,x,3,-1/2*(a+b)^8*ln(1-sin(d*x+c))/d+1/2*(a-b)^8*ln(1+sin(d*x+c))/d-b^2*(28*a^6+70*a^4*b^2+28*a^2*b^4+b^6)*sin(d*x+c)/d-4*a*b^3*(7*a^4+7*a^2*b^2+b^4)*sin(d*x+c)^2/d-1/3*b^4*(70*a^4+28*a^2*b^2+b^4)*sin(d*x+c)^3/d-2*a*b^5*(7*a^2+b^2)*sin(d*x+c)^4/d-1/5*b^6*(28*a^2+b^2)*sin(d*x+c)^5/d-4/3*a*b^7*sin(d*x+c)^6/d-1/7*b^8*sin(d*x+c)^7/d,1],
[sec(d*x+c)^3*(a+b*sin(d*x+c))^8,x,3,-1/4*(a-7*b)*(a+b)^7*ln(1-sin(d*x+c))/d+1/4*(a-b)^7*(a+7*b)*ln(1+sin(d*x+c))/d+1/4*(a+b)^8/d/(1-sin(d*x+c))+b^4*(70*a^4+56*a^2*b^2+3*b^4)*sin(d*x+c)/d+4*a*b^5*(7*a^2+2*b^2)*sin(d*x+c)^2/d+2/3*b^6*(14*a^2+b^2)*sin(d*x+c)^3/d+2*a*b^7*sin(d*x+c)^4/d+1/5*b^8*sin(d*x+c)^5/d-1/4*(a-b)^8/d/(1+sin(d*x+c)),1],
[sec(d*x+c)^5*(a+b*sin(d*x+c))^8,x,3,-1/16*(a+b)^6*(3*a^2-18*a*b+35*b^2)*ln(1-sin(d*x+c))/d+1/16*(a-b)^6*(3*a^2+18*a*b+35*b^2)*ln(1+sin(d*x+c))/d+1/16*(a+b)^8/d/(1-sin(d*x+c))^2+1/16*(3*a-13*b)*(a+b)^7/d/(1-sin(d*x+c))-b^6*(28*a^2+3*b^2)*sin(d*x+c)/d-4*a*b^7*sin(d*x+c)^2/d-1/3*b^8*sin(d*x+c)^3/d-1/16*(a-b)^8/d/(1+sin(d*x+c))^2-1/16*(a-b)^7*(3*a+13*b)/d/(1+sin(d*x+c)),1],
[cos(d*x+c)^2*(a+b*sin(d*x+c))^8,x,10,1/256*(128*a^8+896*a^6*b^2+1120*a^4*b^4+280*a^2*b^6+7*b^8)*x-11/40320*a*b*(1792*a^6+10536*a^4*b^2+9588*a^2*b^4+1289*b^6)*cos(d*x+c)^3/d+1/256*(128*a^8+896*a^6*b^2+1120*a^4*b^4+280*a^2*b^6+7*b^8)*cos(d*x+c)*sin(d*x+c)/d-1/13440*b*(6272*a^6+28088*a^4*b^2+15956*a^2*b^4+735*b^6)*cos(d*x+c)^3*(a+b*sin(d*x+c))/d-13/3360*a*b*(112*a^4+348*a^2*b^2+101*b^4)*cos(d*x+c)^3*(a+b*sin(d*x+c))^2/d-1/2016*b*(784*a^4+1500*a^2*b^2+147*b^4)*cos(d*x+c)^3*(a+b*sin(d*x+c))^3/d-1/336*a*b*(112*a^2+109*b^2)*cos(d*x+c)^3*(a+b*sin(d*x+c))^4/d-1/240*b*(64*a^2+21*b^2)*cos(d*x+c)^3*(a+b*sin(d*x+c))^5/d-17/90*a*b*cos(d*x+c)^3*(a+b*sin(d*x+c))^6/d-1/10*b*cos(d*x+c)^3*(a+b*sin(d*x+c))^7/d,1],
[sec(d*x+c)^2*(a+b*sin(d*x+c))^8,x,7,-7/16*b^2*(64*a^6+240*a^4*b^2+120*a^2*b^4+5*b^6)*x+1/20*a*b*(40*a^6+1664*a^4*b^2+2789*a^2*b^4+512*b^6)*cos(d*x+c)/d+1/80*b^2*(80*a^6+2248*a^4*b^2+2502*a^2*b^4+175*b^6)*cos(d*x+c)*sin(d*x+c)/d+1/40*a*b*(40*a^4+624*a^2*b^2+337*b^4)*cos(d*x+c)*(a+b*sin(d*x+c))^2/d+1/120*b*(120*a^4+992*a^2*b^2+175*b^4)*cos(d*x+c)*(a+b*sin(d*x+c))^3/d+1/30*a*b*(30*a^2+113*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^4/d+1/6*b*(6*a^2+7*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^5/d+a*b*cos(d*x+c)*(a+b*sin(d*x+c))^6/d+sec(d*x+c)*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^7/d,1],
[sec(d*x+c)^4*(a+b*sin(d*x+c))^8,x,7,35/8*b^4*(16*a^4+16*a^2*b^2+b^4)*x+1/6*a*b*(8*a^6-104*a^4*b^2-803*a^2*b^4-256*b^6)*cos(d*x+c)/d+1/24*b^2*(16*a^6-200*a^4*b^2-866*a^2*b^4-105*b^6)*cos(d*x+c)*sin(d*x+c)/d+1/12*a*b*(8*a^4-88*a^2*b^2-151*b^4)*cos(d*x+c)*(a+b*sin(d*x+c))^2/d+1/12*b*(8*a^4-72*a^2*b^2-35*b^4)*cos(d*x+c)*(a+b*sin(d*x+c))^3/d+1/3*a*b*(2*a^2-13*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^4/d+1/3*b*(2*a^2-7*b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^5/d+1/3*sec(d*x+c)^3*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^7/d-1/3*sec(d*x+c)*(a+b*sin(d*x+c))^6*(5*a*b-(2*a^2-7*b^2)*sin(d*x+c))/d,1],
[sec(d*x+c)^6*(a+b*sin(d*x+c))^8,x,7,-7/2*b^6*(8*a^2+b^2)*x+2/15*a*b*(8*a^6-48*a^4*b^2+163*a^2*b^4+192*b^6)*cos(d*x+c)/d+1/30*b^2*(16*a^6-88*a^4*b^2+282*a^2*b^4+105*b^6)*cos(d*x+c)*sin(d*x+c)/d+1/15*a*b*(8*a^4-32*a^2*b^2+87*b^4)*cos(d*x+c)*(a+b*sin(d*x+c))^2/d+1/15*b*(8*a^4-16*a^2*b^2+35*b^4)*cos(d*x+c)*(a+b*sin(d*x+c))^3/d+4/15*a*b*(2*a^2+b^2)*cos(d*x+c)*(a+b*sin(d*x+c))^4/d+1/5*sec(d*x+c)^5*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^7/d-1/15*sec(d*x+c)^3*(a+b*sin(d*x+c))^6*(3*a*b-(4*a^2-7*b^2)*sin(d*x+c))/d-4/15*sec(d*x+c)*(a+b*sin(d*x+c))^5*(b*(4*a^2-7*b^2)-a*(2*a^2+b^2)*sin(d*x+c))/d,1],
[sec(d*x+c)^8*(a+b*sin(d*x+c))^8,x,7,b^8*x+4/105*a*b*(24*a^6-88*a^4*b^2+125*a^2*b^4-96*b^6)*cos(d*x+c)/d+1/105*b^2*(48*a^6-152*a^4*b^2+174*a^2*b^4-105*b^6)*cos(d*x+c)*sin(d*x+c)/d+2/105*a*b*(24*a^4-40*a^2*b^2+9*b^4)*cos(d*x+c)*(a+b*sin(d*x+c))^2/d+2/105*b*(24*a^4+8*a^2*b^2-35*b^4)*cos(d*x+c)*(a+b*sin(d*x+c))^3/d+1/7*sec(d*x+c)^7*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^7/d-2/105*sec(d*x+c)^3*(a+b*sin(d*x+c))^5*(b*(6*a^2-7*b^2)-a*(12*a^2-11*b^2)*sin(d*x+c))/d-1/35*sec(d*x+c)^5*(a+b*sin(d*x+c))^6*(a*b-(6*a^2-7*b^2)*sin(d*x+c))/d-2/105*sec(d*x+c)*(a+b*sin(d*x+c))^4*(3*a*b*(12*a^2-11*b^2)-(24*a^4+8*a^2*b^2-35*b^4)*sin(d*x+c))/d,1],
[sec(d*x+c)^10*(a+b*sin(d*x+c))^8,x,10,128/315*a*b*(a^2-b^2)^3*sec(d*x+c)/d+64/315*a*(a^2-b^2)^2*sec(d*x+c)^3*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^2/d+16/105*a*(a^2-b^2)*sec(d*x+c)^5*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^4/d+1/9*sec(d*x+c)^9*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^7/d+1/63*sec(d*x+c)^7*(a+b*sin(d*x+c))^6*(a*b+(8*a^2-7*b^2)*sin(d*x+c))/d+128/315*a^2*(a^2-b^2)^3*tan(d*x+c)/d,1],
[cos(d*x+c)^5/(a+b*sin(d*x+c)),x,3,(a^2-b^2)^2*ln(a+b*sin(d*x+c))/b^5/d-a*(a^2-2*b^2)*sin(d*x+c)/b^4/d+1/2*(a^2-2*b^2)*sin(d*x+c)^2/b^3/d-1/3*a*sin(d*x+c)^3/b^2/d+1/4*sin(d*x+c)^4/b/d,1],
[cos(d*x+c)^3/(a+b*sin(d*x+c)),x,3,-(a^2-b^2)*ln(a+b*sin(d*x+c))/b^3/d+a*sin(d*x+c)/b^2/d-1/2*sin(d*x+c)^2/b/d,1],
[cos(d*x+c)/(a+b*sin(d*x+c)),x,2,ln(a+b*sin(d*x+c))/b/d,1],
[sec(d*x+c)/(a+b*sin(d*x+c)),x,3,-1/2*ln(1-sin(d*x+c))/(a+b)/d+1/2*ln(1+sin(d*x+c))/(a-b)/d-b*ln(a+b*sin(d*x+c))/(a^2-b^2)/d,1],
[sec(d*x+c)^3/(a+b*sin(d*x+c)),x,3,-1/4*(a+2*b)*ln(1-sin(d*x+c))/(a+b)^2/d+1/4*(a-2*b)*ln(1+sin(d*x+c))/(a-b)^2/d+b^3*ln(a+b*sin(d*x+c))/(a^2-b^2)^2/d+1/4/(a+b)/d/(1-sin(d*x+c))-1/4/(a-b)/d/(1+sin(d*x+c)),1],
[sec(d*x+c)^5/(a+b*sin(d*x+c)),x,3,-1/16*(3*a^2+9*a*b+8*b^2)*ln(1-sin(d*x+c))/(a+b)^3/d+1/16*(3*a^2-9*a*b+8*b^2)*ln(1+sin(d*x+c))/(a-b)^3/d-b^5*ln(a+b*sin(d*x+c))/(a^2-b^2)^3/d+1/16/(a+b)/d/(1-sin(d*x+c))^2+1/16*(3*a+5*b)/(a+b)^2/d/(1-sin(d*x+c))-1/16/(a-b)/d/(1+sin(d*x+c))^2-1/16*(3*a-5*b)/(a-b)^2/d/(1+sin(d*x+c)),1],
[cos(d*x+c)^6/(a+b*sin(d*x+c)),x,7,1/8*a*(8*a^4-20*a^2*b^2+15*b^4)*x/b^6-2*(a^2-b^2)^(5/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^6/d+1/5*cos(d*x+c)^5/b/d-1/12*cos(d*x+c)^3*(4*a^2-4*b^2-3*a*b*sin(d*x+c))/b^3/d+1/8*cos(d*x+c)*(8*(a^2-b^2)^2-a*b*(4*a^2-7*b^2)*sin(d*x+c))/b^5/d,1],
[cos(d*x+c)^4/(a+b*sin(d*x+c)),x,6,-1/2*a*(2*a^2-3*b^2)*x/b^4+2*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^4/d+1/3*cos(d*x+c)^3/b/d-1/2*cos(d*x+c)*(2*a^2-2*b^2-a*b*sin(d*x+c))/b^3/d,1],
[cos(d*x+c)^2/(a+b*sin(d*x+c)),x,5,a*x/b^2-2*sqrt(a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^2/d+cos(d*x+c)/b/d,1],
[sec(d*x+c)^2/(a+b*sin(d*x+c)),x,5,-2*b^2*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(3/2)/d-sec(d*x+c)*(b-a*sin(d*x+c))/(a^2-b^2)/d,1],
[sec(d*x+c)^4/(a+b*sin(d*x+c)),x,6,2*b^4*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)/d-1/3*sec(d*x+c)^3*(b-a*sin(d*x+c))/(a^2-b^2)/d+1/3*sec(d*x+c)*(3*b^3+a*(2*a^2-5*b^2)*sin(d*x+c))/(a^2-b^2)^2/d,1],
[sec(d*x+c)^6/(a+b*sin(d*x+c)),x,7,-2*b^6*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(7/2)/d-1/5*sec(d*x+c)^5*(b-a*sin(d*x+c))/(a^2-b^2)/d+1/15*sec(d*x+c)^3*(5*b^3+a*(4*a^2-9*b^2)*sin(d*x+c))/(a^2-b^2)^2/d-1/15*sec(d*x+c)*(15*b^5-a*(8*a^4-26*a^2*b^2+33*b^4)*sin(d*x+c))/(a^2-b^2)^3/d,1],
[cos(d*x+c)^7/(a+b*sin(d*x+c))^2,x,3,6*a*(a^2-b^2)^2*ln(a+b*sin(d*x+c))/b^7/d-(5*a^4-9*a^2*b^2+3*b^4)*sin(d*x+c)/b^6/d+a*(2*a^2-3*b^2)*sin(d*x+c)^2/b^5/d-(a^2-b^2)*sin(d*x+c)^3/b^4/d+1/2*a*sin(d*x+c)^4/b^3/d-1/5*sin(d*x+c)^5/b^2/d+(a^2-b^2)^3/b^7/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^5/(a+b*sin(d*x+c))^2,x,3,-4*a*(a^2-b^2)*ln(a+b*sin(d*x+c))/b^5/d+(3*a^2-2*b^2)*sin(d*x+c)/b^4/d-a*sin(d*x+c)^2/b^3/d+1/3*sin(d*x+c)^3/b^2/d-(a^2-b^2)^2/b^5/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^3/(a+b*sin(d*x+c))^2,x,3,2*a*ln(a+b*sin(d*x+c))/b^3/d-sin(d*x+c)/b^2/d+(a^2-b^2)/b^3/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)/(a+b*sin(d*x+c))^2,x,2,-1/b/d/(a+b*sin(d*x+c)),1],
[sec(d*x+c)/(a+b*sin(d*x+c))^2,x,3,-1/2*ln(1-sin(d*x+c))/(a+b)^2/d+1/2*ln(1+sin(d*x+c))/(a-b)^2/d-2*a*b*ln(a+b*sin(d*x+c))/(a^2-b^2)^2/d+b/(a^2-b^2)/d/(a+b*sin(d*x+c)),1],
[sec(d*x+c)^3/(a+b*sin(d*x+c))^2,x,3,-1/4*(a+3*b)*ln(1-sin(d*x+c))/(a+b)^3/d+1/4*(a-3*b)*ln(1+sin(d*x+c))/(a-b)^3/d+4*a*b^3*ln(a+b*sin(d*x+c))/(a^2-b^2)^3/d+1/4/(a+b)^2/d/(1-sin(d*x+c))-1/4/(a-b)^2/d/(1+sin(d*x+c))-b^3/(a^2-b^2)^2/d/(a+b*sin(d*x+c)),1],
[sec(d*x+c)^5/(a+b*sin(d*x+c))^2,x,3,-3/16*(a^2+4*a*b+5*b^2)*ln(1-sin(d*x+c))/(a+b)^4/d+3/16*(a^2-4*a*b+5*b^2)*ln(1+sin(d*x+c))/(a-b)^4/d-6*a*b^5*ln(a+b*sin(d*x+c))/(a^2-b^2)^4/d+1/16/(a+b)^2/d/(1-sin(d*x+c))^2+1/16*(3*a+7*b)/(a+b)^3/d/(1-sin(d*x+c))-1/16/(a-b)^2/d/(1+sin(d*x+c))^2-1/16*(3*a-7*b)/(a-b)^3/d/(1+sin(d*x+c))+b^5/(a^2-b^2)^3/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^6/(a+b*sin(d*x+c))^2,x,7,-5/8*(8*a^4-12*a^2*b^2+3*b^4)*x/b^6+10*a*(a^2-b^2)^(3/2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^6/d+5/12*cos(d*x+c)^3*(4*a-3*b*sin(d*x+c))/b^3/d-cos(d*x+c)^5/b/d/(a+b*sin(d*x+c))-5/8*cos(d*x+c)*(8*a*(a^2-b^2)-b*(4*a^2-3*b^2)*sin(d*x+c))/b^5/d,1],
[cos(d*x+c)^4/(a+b*sin(d*x+c))^2,x,6,3/2*(2*a^2-b^2)*x/b^4-6*a*sqrt(a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^4/d+3/2*cos(d*x+c)*(2*a-b*sin(d*x+c))/b^3/d-cos(d*x+c)^3/b/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2/(a+b*sin(d*x+c))^2,x,5,-x/b^2+2*a*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^2/sqrt(a^2-b^2)/d-cos(d*x+c)/b/d/(a+b*sin(d*x+c)),1],
[sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x,6,-6*a*b^2*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)/d+b*sec(d*x+c)/(a^2-b^2)/d/(a+b*sin(d*x+c))-sec(d*x+c)*(3*a*b-(a^2+2*b^2)*sin(d*x+c))/(a^2-b^2)^2/d,1],
[sec(d*x+c)^4/(a+b*sin(d*x+c))^2,x,7,10*a*b^4*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(7/2)/d+b*sec(d*x+c)^3/(a^2-b^2)/d/(a+b*sin(d*x+c))-1/3*sec(d*x+c)^3*(5*a*b-(a^2+4*b^2)*sin(d*x+c))/(a^2-b^2)^2/d+1/3*sec(d*x+c)*(15*a*b^3+(2*a^4-9*a^2*b^2-8*b^4)*sin(d*x+c))/(a^2-b^2)^3/d,1],
[cos(d*x+c)^7/(a+b*sin(d*x+c))^3,x,3,-3*(5*a^4-6*a^2*b^2+b^4)*ln(a+b*sin(d*x+c))/b^7/d+a*(10*a^2-9*b^2)*sin(d*x+c)/b^6/d-3/2*(2*a^2-b^2)*sin(d*x+c)^2/b^5/d+a*sin(d*x+c)^3/b^4/d-1/4*sin(d*x+c)^4/b^3/d+1/2*(a^2-b^2)^3/b^7/d/(a+b*sin(d*x+c))^2-6*a*(a^2-b^2)^2/b^7/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^5/(a+b*sin(d*x+c))^3,x,3,2*(3*a^2-b^2)*ln(a+b*sin(d*x+c))/b^5/d-3*a*sin(d*x+c)/b^4/d+1/2*sin(d*x+c)^2/b^3/d-1/2*(a^2-b^2)^2/b^5/d/(a+b*sin(d*x+c))^2+4*a*(a^2-b^2)/b^5/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^3/(a+b*sin(d*x+c))^3,x,3,-ln(a+b*sin(d*x+c))/b^3/d+1/2*(a^2-b^2)/b^3/d/(a+b*sin(d*x+c))^2-2*a/b^3/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)/(a+b*sin(d*x+c))^3,x,2,-1/2/b/d/(a+b*sin(d*x+c))^2,1],
[sec(d*x+c)/(a+b*sin(d*x+c))^3,x,3,-1/2*ln(1-sin(d*x+c))/(a+b)^3/d+1/2*ln(1+sin(d*x+c))/(a-b)^3/d-b*(3*a^2+b^2)*ln(a+b*sin(d*x+c))/(a^2-b^2)^3/d+1/2*b/(a^2-b^2)/d/(a+b*sin(d*x+c))^2+2*a*b/(a^2-b^2)^2/d/(a+b*sin(d*x+c)),1],
[sec(d*x+c)^3/(a+b*sin(d*x+c))^3,x,3,-1/4*(a+4*b)*ln(1-sin(d*x+c))/(a+b)^4/d+1/4*(a-4*b)*ln(1+sin(d*x+c))/(a-b)^4/d+2*b^3*(5*a^2+b^2)*ln(a+b*sin(d*x+c))/(a^2-b^2)^4/d+1/4/(a+b)^3/d/(1-sin(d*x+c))-1/4/(a-b)^3/d/(1+sin(d*x+c))-1/2*b^3/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^2-4*a*b^3/(a^2-b^2)^3/d/(a+b*sin(d*x+c)),1],
[sec(d*x+c)^5/(a+b*sin(d*x+c))^3,x,3,-3/16*(a^2+5*a*b+8*b^2)*ln(1-sin(d*x+c))/(a+b)^5/d+3/16*(a^2-5*a*b+8*b^2)*ln(1+sin(d*x+c))/(a-b)^5/d-3*b^5*(7*a^2+b^2)*ln(a+b*sin(d*x+c))/(a^2-b^2)^5/d+1/16/(a+b)^3/d/(1-sin(d*x+c))^2+3/16*(a+3*b)/(a+b)^4/d/(1-sin(d*x+c))-1/16/(a-b)^3/d/(1+sin(d*x+c))^2-3/16*(a-3*b)/(a-b)^4/d/(1+sin(d*x+c))+1/2*b^5/(a^2-b^2)^3/d/(a+b*sin(d*x+c))^2+6*a*b^5/(a^2-b^2)^4/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^6/(a+b*sin(d*x+c))^3,x,7,5/2*a*(4*a^2-3*b^2)*x/b^6-5*(4*a^4-5*a^2*b^2+b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^6/sqrt(a^2-b^2)/d-1/2*cos(d*x+c)^5/b/d/(a+b*sin(d*x+c))^2-5/6*cos(d*x+c)^3*(4*a+b*sin(d*x+c))/b^3/d/(a+b*sin(d*x+c))+5/2*cos(d*x+c)*(4*a^2-b^2-2*a*b*sin(d*x+c))/b^5/d,1],
[cos(d*x+c)^4/(a+b*sin(d*x+c))^3,x,6,-3*a*x/b^4+3*(2*a^2-b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^4/sqrt(a^2-b^2)/d-1/2*cos(d*x+c)^3/b/d/(a+b*sin(d*x+c))^2-3/2*cos(d*x+c)*(2*a+b*sin(d*x+c))/b^3/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2/(a+b*sin(d*x+c))^3,x,6,arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(3/2)/d-1/2*cos(d*x+c)/b/d/(a+b*sin(d*x+c))^2+1/2*a*cos(d*x+c)/b/(a^2-b^2)/d/(a+b*sin(d*x+c)),1],
[sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x,7,-3*b^2*(4*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(7/2)/d+1/2*b*sec(d*x+c)/(a^2-b^2)/d/(a+b*sin(d*x+c))^2+5/2*a*b*sec(d*x+c)/(a^2-b^2)^2/d/(a+b*sin(d*x+c))-1/2*sec(d*x+c)*(3*b*(4*a^2+b^2)-a*(2*a^2+13*b^2)*sin(d*x+c))/(a^2-b^2)^3/d,1],
[sec(d*x+c)^4/(a+b*sin(d*x+c))^3,x,8,5*b^4*(6*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(9/2)/d+1/2*b*sec(d*x+c)^3/(a^2-b^2)/d/(a+b*sin(d*x+c))^2+7/2*a*b*sec(d*x+c)^3/(a^2-b^2)^2/d/(a+b*sin(d*x+c))-1/6*sec(d*x+c)^3*(5*b*(6*a^2+b^2)-a*(2*a^2+33*b^2)*sin(d*x+c))/(a^2-b^2)^3/d+1/6*sec(d*x+c)*(15*b^3*(6*a^2+b^2)+a*(4*a^4-28*a^2*b^2-81*b^4)*sin(d*x+c))/(a^2-b^2)^4/d,1],
[cos(d*x+c)^7/(a+b*sin(d*x+c))^8,x,3,1/7*(a^2-b^2)^3/b^7/d/(a+b*sin(d*x+c))^7-a*(a^2-b^2)^2/b^7/d/(a+b*sin(d*x+c))^6+3/5*(5*a^4-6*a^2*b^2+b^4)/b^7/d/(a+b*sin(d*x+c))^5-a*(5*a^2-3*b^2)/b^7/d/(a+b*sin(d*x+c))^4+(5*a^2-b^2)/b^7/d/(a+b*sin(d*x+c))^3-3*a/b^7/d/(a+b*sin(d*x+c))^2+1/b^7/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^5/(a+b*sin(d*x+c))^8,x,3,-1/7*(a^2-b^2)^2/b^5/d/(a+b*sin(d*x+c))^7+2/3*a*(a^2-b^2)/b^5/d/(a+b*sin(d*x+c))^6-2/5*(3*a^2-b^2)/b^5/d/(a+b*sin(d*x+c))^5+a/b^5/d/(a+b*sin(d*x+c))^4-1/3/b^5/d/(a+b*sin(d*x+c))^3,1],
[cos(d*x+c)^3/(a+b*sin(d*x+c))^8,x,3,1/7*(a^2-b^2)/b^3/d/(a+b*sin(d*x+c))^7-1/3*a/b^3/d/(a+b*sin(d*x+c))^6+1/5/b^3/d/(a+b*sin(d*x+c))^5,1],
[cos(d*x+c)/(a+b*sin(d*x+c))^8,x,2,-1/7/b/d/(a+b*sin(d*x+c))^7,1],
[sec(d*x+c)/(a+b*sin(d*x+c))^8,x,3,-1/2*ln(1-sin(d*x+c))/(a+b)^8/d+1/2*ln(1+sin(d*x+c))/(a-b)^8/d-8*a*b*(a^2+b^2)*(a^4+6*a^2*b^2+b^4)*ln(a+b*sin(d*x+c))/(a^2-b^2)^8/d+1/7*b/(a^2-b^2)/d/(a+b*sin(d*x+c))^7+1/3*a*b/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^6+1/5*b*(3*a^2+b^2)/(a^2-b^2)^3/d/(a+b*sin(d*x+c))^5+a*b*(a^2+b^2)/(a^2-b^2)^4/d/(a+b*sin(d*x+c))^4+1/3*b*(5*a^4+10*a^2*b^2+b^4)/(a^2-b^2)^5/d/(a+b*sin(d*x+c))^3+a*b*(3*a^2+b^2)*(a^2+3*b^2)/(a^2-b^2)^6/d/(a+b*sin(d*x+c))^2+b*(7*a^6+35*a^4*b^2+21*a^2*b^4+b^6)/(a^2-b^2)^7/d/(a+b*sin(d*x+c)),1],
[sec(d*x+c)^3/(a+b*sin(d*x+c))^8,x,3,-1/4*(a+9*b)*ln(1-sin(d*x+c))/(a+b)^9/d+1/4*(a-9*b)*ln(1+sin(d*x+c))/(a-b)^9/d+8*a*b^3*(15*a^6+63*a^4*b^2+45*a^2*b^4+5*b^6)*ln(a+b*sin(d*x+c))/(a^2-b^2)^9/d+1/4/(a+b)^8/d/(1-sin(d*x+c))-1/4/(a-b)^8/d/(1+sin(d*x+c))-1/7*b^3/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^7-2/3*a*b^3/(a^2-b^2)^3/d/(a+b*sin(d*x+c))^6-2/5*b^3*(5*a^2+b^2)/(a^2-b^2)^4/d/(a+b*sin(d*x+c))^5-a*b^3*(5*a^2+3*b^2)/(a^2-b^2)^5/d/(a+b*sin(d*x+c))^4-1/3*b^3*(35*a^4+42*a^2*b^2+3*b^4)/(a^2-b^2)^6/d/(a+b*sin(d*x+c))^3-4*a*b^3*(7*a^4+14*a^2*b^2+3*b^4)/(a^2-b^2)^7/d/(a+b*sin(d*x+c))^2-4*b^3*(21*a^6+63*a^4*b^2+27*a^2*b^4+b^6)/(a^2-b^2)^8/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^8/(a+b*sin(d*x+c))^8,x,11,x/b^8-1/8*a*(16*a^6-56*a^4*b^2+70*a^2*b^4-35*b^6)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/b^8/(a^2-b^2)^(7/2)/d-1/7*cos(d*x+c)^7/b/d/(a+b*sin(d*x+c))^7+1/6*a*cos(d*x+c)^7/b/(a^2-b^2)/d/(a+b*sin(d*x+c))^6-1/24*a*(6*a^2-11*b^2)*cos(d*x+c)^5/b^3/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^4+1/16*a*(8*a^4-22*a^2*b^2+19*b^4)*cos(d*x+c)^3/b^5/(a^2-b^2)^3/d/(a+b*sin(d*x+c))^2+1/30*cos(d*x+c)^5*(6*a^2-6*b^2+5*a*b*sin(d*x+c))/b^3/(a^2-b^2)/d/(a+b*sin(d*x+c))^5-1/24*cos(d*x+c)^3*(8*(a^2-b^2)^2+a*b*(6*a^2-11*b^2)*sin(d*x+c))/b^5/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^3+1/16*cos(d*x+c)*(16*(a^2-b^2)^3+a*b*(8*a^4-22*a^2*b^2+19*b^4)*sin(d*x+c))/b^7/(a^2-b^2)^3/d/(a+b*sin(d*x+c)),1],
[cos(d*x+c)^6/(a+b*sin(d*x+c))^8,x,11,5/8*a*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(9/2)/d-1/7*cos(d*x+c)^5/b/d/(a+b*sin(d*x+c))^7+1/168*a*(4*a^2-b^2)*cos(d*x+c)/b^5/(a^2-b^2)/d/(a+b*sin(d*x+c))^4+1/168*(4*a^4-9*a^2*b^2+12*b^4)*cos(d*x+c)/b^5/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^3+1/336*a*(8*a^4-30*a^2*b^2+57*b^4)*cos(d*x+c)/b^5/(a^2-b^2)^3/d/(a+b*sin(d*x+c))^2+1/336*(8*a^6-38*a^4*b^2+87*a^2*b^4+48*b^6)*cos(d*x+c)/b^5/(a^2-b^2)^4/d/(a+b*sin(d*x+c))+5/42*cos(d*x+c)^3*(2*a+3*b*sin(d*x+c))/b^3/d/(a+b*sin(d*x+c))^6-1/42*cos(d*x+c)*(4*a^2+9*b^2+10*a*b*sin(d*x+c))/b^5/d/(a+b*sin(d*x+c))^5,1],
[cos(d*x+c)^4/(a+b*sin(d*x+c))^8,x,11,3/8*a*(2*a^2+b^2)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(11/2)/d-1/7*cos(d*x+c)^3/b/d/(a+b*sin(d*x+c))^7-1/140*(a^2-3*b^2)*cos(d*x+c)/b^3/(a^2-b^2)/d/(a+b*sin(d*x+c))^5-1/280*a*(2*a^2-11*b^2)*cos(d*x+c)/b^3/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^4-1/280*(2*a^4-15*a^2*b^2-8*b^4)*cos(d*x+c)/b^3/(a^2-b^2)^3/d/(a+b*sin(d*x+c))^3-1/560*a*(4*a^4-36*a^2*b^2-73*b^4)*cos(d*x+c)/b^3/(a^2-b^2)^4/d/(a+b*sin(d*x+c))^2-1/560*(4*a^6-40*a^4*b^2-247*a^2*b^4-32*b^6)*cos(d*x+c)/b^3/(a^2-b^2)^5/d/(a+b*sin(d*x+c))+1/28*cos(d*x+c)*(a+3*b*sin(d*x+c))/b^3/d/(a+b*sin(d*x+c))^6,1],
[cos(d*x+c)^2/(a+b*sin(d*x+c))^8,x,11,1/8*a*(8*a^4+20*a^2*b^2+5*b^4)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(13/2)/d-1/7*cos(d*x+c)/b/d/(a+b*sin(d*x+c))^7+1/42*a*cos(d*x+c)/b/(a^2-b^2)/d/(a+b*sin(d*x+c))^6+1/210*(5*a^2+6*b^2)*cos(d*x+c)/b/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^5+1/840*a*(20*a^2+79*b^2)*cos(d*x+c)/b/(a^2-b^2)^3/d/(a+b*sin(d*x+c))^4+1/840*(20*a^4+179*a^2*b^2+32*b^4)*cos(d*x+c)/b/(a^2-b^2)^4/d/(a+b*sin(d*x+c))^3+1/1680*a*(40*a^4+718*a^2*b^2+397*b^4)*cos(d*x+c)/b/(a^2-b^2)^5/d/(a+b*sin(d*x+c))^2+1/1680*(40*a^6+1518*a^4*b^2+1779*a^2*b^4+128*b^6)*cos(d*x+c)/b/(a^2-b^2)^6/d/(a+b*sin(d*x+c)),1],
[sec(d*x+c)^2/(a+b*sin(d*x+c))^8,x,12,-9/8*a*b^2*(64*a^6+336*a^4*b^2+280*a^2*b^4+35*b^6)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(17/2)/d+1/7*b*sec(d*x+c)/(a^2-b^2)/d/(a+b*sin(d*x+c))^7+5/14*a*b*sec(d*x+c)/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^6+1/70*b*(49*a^2+16*b^2)*sec(d*x+c)/(a^2-b^2)^3/d/(a+b*sin(d*x+c))^5+13/280*a*b*(28*a^2+27*b^2)*sec(d*x+c)/(a^2-b^2)^4/d/(a+b*sin(d*x+c))^4+1/280*b*(700*a^4+1317*a^2*b^2+128*b^4)*sec(d*x+c)/(a^2-b^2)^5/d/(a+b*sin(d*x+c))^3+11/560*a*b*(280*a^4+844*a^2*b^2+241*b^4)*sec(d*x+c)/(a^2-b^2)^6/d/(a+b*sin(d*x+c))^2+1/560*b*(9800*a^6+41484*a^4*b^2+22767*a^2*b^4+1024*b^6)*sec(d*x+c)/(a^2-b^2)^7/d/(a+b*sin(d*x+c))-1/560*sec(d*x+c)*(315*a*b*(64*a^6+336*a^4*b^2+280*a^2*b^4+35*b^6)-(560*a^8+42472*a^6*b^2+125634*a^4*b^4+54511*a^2*b^6+2048*b^8)*sin(d*x+c))/(a^2-b^2)^8/d,1],
[sec(d*x+c)^4/(a+b*sin(d*x+c))^8,x,13,165/8*a*b^4*(32*a^6+112*a^4*b^2+70*a^2*b^4+7*b^6)*arctan((b+a*tan(1/2*d*x+1/2*c))/sqrt(a^2-b^2))/(a^2-b^2)^(19/2)/d+1/7*b*sec(d*x+c)^3/(a^2-b^2)/d/(a+b*sin(d*x+c))^7+17/42*a*b*sec(d*x+c)^3/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^6+1/14*b*(13*a^2+4*b^2)*sec(d*x+c)^3/(a^2-b^2)^3/d/(a+b*sin(d*x+c))^5+1/56*a*b*(118*a^2+103*b^2)*sec(d*x+c)^3/(a^2-b^2)^4/d/(a+b*sin(d*x+c))^4+1/168*b*(882*a^4+1421*a^2*b^2+128*b^4)*sec(d*x+c)^3/(a^2-b^2)^5/d/(a+b*sin(d*x+c))^3+13/112*a*b*(140*a^4+336*a^2*b^2+85*b^4)*sec(d*x+c)^3/(a^2-b^2)^6/d/(a+b*sin(d*x+c))^2+1/112*b*(9212*a^6+28420*a^4*b^2+12907*a^2*b^4+512*b^6)*sec(d*x+c)^3/(a^2-b^2)^7/d/(a+b*sin(d*x+c))-1/336*sec(d*x+c)^3*(1155*a*b*(32*a^6+112*a^4*b^2+70*a^2*b^4+7*b^6)-(112*a^8+52528*a^6*b^2+142902*a^4*b^4+57665*a^2*b^6+2048*b^8)*sin(d*x+c))/(a^2-b^2)^8/d+1/336*sec(d*x+c)*(3465*a*b^3*(32*a^6+112*a^4*b^2+70*a^2*b^4+7*b^6)+(224*a^10-6048*a^8*b^2-207332*a^6*b^4-413024*a^4*b^6-135489*a^2*b^8-4096*b^10)*sin(d*x+c))/(a^2-b^2)^9/d,1],
[cos(d*x+c)^5*sqrt(a+b*sin(d*x+c)),x,3,2/3*(a^2-b^2)^2*(a+b*sin(d*x+c))^(3/2)/b^5/d-8/5*a*(a^2-b^2)*(a+b*sin(d*x+c))^(5/2)/b^5/d+4/7*(3*a^2-b^2)*(a+b*sin(d*x+c))^(7/2)/b^5/d-8/9*a*(a+b*sin(d*x+c))^(9/2)/b^5/d+2/11*(a+b*sin(d*x+c))^(11/2)/b^5/d,1],
[cos(d*x+c)^3*sqrt(a+b*sin(d*x+c)),x,3,-2/3*(a^2-b^2)*(a+b*sin(d*x+c))^(3/2)/b^3/d+4/5*a*(a+b*sin(d*x+c))^(5/2)/b^3/d-2/7*(a+b*sin(d*x+c))^(7/2)/b^3/d,1],
[cos(d*x+c)*sqrt(a+b*sin(d*x+c)),x,2,2/3*(a+b*sin(d*x+c))^(3/2)/b/d,1],
[sec(d*x+c)*sqrt(a+b*sin(d*x+c)),x,5,-sqrt(a-b)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a-b))/d+sqrt(a+b)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a+b))/d,1],
[sec(d*x+c)^3*sqrt(a+b*sin(d*x+c)),x,6,-1/4*(2*a-b)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a-b))/sqrt(a-b)/d+1/4*(2*a+b)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a+b))/sqrt(a+b)/d+1/2*sec(d*x+c)*sqrt(a+b*sin(d*x+c))*tan(d*x+c)/d,1],
[sec(d*x+c)^5*sqrt(a+b*sin(d*x+c)),x,7,-1/32*(12*a^2-18*a*b+5*b^2)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a-b))/(a-b)^(3/2)/d+1/32*(12*a^2+18*a*b+5*b^2)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a+b))/(a+b)^(3/2)/d-1/16*sec(d*x+c)^2*sqrt(a+b*sin(d*x+c))*(a*b-(6*a^2-5*b^2)*sin(d*x+c))/(a^2-b^2)/d+1/4*sec(d*x+c)^3*sqrt(a+b*sin(d*x+c))*tan(d*x+c)/d,1],
[cos(d*x+c)^4*sqrt(a+b*sin(d*x+c)),x,8,-4/21*a*cos(d*x+c)^3*sqrt(a+b*sin(d*x+c))/b/d+2/9*cos(d*x+c)^3*(a+b*sin(d*x+c))^(3/2)/b/d-8/315*(4*a^4-15*a^2*b^2-21*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^4/d/sqrt((a+b*sin(d*x+c))/(a+b))+32/315*a*(a^4-4*a^2*b^2+3*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^4/d/sqrt(a+b*sin(d*x+c))-4/315*cos(d*x+c)*sqrt(a+b*sin(d*x+c))*(4*a*(a^2-3*b^2)-3*b*(a^2+7*b^2)*sin(d*x+c))/b^3/d,1],
[cos(d*x+c)^2*sqrt(a+b*sin(d*x+c)),x,7,-4/15*a*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/b/d+2/5*cos(d*x+c)*(a+b*sin(d*x+c))^(3/2)/b/d+4/15*(a^2+3*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^2/d/sqrt((a+b*sin(d*x+c))/(a+b))-4/15*a*(a^2-b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^2/d/sqrt(a+b*sin(d*x+c)),1],
[sec(d*x+c)^2*sqrt(a+b*sin(d*x+c)),x,7,-EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/d/sqrt((a+b*sin(d*x+c))/(a+b))+a*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c))+sqrt(a+b*sin(d*x+c))*tan(d*x+c)/d,1],
[sec(d*x+c)^4*sqrt(a+b*sin(d*x+c)),x,7,-1/6*(4*a^2-3*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/(a^2-b^2)/d/sqrt((a+b*sin(d*x+c))/(a+b))+2/3*a*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c))-1/6*sec(d*x+c)*sqrt(a+b*sin(d*x+c))*(a*b-(4*a^2-3*b^2)*sin(d*x+c))/(a^2-b^2)/d+1/3*sec(d*x+c)^2*sqrt(a+b*sin(d*x+c))*tan(d*x+c)/d,1],
[cos(d*x+c)^5*(a+b*sin(d*x+c))^(3/2),x,3,2/5*(a^2-b^2)^2*(a+b*sin(d*x+c))^(5/2)/b^5/d-8/7*a*(a^2-b^2)*(a+b*sin(d*x+c))^(7/2)/b^5/d+4/9*(3*a^2-b^2)*(a+b*sin(d*x+c))^(9/2)/b^5/d-8/11*a*(a+b*sin(d*x+c))^(11/2)/b^5/d+2/13*(a+b*sin(d*x+c))^(13/2)/b^5/d,1],
[cos(d*x+c)^3*(a+b*sin(d*x+c))^(3/2),x,3,-2/5*(a^2-b^2)*(a+b*sin(d*x+c))^(5/2)/b^3/d+4/7*a*(a+b*sin(d*x+c))^(7/2)/b^3/d-2/9*(a+b*sin(d*x+c))^(9/2)/b^3/d,1],
[cos(d*x+c)*(a+b*sin(d*x+c))^(3/2),x,2,2/5*(a+b*sin(d*x+c))^(5/2)/b/d,1],
[sec(d*x+c)*(a+b*sin(d*x+c))^(3/2),x,6,-(a-b)^(3/2)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a-b))/d+(a+b)^(3/2)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a+b))/d-2*b*sqrt(a+b*sin(d*x+c))/d,1],
[sec(d*x+c)^3*(a+b*sin(d*x+c))^(3/2),x,6,-1/4*sqrt(a-b)*(2*a+b)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a-b))/d+1/4*(2*a-b)*sqrt(a+b)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a+b))/d+1/2*sec(d*x+c)^2*(b+a*sin(d*x+c))*sqrt(a+b*sin(d*x+c))/d,1],
[sec(d*x+c)^5*(a+b*sin(d*x+c))^(3/2),x,7,-3/32*(4*a^2-2*a*b-b^2)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a-b))/sqrt(a-b)/d+3/32*(4*a^2+2*a*b-b^2)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a+b))/sqrt(a+b)/d-1/16*sec(d*x+c)^2*(b-6*a*sin(d*x+c))*sqrt(a+b*sin(d*x+c))/d+1/4*sec(d*x+c)^4*(b+a*sin(d*x+c))*sqrt(a+b*sin(d*x+c))/d,1],
[cos(d*x+c)^4*(a+b*sin(d*x+c))^(3/2),x,8,-2/11*b*cos(d*x+c)^5*sqrt(a+b*sin(d*x+c))/d-32/1155*a*(a^4-6*a^2*b^2-27*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^4/d/sqrt((a+b*sin(d*x+c))/(a+b))+8/1155*(4*a^6-25*a^4*b^2+6*a^2*b^4+15*b^6)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^4/d/sqrt(a+b*sin(d*x+c))+2/231*cos(d*x+c)^3*sqrt(a+b*sin(d*x+c))*(a^2+3*b^2+28*a*b*sin(d*x+c))/b/d-4/1155*cos(d*x+c)*sqrt(a+b*sin(d*x+c))*(4*a^4-21*a^2*b^2-15*b^4-3*a*b*(a^2+31*b^2)*sin(d*x+c))/b^3/d,1],
[cos(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x,7,-2/7*b*cos(d*x+c)^3*sqrt(a+b*sin(d*x+c))/d+4/105*a*(3*a^2+29*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^2/d/sqrt((a+b*sin(d*x+c))/(a+b))-4/105*(3*a^4+2*a^2*b^2-5*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^2/d/sqrt(a+b*sin(d*x+c))+2/105*cos(d*x+c)*sqrt(a+b*sin(d*x+c))*(3*a^2+5*b^2+24*a*b*sin(d*x+c))/b/d,1],
[sec(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x,6,sec(d*x+c)*(b+a*sin(d*x+c))*sqrt(a+b*sin(d*x+c))/d-a*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/d/sqrt((a+b*sin(d*x+c))/(a+b))+(a^2-b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c)),1],
[sec(d*x+c)^4*(a+b*sin(d*x+c))^(3/2),x,7,-1/6*sec(d*x+c)*(b-4*a*sin(d*x+c))*sqrt(a+b*sin(d*x+c))/d+1/3*sec(d*x+c)^3*(b+a*sin(d*x+c))*sqrt(a+b*sin(d*x+c))/d-2/3*a*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/6*(4*a^2-b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c)),1],
[sec(d*x+c)^6*(a+b*sin(d*x+c))^(3/2),x,8,-1/30*sec(d*x+c)^3*(b-8*a*sin(d*x+c))*sqrt(a+b*sin(d*x+c))/d+1/5*sec(d*x+c)^5*(b+a*sin(d*x+c))*sqrt(a+b*sin(d*x+c))/d-1/60*a*(32*a^2-29*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/(a^2-b^2)/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/60*(32*a^2-5*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c))-1/60*sec(d*x+c)*sqrt(a+b*sin(d*x+c))*(b*(8*a^4-13*a^2*b^2+5*b^4)-a*(32*a^4-61*a^2*b^2+29*b^4)*sin(d*x+c))/(a^2-b^2)^2/d,1],
[cos(d*x+c)^5*(a+b*sin(d*x+c))^(5/2),x,3,2/7*(a^2-b^2)^2*(a+b*sin(d*x+c))^(7/2)/b^5/d-8/9*a*(a^2-b^2)*(a+b*sin(d*x+c))^(9/2)/b^5/d+4/11*(3*a^2-b^2)*(a+b*sin(d*x+c))^(11/2)/b^5/d-8/13*a*(a+b*sin(d*x+c))^(13/2)/b^5/d+2/15*(a+b*sin(d*x+c))^(15/2)/b^5/d,1],
[cos(d*x+c)^3*(a+b*sin(d*x+c))^(5/2),x,3,-2/7*(a^2-b^2)*(a+b*sin(d*x+c))^(7/2)/b^3/d+4/9*a*(a+b*sin(d*x+c))^(9/2)/b^3/d-2/11*(a+b*sin(d*x+c))^(11/2)/b^3/d,1],
[cos(d*x+c)*(a+b*sin(d*x+c))^(5/2),x,2,2/7*(a+b*sin(d*x+c))^(7/2)/b/d,1],
[sec(d*x+c)*(a+b*sin(d*x+c))^(5/2),x,8,-(a-b)^(5/2)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a-b))/d+(a+b)^(5/2)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a+b))/d-4*a*b*sqrt(a+b*sin(d*x+c))/d-2/3*b*(a+b*sin(d*x+c))^(3/2)/d,1],
[sec(d*x+c)^3*(a+b*sin(d*x+c))^(5/2),x,8,-1/4*(a-b)^(3/2)*(2*a+3*b)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a-b))/d+1/4*(2*a-3*b)*(a+b)^(3/2)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a+b))/d+1/2*a*b*sqrt(a+b*sin(d*x+c))/d+1/2*sec(d*x+c)^2*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^(3/2)/d,1],
[sec(d*x+c)^5*(a+b*sin(d*x+c))^(5/2),x,7,-3/32*sqrt(a-b)*(4*a^2+2*a*b-b^2)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a-b))/d+3/32*sqrt(a+b)*(4*a^2-2*a*b-b^2)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a+b))/d+1/4*sec(d*x+c)^4*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^(3/2)/d+3/16*sec(d*x+c)^2*sqrt(a+b*sin(d*x+c))*(a*b+(2*a^2-b^2)*sin(d*x+c))/d,1],
[cos(d*x+c)^4*(a+b*sin(d*x+c))^(5/2),x,9,-32/143*a*b*cos(d*x+c)^5*sqrt(a+b*sin(d*x+c))/d-2/13*b*cos(d*x+c)^5*(a+b*sin(d*x+c))^(3/2)/d-8/15015*(20*a^6-175*a^4*b^2-1662*a^2*b^4-231*b^6)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^4/d/sqrt((a+b*sin(d*x+c))/(a+b))+32/15015*a*(5*a^6-45*a^4*b^2-53*a^2*b^4+93*b^6)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^4/d/sqrt(a+b*sin(d*x+c))+2/3003*cos(d*x+c)^3*sqrt(a+b*sin(d*x+c))*(a*(5*a^2+59*b^2)+7*b*(53*a^2+11*b^2)*sin(d*x+c))/b/d-4/15015*cos(d*x+c)*sqrt(a+b*sin(d*x+c))*(4*a*(5*a^4-40*a^2*b^2-93*b^4)-3*b*(5*a^4+430*a^2*b^2+77*b^4)*sin(d*x+c))/b^3/d,1],
[cos(d*x+c)^2*(a+b*sin(d*x+c))^(5/2),x,8,-8/21*a*b*cos(d*x+c)^3*sqrt(a+b*sin(d*x+c))/d-2/9*b*cos(d*x+c)^3*(a+b*sin(d*x+c))^(3/2)/d+4/315*(5*a^4+102*a^2*b^2+21*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^2/d/sqrt((a+b*sin(d*x+c))/(a+b))-4/315*a*(5*a^4+22*a^2*b^2-27*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^2/d/sqrt(a+b*sin(d*x+c))+2/315*cos(d*x+c)*sqrt(a+b*sin(d*x+c))*(a*(5*a^2+27*b^2)+3*b*(25*a^2+7*b^2)*sin(d*x+c))/b/d,1],
[sec(d*x+c)^2*(a+b*sin(d*x+c))^(5/2),x,7,a*b*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/d+sec(d*x+c)*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^(3/2)/d-(a^2+3*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/d/sqrt((a+b*sin(d*x+c))/(a+b))+a*(a^2-b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c)),1],
[sec(d*x+c)^4*(a+b*sin(d*x+c))^(5/2),x,7,1/3*sec(d*x+c)^3*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^(3/2)/d-1/6*(4*a^2-3*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/d/sqrt((a+b*sin(d*x+c))/(a+b))+2/3*a*(a^2-b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c))+1/6*sec(d*x+c)*sqrt(a+b*sin(d*x+c))*(a*b+(4*a^2-3*b^2)*sin(d*x+c))/d,1],
[sec(d*x+c)^6*(a+b*sin(d*x+c))^(5/2),x,8,1/5*sec(d*x+c)^5*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^(3/2)/d-1/60*(32*a^2-9*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/60*a*(32*a^2-17*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c))+1/30*sec(d*x+c)^3*sqrt(a+b*sin(d*x+c))*(5*a*b+(8*a^2-3*b^2)*sin(d*x+c))/d-1/60*sec(d*x+c)*sqrt(a+b*sin(d*x+c))*(8*a*b*(a^2-b^2)-(32*a^4-41*a^2*b^2+9*b^4)*sin(d*x+c))/(a^2-b^2)/d,1],
[sec(d*x+c)^8*(a+b*sin(d*x+c))^(5/2),x,9,1/7*sec(d*x+c)^7*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^(3/2)/d-1/280*(128*a^4-144*a^2*b^2+21*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/(a^2-b^2)/d/sqrt((a+b*sin(d*x+c))/(a+b))+2/35*a*(8*a^2-3*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c))+3/70*sec(d*x+c)^5*sqrt(a+b*sin(d*x+c))*(3*a*b+(4*a^2-b^2)*sin(d*x+c))/d-1/140*sec(d*x+c)^3*sqrt(a+b*sin(d*x+c))*(4*a*b*(a^2-b^2)-(32*a^4-39*a^2*b^2+7*b^4)*sin(d*x+c))/(a^2-b^2)/d-1/280*sec(d*x+c)*sqrt(a+b*sin(d*x+c))*(a*b*(32*a^4-59*a^2*b^2+27*b^4)-(128*a^6-272*a^4*b^2+165*a^2*b^4-21*b^6)*sin(d*x+c))/(a^2-b^2)^2/d,1],
[cos(d*x+c)^5/sqrt(a+b*sin(d*x+c)),x,3,2*(a^2-b^2)^2*sqrt(a+b*sin(d*x+c))/b^5/d-8/3*a*(a^2-b^2)*(a+b*sin(d*x+c))^(3/2)/b^5/d+4/5*(3*a^2-b^2)*(a+b*sin(d*x+c))^(5/2)/b^5/d-8/7*a*(a+b*sin(d*x+c))^(7/2)/b^5/d+2/9*(a+b*sin(d*x+c))^(9/2)/b^5/d,1],
[cos(d*x+c)^3/sqrt(a+b*sin(d*x+c)),x,3,-2*(a^2-b^2)*sqrt(a+b*sin(d*x+c))/b^3/d+4/3*a*(a+b*sin(d*x+c))^(3/2)/b^3/d-2/5*(a+b*sin(d*x+c))^(5/2)/b^3/d,1],
[cos(d*x+c)/sqrt(a+b*sin(d*x+c)),x,2,2*sqrt(a+b*sin(d*x+c))/b/d,1],
[sec(d*x+c)/sqrt(a+b*sin(d*x+c)),x,5,-arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a-b))/sqrt(a-b)/d+arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a+b))/sqrt(a+b)/d,1],
[sec(d*x+c)^3/sqrt(a+b*sin(d*x+c)),x,6,-1/4*(2*a-3*b)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a-b))/(a-b)^(3/2)/d+1/4*(2*a+3*b)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a+b))/(a+b)^(3/2)/d-1/2*sec(d*x+c)^2*(b-a*sin(d*x+c))*sqrt(a+b*sin(d*x+c))/(a^2-b^2)/d,1],
[sec(d*x+c)^5/sqrt(a+b*sin(d*x+c)),x,7,-3/32*(4*a^2-10*a*b+7*b^2)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a-b))/(a-b)^(5/2)/d+3/32*(4*a^2+10*a*b+7*b^2)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a+b))/(a+b)^(5/2)/d-1/4*sec(d*x+c)^4*(b-a*sin(d*x+c))*sqrt(a+b*sin(d*x+c))/(a^2-b^2)/d-1/16*sec(d*x+c)^2*sqrt(a+b*sin(d*x+c))*(b*(a^2-7*b^2)-6*a*(a^2-2*b^2)*sin(d*x+c))/(a^2-b^2)^2/d,1],
[cos(d*x+c)^4/sqrt(a+b*sin(d*x+c)),x,7,2/7*cos(d*x+c)^3*sqrt(a+b*sin(d*x+c))/b/d-32/35*a*(a^2-2*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^4/d/sqrt((a+b*sin(d*x+c))/(a+b))+8/35*(4*a^4-9*a^2*b^2+5*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^4/d/sqrt(a+b*sin(d*x+c))-4/35*cos(d*x+c)*sqrt(a+b*sin(d*x+c))*(4*a^2-5*b^2-3*a*b*sin(d*x+c))/b^3/d,1],
[cos(d*x+c)^2/sqrt(a+b*sin(d*x+c)),x,6,2/3*cos(d*x+c)*sqrt(a+b*sin(d*x+c))/b/d+4/3*a*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^2/d/sqrt((a+b*sin(d*x+c))/(a+b))-4/3*(a^2-b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^2/d/sqrt(a+b*sin(d*x+c)),1],
[sec(d*x+c)^2/sqrt(a+b*sin(d*x+c)),x,6,-sec(d*x+c)*(b-a*sin(d*x+c))*sqrt(a+b*sin(d*x+c))/(a^2-b^2)/d-a*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/(a^2-b^2)/d/sqrt((a+b*sin(d*x+c))/(a+b))+InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/d/sqrt(a+b*sin(d*x+c)),1],
[sec(d*x+c)^4/sqrt(a+b*sin(d*x+c)),x,7,-1/3*sec(d*x+c)^3*(b-a*sin(d*x+c))*sqrt(a+b*sin(d*x+c))/(a^2-b^2)/d-2/3*a*(a^2-2*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/(a^2-b^2)^2/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/6*(4*a^2-5*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/(a^2-b^2)/d/sqrt(a+b*sin(d*x+c))-1/6*sec(d*x+c)*sqrt(a+b*sin(d*x+c))*(b*(a^2-5*b^2)-4*a*(a^2-2*b^2)*sin(d*x+c))/(a^2-b^2)^2/d,1],
[cos(d*x+c)^5/(a+b*sin(d*x+c))^(3/2),x,3,-2*(a^2-b^2)^2/b^5/d/sqrt(a+b*sin(d*x+c))-8*a*(a^2-b^2)*sqrt(a+b*sin(d*x+c))/b^5/d+4/3*(3*a^2-b^2)*(a+b*sin(d*x+c))^(3/2)/b^5/d-8/5*a*(a+b*sin(d*x+c))^(5/2)/b^5/d+2/7*(a+b*sin(d*x+c))^(7/2)/b^5/d,1],
[cos(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x,3,2*(a^2-b^2)/b^3/d/sqrt(a+b*sin(d*x+c))+4*a*sqrt(a+b*sin(d*x+c))/b^3/d-2/3*(a+b*sin(d*x+c))^(3/2)/b^3/d,1],
[cos(d*x+c)/(a+b*sin(d*x+c))^(3/2),x,2,-2/b/d/sqrt(a+b*sin(d*x+c)),1],
[sec(d*x+c)/(a+b*sin(d*x+c))^(3/2),x,6,-arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a-b))/(a-b)^(3/2)/d+arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a+b))/(a+b)^(3/2)/d+2*b/(a^2-b^2)/d/sqrt(a+b*sin(d*x+c)),1],
[sec(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x,7,-1/4*(2*a-5*b)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a-b))/(a-b)^(5/2)/d+1/4*(2*a+5*b)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a+b))/(a+b)^(5/2)/d-1/2*b*(a^2+5*b^2)/(a^2-b^2)^2/d/sqrt(a+b*sin(d*x+c))-1/2*sec(d*x+c)^2*(b-a*sin(d*x+c))/(a^2-b^2)/d/sqrt(a+b*sin(d*x+c)),1],
[sec(d*x+c)^5/(a+b*sin(d*x+c))^(3/2),x,8,-3/32*(4*a^2-14*a*b+15*b^2)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a-b))/(a-b)^(7/2)/d+3/32*(4*a^2+14*a*b+15*b^2)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a+b))/(a+b)^(7/2)/d-3/16*b*(2*a^4-7*a^2*b^2-15*b^4)/(a^2-b^2)^3/d/sqrt(a+b*sin(d*x+c))-1/4*sec(d*x+c)^4*(b-a*sin(d*x+c))/(a^2-b^2)/d/sqrt(a+b*sin(d*x+c))+1/16*sec(d*x+c)^2*(b*(a^2+9*b^2)+2*a*(3*a^2-8*b^2)*sin(d*x+c))/(a^2-b^2)^2/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^6/(a+b*sin(d*x+c))^(3/2),x,8,-2*cos(d*x+c)^5/b/d/sqrt(a+b*sin(d*x+c))+20/63*cos(d*x+c)^3*(8*a-7*b*sin(d*x+c))*sqrt(a+b*sin(d*x+c))/b^3/d-16/63*(32*a^4-57*a^2*b^2+21*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^6/d/sqrt((a+b*sin(d*x+c))/(a+b))+16/63*a*(32*a^4-65*a^2*b^2+33*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^6/d/sqrt(a+b*sin(d*x+c))-8/63*cos(d*x+c)*sqrt(a+b*sin(d*x+c))*(a*(32*a^2-33*b^2)-3*b*(8*a^2-7*b^2)*sin(d*x+c))/b^5/d,1],
[cos(d*x+c)^4/(a+b*sin(d*x+c))^(3/2),x,7,-2*cos(d*x+c)^3/b/d/sqrt(a+b*sin(d*x+c))+4/5*cos(d*x+c)*(4*a-3*b*sin(d*x+c))*sqrt(a+b*sin(d*x+c))/b^3/d+8/5*(4*a^2-3*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^4/d/sqrt((a+b*sin(d*x+c))/(a+b))-32/5*a*(a^2-b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^4/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2/(a+b*sin(d*x+c))^(3/2),x,6,-2*cos(d*x+c)/b/d/sqrt(a+b*sin(d*x+c))-4*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^2/d/sqrt((a+b*sin(d*x+c))/(a+b))+4*a*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^2/d/sqrt(a+b*sin(d*x+c)),1],
[sec(d*x+c)^2/(a+b*sin(d*x+c))^(3/2),x,7,2*b*sec(d*x+c)/(a^2-b^2)/d/sqrt(a+b*sin(d*x+c))-(a^2+3*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/(a^2-b^2)^2/d/sqrt((a+b*sin(d*x+c))/(a+b))+a*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/(a^2-b^2)/d/sqrt(a+b*sin(d*x+c))-sec(d*x+c)*sqrt(a+b*sin(d*x+c))*(4*a*b-(a^2+3*b^2)*sin(d*x+c))/(a^2-b^2)^2/d,1],
[sec(d*x+c)^4/(a+b*sin(d*x+c))^(3/2),x,8,2*b*sec(d*x+c)^3/(a^2-b^2)/d/sqrt(a+b*sin(d*x+c))-1/6*(4*a^4-15*a^2*b^2-21*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/(a^2-b^2)^3/d/sqrt((a+b*sin(d*x+c))/(a+b))+2/3*a*(a^2-3*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/(a^2-b^2)^2/d/sqrt(a+b*sin(d*x+c))-1/3*sec(d*x+c)^3*sqrt(a+b*sin(d*x+c))*(8*a*b-(a^2+7*b^2)*sin(d*x+c))/(a^2-b^2)^2/d-1/6*sec(d*x+c)*sqrt(a+b*sin(d*x+c))*(a*b*(a^2-33*b^2)-(4*a^4-15*a^2*b^2-21*b^4)*sin(d*x+c))/(a^2-b^2)^3/d,1],
[cos(d*x+c)^5/(a+b*sin(d*x+c))^(5/2),x,3,-2/3*(a^2-b^2)^2/b^5/d/(a+b*sin(d*x+c))^(3/2)+8*a*(a^2-b^2)/b^5/d/sqrt(a+b*sin(d*x+c))+4*(3*a^2-b^2)*sqrt(a+b*sin(d*x+c))/b^5/d-8/3*a*(a+b*sin(d*x+c))^(3/2)/b^5/d+2/5*(a+b*sin(d*x+c))^(5/2)/b^5/d,1],
[cos(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x,3,2/3*(a^2-b^2)/b^3/d/(a+b*sin(d*x+c))^(3/2)-4*a/b^3/d/sqrt(a+b*sin(d*x+c))-2*sqrt(a+b*sin(d*x+c))/b^3/d,1],
[cos(d*x+c)/(a+b*sin(d*x+c))^(5/2),x,2,-2/3/b/d/(a+b*sin(d*x+c))^(3/2),1],
[sec(d*x+c)/(a+b*sin(d*x+c))^(5/2),x,7,-arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a-b))/(a-b)^(5/2)/d+arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a+b))/(a+b)^(5/2)/d+2/3*b/(a^2-b^2)/d/(a+b*sin(d*x+c))^(3/2)+4*a*b/(a^2-b^2)^2/d/sqrt(a+b*sin(d*x+c)),1],
[sec(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x,8,-1/4*(2*a-7*b)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a-b))/(a-b)^(7/2)/d+1/4*(2*a+7*b)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a+b))/(a+b)^(7/2)/d-1/6*b*(3*a^2+7*b^2)/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^(3/2)-1/2*sec(d*x+c)^2*(b-a*sin(d*x+c))/(a^2-b^2)/d/(a+b*sin(d*x+c))^(3/2)-1/2*a*b*(a^2+19*b^2)/(a^2-b^2)^3/d/sqrt(a+b*sin(d*x+c)),1],
[sec(d*x+c)^5/(a+b*sin(d*x+c))^(5/2),x,9,-1/32*(12*a^2-54*a*b+77*b^2)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a-b))/(a-b)^(9/2)/d+1/32*(12*a^2+54*a*b+77*b^2)*arctanh(sqrt(a+b*sin(d*x+c))/sqrt(a+b))/(a+b)^(9/2)/d-1/48*b*(18*a^4-81*a^2*b^2-77*b^4)/(a^2-b^2)^3/d/(a+b*sin(d*x+c))^(3/2)-1/4*sec(d*x+c)^4*(b-a*sin(d*x+c))/(a^2-b^2)/d/(a+b*sin(d*x+c))^(3/2)-1/8*a*b*(3*a^4-16*a^2*b^2-127*b^4)/(a^2-b^2)^4/d/sqrt(a+b*sin(d*x+c))+1/16*sec(d*x+c)^2*(b*(3*a^2+11*b^2)+2*a*(3*a^2-10*b^2)*sin(d*x+c))/(a^2-b^2)^2/d/(a+b*sin(d*x+c))^(3/2),1],
[cos(d*x+c)^8/(a+b*sin(d*x+c))^(5/2),x,9,-2/3*cos(d*x+c)^7/b/d/(a+b*sin(d*x+c))^(3/2)-128/99*a*(8*a^2-9*b^2)*(4*a^2-3*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^8/d/sqrt((a+b*sin(d*x+c))/(a+b))+32/99*(128*a^6-272*a^4*b^2+159*a^2*b^4-15*b^6)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^8/d/sqrt(a+b*sin(d*x+c))-28/33*cos(d*x+c)^5*(12*a+b*sin(d*x+c))/b^3/d/sqrt(a+b*sin(d*x+c))+40/99*cos(d*x+c)^3*sqrt(a+b*sin(d*x+c))*(32*a^2-3*b^2-28*a*b*sin(d*x+c))/b^5/d-16/99*cos(d*x+c)*sqrt(a+b*sin(d*x+c))*(128*a^4-144*a^2*b^2+15*b^4-3*a*b*(32*a^2-31*b^2)*sin(d*x+c))/b^7/d,1],
[cos(d*x+c)^6/(a+b*sin(d*x+c))^(5/2),x,8,-2/3*cos(d*x+c)^5/b/d/(a+b*sin(d*x+c))^(3/2)+16/21*a*(32*a^2-29*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^6/d/sqrt((a+b*sin(d*x+c))/(a+b))-16/21*(32*a^4-37*a^2*b^2+5*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^6/d/sqrt(a+b*sin(d*x+c))-20/21*cos(d*x+c)^3*(8*a+b*sin(d*x+c))/b^3/d/sqrt(a+b*sin(d*x+c))+8/21*cos(d*x+c)*sqrt(a+b*sin(d*x+c))*(32*a^2-5*b^2-24*a*b*sin(d*x+c))/b^5/d,1],
[cos(d*x+c)^4/(a+b*sin(d*x+c))^(5/2),x,7,-2/3*cos(d*x+c)^3/b/d/(a+b*sin(d*x+c))^(3/2)-32/3*a*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^4/d/sqrt((a+b*sin(d*x+c))/(a+b))+8/3*(4*a^2-b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^4/d/sqrt(a+b*sin(d*x+c))-4/3*cos(d*x+c)*(4*a+b*sin(d*x+c))/b^3/d/sqrt(a+b*sin(d*x+c)),1],
[cos(d*x+c)^2/(a+b*sin(d*x+c))^(5/2),x,7,-2/3*cos(d*x+c)/b/d/(a+b*sin(d*x+c))^(3/2)+4/3*a*cos(d*x+c)/b/(a^2-b^2)/d/sqrt(a+b*sin(d*x+c))+4/3*a*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/b^2/(a^2-b^2)/d/sqrt((a+b*sin(d*x+c))/(a+b))-4/3*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/b^2/d/sqrt(a+b*sin(d*x+c)),1],
[sec(d*x+c)^2/(a+b*sin(d*x+c))^(5/2),x,8,2/3*b*sec(d*x+c)/(a^2-b^2)/d/(a+b*sin(d*x+c))^(3/2)+16/3*a*b*sec(d*x+c)/(a^2-b^2)^2/d/sqrt(a+b*sin(d*x+c))-1/3*a*(3*a^2+29*b^2)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/(a^2-b^2)^3/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/3*(3*a^2+5*b^2)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/(a^2-b^2)^2/d/sqrt(a+b*sin(d*x+c))-1/3*sec(d*x+c)*sqrt(a+b*sin(d*x+c))*(b*(27*a^2+5*b^2)-a*(3*a^2+29*b^2)*sin(d*x+c))/(a^2-b^2)^3/d,1],
[sec(d*x+c)^4/(a+b*sin(d*x+c))^(5/2),x,9,2/3*b*sec(d*x+c)^3/(a^2-b^2)/d/(a+b*sin(d*x+c))^(3/2)+8*a*b*sec(d*x+c)^3/(a^2-b^2)^2/d/sqrt(a+b*sin(d*x+c))-2/3*a*(a^4-6*a^2*b^2-27*b^4)*EllipticE(sin(1/2*c-1/4*Pi+1/2*d*x),sqrt(2*b/(a+b)))*sqrt(a+b*sin(d*x+c))/(a^2-b^2)^4/d/sqrt((a+b*sin(d*x+c))/(a+b))+1/6*(4*a^4-21*a^2*b^2-15*b^4)*InverseJacobiAM(1/2*c-1/4*Pi+1/2*d*x,sqrt(2*b/(a+b)))*sqrt((a+b*sin(d*x+c))/(a+b))/(a^2-b^2)^3/d/sqrt(a+b*sin(d*x+c))-1/3*sec(d*x+c)^3*sqrt(a+b*sin(d*x+c))*(b*(29*a^2+3*b^2)-a*(a^2+31*b^2)*sin(d*x+c))/(a^2-b^2)^3/d-1/6*sec(d*x+c)*sqrt(a+b*sin(d*x+c))*(b*(a^4-114*a^2*b^2-15*b^4)-4*a*(a^4-6*a^2*b^2-27*b^4)*sin(d*x+c))/(a^2-b^2)^4/d,1],
[(e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c)),x,5,-2/9*b*(e*cos(d*x+c))^(9/2)/d/e+10/21*a*e^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))+10/21*a*e^3*sqrt(e*cos(d*x+c))*sin(d*x+c)/d+2/7*a*e*(e*cos(d*x+c))^(5/2)*sin(d*x+c)/d,1],
[(e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c)),x,4,-2/7*b*(e*cos(d*x+c))^(7/2)/d/e+6/5*a*e^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/sqrt(cos(d*x+c))+2/5*a*e*(e*cos(d*x+c))^(3/2)*sin(d*x+c)/d,1],
[(e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c)),x,4,-2/5*b*(e*cos(d*x+c))^(5/2)/d/e+2/3*a*e^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))+2/3*a*e*sqrt(e*cos(d*x+c))*sin(d*x+c)/d,1],
[sqrt(e*cos(d*x+c))*(a+b*sin(d*x+c)),x,3,-2/3*b*(e*cos(d*x+c))^(3/2)/d/e+2*a*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/sqrt(cos(d*x+c)),1],
[(a+b*sin(d*x+c))/sqrt(e*cos(d*x+c)),x,3,-2*b*sqrt(e*cos(d*x+c))/d/e+2*a*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c)),1],
[(a+b*sin(d*x+c))/(e*cos(d*x+c))^(3/2),x,4,2*b/d/e/sqrt(e*cos(d*x+c))-2*a*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^2/sqrt(cos(d*x+c))+2*a*sin(d*x+c)/d/e/sqrt(e*cos(d*x+c)),1],
[(a+b*sin(d*x+c))/(e*cos(d*x+c))^(5/2),x,4,2/3*b/d/e/(e*cos(d*x+c))^(3/2)+2/3*a*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/e^2/sqrt(e*cos(d*x+c))+2/3*a*sin(d*x+c)/d/e/(e*cos(d*x+c))^(3/2),1],
[(a+b*sin(d*x+c))/(e*cos(d*x+c))^(7/2),x,5,2/5*b/d/e/(e*cos(d*x+c))^(5/2)-6/5*a*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^4/sqrt(cos(d*x+c))+2/5*a*sin(d*x+c)/d/e/(e*cos(d*x+c))^(5/2)+6/5*a*sin(d*x+c)/d/e^3/sqrt(e*cos(d*x+c)),1],
[(e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))^2,x,6,-26/99*a*b*(e*cos(d*x+c))^(9/2)/d/e+10/231*(11*a^2+2*b^2)*e^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))+10/231*(11*a^2+2*b^2)*e^3*sqrt(e*cos(d*x+c))*sin(d*x+c)/d+2/77*(11*a^2+2*b^2)*e*(e*cos(d*x+c))^(5/2)*sin(d*x+c)/d-2/11*b*(e*cos(d*x+c))^(9/2)*(a+b*sin(d*x+c))/d/e,1],
[(e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^2,x,5,-22/63*a*b*(e*cos(d*x+c))^(7/2)/d/e+2/15*(9*a^2+2*b^2)*e^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/sqrt(cos(d*x+c))+2/45*(9*a^2+2*b^2)*e*(e*cos(d*x+c))^(3/2)*sin(d*x+c)/d-2/9*b*(e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))/d/e,1],
[(e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^2,x,5,-18/35*a*b*(e*cos(d*x+c))^(5/2)/d/e+2/21*(7*a^2+2*b^2)*e^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))+2/21*(7*a^2+2*b^2)*e*sqrt(e*cos(d*x+c))*sin(d*x+c)/d-2/7*b*(e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))/d/e,1],
[sqrt(e*cos(d*x+c))*(a+b*sin(d*x+c))^2,x,4,-14/15*a*b*(e*cos(d*x+c))^(3/2)/d/e+2/5*(5*a^2+2*b^2)*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/sqrt(cos(d*x+c))-2/5*b*(e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))/d/e,1],
[(a+b*sin(d*x+c))^2/sqrt(e*cos(d*x+c)),x,4,-10/3*a*b*sqrt(e*cos(d*x+c))/d/e+2/3*(3*a^2+2*b^2)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))-2/3*b*sqrt(e*cos(d*x+c))*(a+b*sin(d*x+c))/d/e,1],
[(a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(3/2),x,4,2*a*b*(e*cos(d*x+c))^(3/2)/d/e^3-2*(a^2+2*b^2)*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^2/sqrt(cos(d*x+c))+2*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))/d/e/sqrt(e*cos(d*x+c)),1],
[(a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(5/2),x,4,2/3*a*b*sqrt(e*cos(d*x+c))/d/e^3+2/3*(a^2-2*b^2)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/e^2/sqrt(e*cos(d*x+c))+2/3*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))/d/e/(e*cos(d*x+c))^(3/2),1],
[(a+b*sin(d*x+c))^2/(e*cos(d*x+c))^(7/2),x,5,2/5*a*b/d/e^3/sqrt(e*cos(d*x+c))-2/5*(3*a^2-2*b^2)*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^4/sqrt(cos(d*x+c))+2/5*(3*a^2-2*b^2)*sin(d*x+c)/d/e^3/sqrt(e*cos(d*x+c))+2/5*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))/d/e/(e*cos(d*x+c))^(5/2),1],
[(e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))^3,x,7,-2/1287*b*(177*a^2+44*b^2)*(e*cos(d*x+c))^(9/2)/d/e+10/231*a*(11*a^2+6*b^2)*e^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))+10/231*a*(11*a^2+6*b^2)*e^3*sqrt(e*cos(d*x+c))*sin(d*x+c)/d+2/77*a*(11*a^2+6*b^2)*e*(e*cos(d*x+c))^(5/2)*sin(d*x+c)/d-34/143*a*b*(e*cos(d*x+c))^(9/2)*(a+b*sin(d*x+c))/d/e-2/13*b*(e*cos(d*x+c))^(9/2)*(a+b*sin(d*x+c))^2/d/e,1],
[(e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^3,x,6,-2/231*b*(43*a^2+12*b^2)*(e*cos(d*x+c))^(7/2)/d/e+2/5*a*(3*a^2+2*b^2)*e^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/sqrt(cos(d*x+c))+2/15*a*(3*a^2+2*b^2)*e*(e*cos(d*x+c))^(3/2)*sin(d*x+c)/d-10/33*a*b*(e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))/d/e-2/11*b*(e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))^2/d/e,1],
[(e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^3,x,6,-2/315*b*(89*a^2+28*b^2)*(e*cos(d*x+c))^(5/2)/d/e+2/21*a*(7*a^2+6*b^2)*e^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))+2/21*a*(7*a^2+6*b^2)*e*sqrt(e*cos(d*x+c))*sin(d*x+c)/d-26/63*a*b*(e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))/d/e-2/9*b*(e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^2/d/e,1],
[sqrt(e*cos(d*x+c))*(a+b*sin(d*x+c))^3,x,5,-2/105*b*(57*a^2+20*b^2)*(e*cos(d*x+c))^(3/2)/d/e+2/5*a*(5*a^2+6*b^2)*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/sqrt(cos(d*x+c))-22/35*a*b*(e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))/d/e-2/7*b*(e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^2/d/e,1],
[(a+b*sin(d*x+c))^3/sqrt(e*cos(d*x+c)),x,5,-2/5*b*(11*a^2+4*b^2)*sqrt(e*cos(d*x+c))/d/e+2*a*(a^2+2*b^2)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))-6/5*a*b*sqrt(e*cos(d*x+c))*(a+b*sin(d*x+c))/d/e-2/5*b*sqrt(e*cos(d*x+c))*(a+b*sin(d*x+c))^2/d/e,1],
[(a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(3/2),x,5,2/3*b*(3*a^2+4*b^2)*(e*cos(d*x+c))^(3/2)/d/e^3-2*a*(a^2+6*b^2)*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^2/sqrt(cos(d*x+c))+2*a*b*(e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))/d/e^3+2*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^2/d/e/sqrt(e*cos(d*x+c)),1],
[(a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(5/2),x,5,2/3*b*(a^2+4*b^2)*sqrt(e*cos(d*x+c))/d/e^3+2/3*a*(a^2-6*b^2)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/e^2/sqrt(e*cos(d*x+c))+2/3*a*b*sqrt(e*cos(d*x+c))*(a+b*sin(d*x+c))/d/e^3+2/3*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^2/d/e/(e*cos(d*x+c))^(3/2),1],
[(a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(7/2),x,5,2/5*b*(3*a^2-4*b^2)*(e*cos(d*x+c))^(3/2)/d/e^5-6/5*a*(a^2-2*b^2)*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^4/sqrt(cos(d*x+c))+2/5*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^2/d/e/(e*cos(d*x+c))^(5/2)-2/5*(a+b*sin(d*x+c))*(a*b-(3*a^2-4*b^2)*sin(d*x+c))/d/e^3/sqrt(e*cos(d*x+c)),1],
[(a+b*sin(d*x+c))^3/(e*cos(d*x+c))^(9/2),x,5,2/21*b*(5*a^2-4*b^2)*sqrt(e*cos(d*x+c))/d/e^5+2/21*a*(5*a^2-6*b^2)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/e^4/sqrt(e*cos(d*x+c))+2/7*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^2/d/e/(e*cos(d*x+c))^(7/2)+2/21*(a+b*sin(d*x+c))*(a*b+(5*a^2-4*b^2)*sin(d*x+c))/d/e^3/(e*cos(d*x+c))^(3/2),1],
[(e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))^4,x,8,-34/6435*a*b*(53*a^2+38*b^2)*(e*cos(d*x+c))^(9/2)/d/e+2/231*(55*a^4+60*a^2*b^2+4*b^4)*e^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))+2/231*(55*a^4+60*a^2*b^2+4*b^4)*e^3*sqrt(e*cos(d*x+c))*sin(d*x+c)/d+2/385*(55*a^4+60*a^2*b^2+4*b^4)*e*(e*cos(d*x+c))^(5/2)*sin(d*x+c)/d-2/715*b*(93*a^2+26*b^2)*(e*cos(d*x+c))^(9/2)*(a+b*sin(d*x+c))/d/e-14/65*a*b*(e*cos(d*x+c))^(9/2)*(a+b*sin(d*x+c))^2/d/e-2/15*b*(e*cos(d*x+c))^(9/2)*(a+b*sin(d*x+c))^3/d/e,1],
[(e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^4,x,7,-10/3003*a*b*(115*a^2+94*b^2)*(e*cos(d*x+c))^(7/2)/d/e+2/65*(39*a^4+52*a^2*b^2+4*b^4)*e^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/sqrt(cos(d*x+c))+2/195*(39*a^4+52*a^2*b^2+4*b^4)*e*(e*cos(d*x+c))^(3/2)*sin(d*x+c)/d-2/429*b*(73*a^2+22*b^2)*(e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))/d/e-38/143*a*b*(e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))^2/d/e-2/13*b*(e*cos(d*x+c))^(7/2)*(a+b*sin(d*x+c))^3/d/e,1],
[(e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^4,x,7,-26/3465*a*b*(79*a^2+74*b^2)*(e*cos(d*x+c))^(5/2)/d/e+2/231*(77*a^4+132*a^2*b^2+12*b^4)*e^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))+2/231*(77*a^4+132*a^2*b^2+12*b^4)*e*sqrt(e*cos(d*x+c))*sin(d*x+c)/d-2/693*b*(167*a^2+54*b^2)*(e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))/d/e-34/99*a*b*(e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^2/d/e-2/11*b*(e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^3/d/e,1],
[sqrt(e*cos(d*x+c))*(a+b*sin(d*x+c))^4,x,6,-22/315*a*b*(17*a^2+18*b^2)*(e*cos(d*x+c))^(3/2)/d/e+2/15*(15*a^4+36*a^2*b^2+4*b^4)*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/sqrt(cos(d*x+c))-2/105*b*(41*a^2+14*b^2)*(e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))/d/e-10/21*a*b*(e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^2/d/e-2/9*b*(e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^3/d/e,1],
[(a+b*sin(d*x+c))^4/sqrt(e*cos(d*x+c)),x,6,-6/35*a*b*(31*a^2+34*b^2)*sqrt(e*cos(d*x+c))/d/e+2/7*(7*a^4+28*a^2*b^2+4*b^4)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/sqrt(e*cos(d*x+c))-2/35*b*(29*a^2+10*b^2)*sqrt(e*cos(d*x+c))*(a+b*sin(d*x+c))/d/e-26/35*a*b*sqrt(e*cos(d*x+c))*(a+b*sin(d*x+c))^2/d/e-2/7*b*sqrt(e*cos(d*x+c))*(a+b*sin(d*x+c))^3/d/e,1],
[(a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(3/2),x,6,2/15*a*b*(15*a^2+62*b^2)*(e*cos(d*x+c))^(3/2)/d/e^3-2/5*(5*a^4+60*a^2*b^2+12*b^4)*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^2/sqrt(cos(d*x+c))+2/5*b*(5*a^2+6*b^2)*(e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))/d/e^3+2*a*b*(e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^2/d/e^3+2*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^3/d/e/sqrt(e*cos(d*x+c)),1],
[(a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(5/2),x,6,2/3*a*b*(a^2+14*b^2)*sqrt(e*cos(d*x+c))/d/e^3+2/3*(a^4-12*a^2*b^2-4*b^4)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/e^2/sqrt(e*cos(d*x+c))+2/3*b*(a^2+2*b^2)*sqrt(e*cos(d*x+c))*(a+b*sin(d*x+c))/d/e^3+2/3*a*b*sqrt(e*cos(d*x+c))*(a+b*sin(d*x+c))^2/d/e^3+2/3*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^3/d/e/(e*cos(d*x+c))^(3/2),1],
[(a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(7/2),x,6,2/5*a*b*(3*a^2-10*b^2)*(e*cos(d*x+c))^(3/2)/d/e^5-6/5*(a^4-4*a^2*b^2-4*b^4)*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^4/sqrt(cos(d*x+c))+6/5*b*(a^2-2*b^2)*(e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))/d/e^5+2/5*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^3/d/e/(e*cos(d*x+c))^(5/2)-6/5*(a+b*sin(d*x+c))^2*(a*b-(a^2-2*b^2)*sin(d*x+c))/d/e^3/sqrt(e*cos(d*x+c)),1],
[(a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(9/2),x,6,10/21*a*b*(a^2-2*b^2)*sqrt(e*cos(d*x+c))/d/e^5+2/21*(5*a^4-12*a^2*b^2+12*b^4)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/d/e^4/sqrt(e*cos(d*x+c))+2/21*b*(5*a^2-6*b^2)*sqrt(e*cos(d*x+c))*(a+b*sin(d*x+c))/d/e^5+2/7*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^3/d/e/(e*cos(d*x+c))^(7/2)-2/21*(a+b*sin(d*x+c))^2*(a*b-(5*a^2-6*b^2)*sin(d*x+c))/d/e^3/(e*cos(d*x+c))^(3/2),1],
[(a+b*sin(d*x+c))^4/(e*cos(d*x+c))^(11/2),x,6,2/45*a*b*(21*a^2-22*b^2)*(e*cos(d*x+c))^(3/2)/d/e^7-2/15*(7*a^4-12*a^2*b^2+4*b^4)*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/d/e^6/sqrt(cos(d*x+c))+2/9*(b+a*sin(d*x+c))*(a+b*sin(d*x+c))^3/d/e/(e*cos(d*x+c))^(9/2)-2/45*(a+b*sin(d*x+c))*(b*(7*a^2-6*b^2)-a*(21*a^2-22*b^2)*sin(d*x+c))/d/e^5/sqrt(e*cos(d*x+c))+2/45*(a+b*sin(d*x+c))^2*(a*b+(7*a^2-6*b^2)*sin(d*x+c))/d/e^3/(e*cos(d*x+c))^(5/2),1],
[(e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c)),x,15,-(-a^2+b^2)^(9/4)*e^(11/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(11/2)/d-(-a^2+b^2)^(9/4)*e^(11/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(11/2)/d+2/9*e*(e*cos(d*x+c))^(9/2)/b/d+2/21*a*(21*a^4-49*a^2*b^2+33*b^4)*e^6*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^6/d/sqrt(e*cos(d*x+c))-a*(a^2-b^2)^3*e^6*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^6/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))-a*(a^2-b^2)^3*e^6*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^6/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))-2/35*e^3*(e*cos(d*x+c))^(5/2)*(7*a^2-7*b^2-5*a*b*sin(d*x+c))/b^3/d+2/21*e^5*sqrt(e*cos(d*x+c))*(21*(a^2-b^2)^2-a*b*(7*a^2-12*b^2)*sin(d*x+c))/b^5/d,1],
[(e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c)),x,14,(-a^2+b^2)^(7/4)*e^(9/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(9/2)/d-(-a^2+b^2)^(7/4)*e^(9/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(9/2)/d+2/7*e*(e*cos(d*x+c))^(7/2)/b/d-2/5*a*(5*a^2-8*b^2)*e^4*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^4/d/sqrt(cos(d*x+c))+a*(a^2-b^2)^2*e^5*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^5/(b-sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))+a*(a^2-b^2)^2*e^5*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^5/(b+sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))-2/15*e^3*(e*cos(d*x+c))^(3/2)*(5*a^2-5*b^2-3*a*b*sin(d*x+c))/b^3/d,1],
[(e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c)),x,14,-(-a^2+b^2)^(5/4)*e^(7/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(7/2)/d-(-a^2+b^2)^(5/4)*e^(7/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(7/2)/d+2/5*e*(e*cos(d*x+c))^(5/2)/b/d-2/3*a*(3*a^2-4*b^2)*e^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^4/d/sqrt(e*cos(d*x+c))+a*(a^2-b^2)^2*e^4*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^4/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))+a*(a^2-b^2)^2*e^4*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^4/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))-2/3*e^3*sqrt(e*cos(d*x+c))*(3*a^2-3*b^2-a*b*sin(d*x+c))/b^3/d,1],
[(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c)),x,13,(-a^2+b^2)^(3/4)*e^(5/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(5/2)/d-(-a^2+b^2)^(3/4)*e^(5/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(5/2)/d+2/3*e*(e*cos(d*x+c))^(3/2)/b/d+2*a*e^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^2/d/sqrt(cos(d*x+c))-a*(a^2-b^2)*e^3*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^3/(b-sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))-a*(a^2-b^2)*e^3*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^3/(b+sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c)),1],
[(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c)),x,13,-(-a^2+b^2)^(1/4)*e^(3/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(3/2)/d-(-a^2+b^2)^(1/4)*e^(3/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(3/2)/d+2*e*sqrt(e*cos(d*x+c))/b/d+2*a*e^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^2/d/sqrt(e*cos(d*x+c))-a*(a^2-b^2)*e^2*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^2/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))-a*(a^2-b^2)*e^2*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^2/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c)),1],
[sqrt(e*cos(d*x+c))/(a+b*sin(d*x+c)),x,9,sqrt(e)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/sqrt(b)/(-a^2+b^2)^(1/4)/d-sqrt(e)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/sqrt(b)/(-a^2+b^2)^(1/4)/d+a*e*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b/(b-sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))+a*e*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b/(b+sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c)),1],
[1/sqrt(e*cos(d*x+c))/(a+b*sin(d*x+c)),x,9,-sqrt(b)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(3/4)/d/sqrt(e)-sqrt(b)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(3/4)/d/sqrt(e)+a*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))+a*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c)),1],
[1/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c)),x,13,b^(3/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(5/4)/d/e^(3/2)-b^(3/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(5/4)/d/e^(3/2)-2*a*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/(a^2-b^2)/d/e^2/sqrt(cos(d*x+c))-a*b*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)/(b-sqrt(-a^2+b^2))/d/e/sqrt(e*cos(d*x+c))-a*b*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)/(b+sqrt(-a^2+b^2))/d/e/sqrt(e*cos(d*x+c))-2*(b-a*sin(d*x+c))/(a^2-b^2)/d/e/sqrt(e*cos(d*x+c)),1],
[1/(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c)),x,13,-b^(5/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(7/4)/d/e^(5/2)-b^(5/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(7/4)/d/e^(5/2)+2/3*a*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/(a^2-b^2)/d/e^2/sqrt(e*cos(d*x+c))-a*b^2*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)/(a^2-b*(b-sqrt(-a^2+b^2)))/d/e^2/sqrt(e*cos(d*x+c))-a*b^2*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)/(a^2-b*(b+sqrt(-a^2+b^2)))/d/e^2/sqrt(e*cos(d*x+c))-2/3*(b-a*sin(d*x+c))/(a^2-b^2)/d/e/(e*cos(d*x+c))^(3/2),1],
[1/(e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c)),x,14,b^(7/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(9/4)/d/e^(7/2)-b^(7/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(9/4)/d/e^(7/2)-2/5*a*(3*a^2-8*b^2)*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/(a^2-b^2)^2/d/e^4/sqrt(cos(d*x+c))+a*b^3*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^2/(b-sqrt(-a^2+b^2))/d/e^3/sqrt(e*cos(d*x+c))+a*b^3*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^2/(b+sqrt(-a^2+b^2))/d/e^3/sqrt(e*cos(d*x+c))-2/5*(b-a*sin(d*x+c))/(a^2-b^2)/d/e/(e*cos(d*x+c))^(5/2)+2/5*(5*b^3+a*(3*a^2-8*b^2)*sin(d*x+c))/(a^2-b^2)^2/d/e^3/sqrt(e*cos(d*x+c)),1],
[(e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c))^2,x,15,-9/2*a*(-a^2+b^2)^(5/4)*e^(11/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(11/2)/d-9/2*a*(-a^2+b^2)^(5/4)*e^(11/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(11/2)/d-3/7*(21*a^4-28*a^2*b^2+5*b^4)*e^6*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^6/d/sqrt(e*cos(d*x+c))+9/2*a^2*(a^2-b^2)^2*e^6*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^6/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))+9/2*a^2*(a^2-b^2)^2*e^6*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^6/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))+9/35*e^3*(e*cos(d*x+c))^(5/2)*(7*a-5*b*sin(d*x+c))/b^3/d-e*(e*cos(d*x+c))^(9/2)/b/d/(a+b*sin(d*x+c))-3/7*e^5*sqrt(e*cos(d*x+c))*(21*a*(a^2-b^2)-b*(7*a^2-5*b^2)*sin(d*x+c))/b^5/d,1],
[(e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c))^2,x,14,7/2*a*(-a^2+b^2)^(3/4)*e^(9/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(9/2)/d-7/2*a*(-a^2+b^2)^(3/4)*e^(9/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(9/2)/d+7/5*(5*a^2-3*b^2)*e^4*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^4/d/sqrt(cos(d*x+c))-7/2*a^2*(a^2-b^2)*e^5*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^5/(b-sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))-7/2*a^2*(a^2-b^2)*e^5*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^5/(b+sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))+7/15*e^3*(e*cos(d*x+c))^(3/2)*(5*a-3*b*sin(d*x+c))/b^3/d-e*(e*cos(d*x+c))^(7/2)/b/d/(a+b*sin(d*x+c)),1],
[(e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^2,x,14,-5/2*a*(-a^2+b^2)^(1/4)*e^(7/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(7/2)/d-5/2*a*(-a^2+b^2)^(1/4)*e^(7/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(7/2)/d+5/3*(3*a^2-b^2)*e^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^4/d/sqrt(e*cos(d*x+c))-5/2*a^2*(a^2-b^2)*e^4*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^4/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))-5/2*a^2*(a^2-b^2)*e^4*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^4/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))+5/3*e^3*sqrt(e*cos(d*x+c))*(3*a-b*sin(d*x+c))/b^3/d-e*(e*cos(d*x+c))^(5/2)/b/d/(a+b*sin(d*x+c)),1],
[(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^2,x,13,3/2*a*e^(5/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(5/2)/(-a^2+b^2)^(1/4)/d-3/2*a*e^(5/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(5/2)/(-a^2+b^2)^(1/4)/d-3*e^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^2/d/sqrt(cos(d*x+c))+3/2*a^2*e^3*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^3/(b-sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))+3/2*a^2*e^3*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^3/(b+sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))-e*(e*cos(d*x+c))^(3/2)/b/d/(a+b*sin(d*x+c)),1],
[(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^2,x,13,-1/2*a*e^(3/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(3/2)/(-a^2+b^2)^(3/4)/d-1/2*a*e^(3/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(3/2)/(-a^2+b^2)^(3/4)/d-e^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^2/d/sqrt(e*cos(d*x+c))+1/2*a^2*e^2*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^2/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))+1/2*a^2*e^2*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^2/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))-e*sqrt(e*cos(d*x+c))/b/d/(a+b*sin(d*x+c)),1],
[sqrt(e*cos(d*x+c))/(a+b*sin(d*x+c))^2,x,13,-1/2*a*sqrt(e)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/sqrt(b)/(-a^2+b^2)^(5/4)/d+1/2*a*sqrt(e)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/sqrt(b)/(-a^2+b^2)^(5/4)/d+sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/(a^2-b^2)/d/sqrt(cos(d*x+c))+1/2*a^2*e*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b/(a^2-b^2)/(b-sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))+1/2*a^2*e*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b/(a^2-b^2)/(b+sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))+b*(e*cos(d*x+c))^(3/2)/(a^2-b^2)/d/e/(a+b*sin(d*x+c)),1],
[1/sqrt(e*cos(d*x+c))/(a+b*sin(d*x+c))^2,x,13,3/2*a*sqrt(b)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(7/4)/d/sqrt(e)+3/2*a*sqrt(b)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(7/4)/d/sqrt(e)-sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/(a^2-b^2)/d/sqrt(e*cos(d*x+c))+3/2*a^2*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))+3/2*a^2*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))+b*sqrt(e*cos(d*x+c))/(a^2-b^2)/d/e/(a+b*sin(d*x+c)),1],
[1/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^2,x,14,-5/2*a*b^(3/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(9/4)/d/e^(3/2)+5/2*a*b^(3/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(9/4)/d/e^(3/2)-(2*a^2+3*b^2)*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/(a^2-b^2)^2/d/e^2/sqrt(cos(d*x+c))-5/2*a^2*b*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^2/(b-sqrt(-a^2+b^2))/d/e/sqrt(e*cos(d*x+c))-5/2*a^2*b*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^2/(b+sqrt(-a^2+b^2))/d/e/sqrt(e*cos(d*x+c))+b/(a^2-b^2)/d/e/sqrt(e*cos(d*x+c))/(a+b*sin(d*x+c))-(5*a*b-(2*a^2+3*b^2)*sin(d*x+c))/(a^2-b^2)^2/d/e/sqrt(e*cos(d*x+c)),1],
[1/(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^2,x,14,7/2*a*b^(5/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(11/4)/d/e^(5/2)+7/2*a*b^(5/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(11/4)/d/e^(5/2)+1/3*(2*a^2+5*b^2)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/(a^2-b^2)^2/d/e^2/sqrt(e*cos(d*x+c))-7/2*a^2*b^2*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^2/(a^2-b*(b-sqrt(-a^2+b^2)))/d/e^2/sqrt(e*cos(d*x+c))-7/2*a^2*b^2*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^2/(a^2-b*(b+sqrt(-a^2+b^2)))/d/e^2/sqrt(e*cos(d*x+c))+b/(a^2-b^2)/d/e/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))-1/3*(7*a*b-(2*a^2+5*b^2)*sin(d*x+c))/(a^2-b^2)^2/d/e/(e*cos(d*x+c))^(3/2),1],
[1/(e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^2,x,15,-9/2*a*b^(7/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(13/4)/d/e^(7/2)+9/2*a*b^(7/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(13/4)/d/e^(7/2)-3/5*(2*a^4-10*a^2*b^2-7*b^4)*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/(a^2-b^2)^3/d/e^4/sqrt(cos(d*x+c))+9/2*a^2*b^3*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^3/(b-sqrt(-a^2+b^2))/d/e^3/sqrt(e*cos(d*x+c))+9/2*a^2*b^3*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^3/(b+sqrt(-a^2+b^2))/d/e^3/sqrt(e*cos(d*x+c))+b/(a^2-b^2)/d/e/(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))-1/5*(9*a*b-(2*a^2+7*b^2)*sin(d*x+c))/(a^2-b^2)^2/d/e/(e*cos(d*x+c))^(5/2)+3/5*(15*a*b^3+(2*a^4-10*a^2*b^2-7*b^4)*sin(d*x+c))/(a^2-b^2)^3/d/e^3/sqrt(e*cos(d*x+c)),1],
[(e*cos(d*x+c))^(13/2)/(a+b*sin(d*x+c))^3,x,15,-11/8*(9*a^4-11*a^2*b^2+2*b^4)*e^(13/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(13/2)/(-a^2+b^2)^(1/4)/d+11/8*(9*a^4-11*a^2*b^2+2*b^4)*e^(13/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(13/2)/(-a^2+b^2)^(1/4)/d+11/20*a*(45*a^2-37*b^2)*e^6*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^6/d/sqrt(cos(d*x+c))-11/8*a*(9*a^4-11*a^2*b^2+2*b^4)*e^7*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^7/(b-sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))-11/8*a*(9*a^4-11*a^2*b^2+2*b^4)*e^7*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^7/(b+sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))-1/2*e*(e*cos(d*x+c))^(11/2)/b/d/(a+b*sin(d*x+c))^2-11/28*e^3*(e*cos(d*x+c))^(7/2)*(9*a+2*b*sin(d*x+c))/b^3/d/(a+b*sin(d*x+c))+11/60*e^5*(e*cos(d*x+c))^(3/2)*(45*a^2-10*b^2-27*a*b*sin(d*x+c))/b^5/d,1],
[(e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c))^3,x,15,9/8*(7*a^4-9*a^2*b^2+2*b^4)*e^(11/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(11/2)/(-a^2+b^2)^(3/4)/d+9/8*(7*a^4-9*a^2*b^2+2*b^4)*e^(11/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(11/2)/(-a^2+b^2)^(3/4)/d+3/4*a*(21*a^2-13*b^2)*e^6*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^6/d/sqrt(e*cos(d*x+c))-9/8*a*(7*a^4-9*a^2*b^2+2*b^4)*e^6*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^6/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))-9/8*a*(7*a^4-9*a^2*b^2+2*b^4)*e^6*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^6/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))-1/2*e*(e*cos(d*x+c))^(9/2)/b/d/(a+b*sin(d*x+c))^2-9/20*e^3*(e*cos(d*x+c))^(5/2)*(7*a+2*b*sin(d*x+c))/b^3/d/(a+b*sin(d*x+c))+3/4*e^5*sqrt(e*cos(d*x+c))*(21*a^2-6*b^2-7*a*b*sin(d*x+c))/b^5/d,1],
[(e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c))^3,x,14,7/8*(5*a^2-2*b^2)*e^(9/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(9/2)/(-a^2+b^2)^(1/4)/d-7/8*(5*a^2-2*b^2)*e^(9/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(9/2)/(-a^2+b^2)^(1/4)/d-35/4*a*e^4*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^4/d/sqrt(cos(d*x+c))+7/8*a*(5*a^2-2*b^2)*e^5*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^5/(b-sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))+7/8*a*(5*a^2-2*b^2)*e^5*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^5/(b+sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))-1/2*e*(e*cos(d*x+c))^(7/2)/b/d/(a+b*sin(d*x+c))^2-7/12*e^3*(e*cos(d*x+c))^(3/2)*(5*a+2*b*sin(d*x+c))/b^3/d/(a+b*sin(d*x+c)),1],
[(e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^3,x,14,-5/8*(3*a^2-2*b^2)*e^(7/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(7/2)/(-a^2+b^2)^(3/4)/d-5/8*(3*a^2-2*b^2)*e^(7/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(7/2)/(-a^2+b^2)^(3/4)/d-15/4*a*e^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^4/d/sqrt(e*cos(d*x+c))+5/8*a*(3*a^2-2*b^2)*e^4*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^4/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))+5/8*a*(3*a^2-2*b^2)*e^4*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^4/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))-1/2*e*(e*cos(d*x+c))^(5/2)/b/d/(a+b*sin(d*x+c))^2-5/4*e^3*sqrt(e*cos(d*x+c))*(3*a+2*b*sin(d*x+c))/b^3/d/(a+b*sin(d*x+c)),1],
[(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^3,x,14,3/8*(a^2-2*b^2)*e^(5/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(5/2)/(-a^2+b^2)^(5/4)/d-3/8*(a^2-2*b^2)*e^(5/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(5/2)/(-a^2+b^2)^(5/4)/d+3/4*a*e^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^2/(a^2-b^2)/d/sqrt(cos(d*x+c))-3/8*a*(a^2-2*b^2)*e^3*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^3/(a^2-b^2)/(b-sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))-3/8*a*(a^2-2*b^2)*e^3*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^3/(a^2-b^2)/(b+sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))-1/2*e*(e*cos(d*x+c))^(3/2)/b/d/(a+b*sin(d*x+c))^2+3/4*a*e*(e*cos(d*x+c))^(3/2)/b/(a^2-b^2)/d/(a+b*sin(d*x+c)),1],
[(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^3,x,14,1/8*(a^2+2*b^2)*e^(3/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(3/2)/(-a^2+b^2)^(7/4)/d+1/8*(a^2+2*b^2)*e^(3/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(3/2)/(-a^2+b^2)^(7/4)/d-1/4*a*e^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^2/(a^2-b^2)/d/sqrt(e*cos(d*x+c))+1/8*a*(a^2+2*b^2)*e^2*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^2/(a^2-b^2)/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))+1/8*a*(a^2+2*b^2)*e^2*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^2/(a^2-b^2)/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))-1/2*e*sqrt(e*cos(d*x+c))/b/d/(a+b*sin(d*x+c))^2+1/4*a*e*sqrt(e*cos(d*x+c))/b/(a^2-b^2)/d/(a+b*sin(d*x+c)),1],
[sqrt(e*cos(d*x+c))/(a+b*sin(d*x+c))^3,x,14,1/8*(3*a^2+2*b^2)*sqrt(e)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/sqrt(b)/(-a^2+b^2)^(9/4)/d-1/8*(3*a^2+2*b^2)*sqrt(e)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/sqrt(b)/(-a^2+b^2)^(9/4)/d+5/4*a*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/(a^2-b^2)^2/d/sqrt(cos(d*x+c))+1/8*a*(3*a^2+2*b^2)*e*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b/(a^2-b^2)^2/(b-sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))+1/8*a*(3*a^2+2*b^2)*e*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b/(a^2-b^2)^2/(b+sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))+1/2*b*(e*cos(d*x+c))^(3/2)/(a^2-b^2)/d/e/(a+b*sin(d*x+c))^2+5/4*a*b*(e*cos(d*x+c))^(3/2)/(a^2-b^2)^2/d/e/(a+b*sin(d*x+c)),1],
[1/sqrt(e*cos(d*x+c))/(a+b*sin(d*x+c))^3,x,14,-3/8*sqrt(b)*(5*a^2+2*b^2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(11/4)/d/sqrt(e)-3/8*sqrt(b)*(5*a^2+2*b^2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(11/4)/d/sqrt(e)-7/4*a*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/(a^2-b^2)^2/d/sqrt(e*cos(d*x+c))+3/8*a*(5*a^2+2*b^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^2/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))+3/8*a*(5*a^2+2*b^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^2/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))+1/2*b*sqrt(e*cos(d*x+c))/(a^2-b^2)/d/e/(a+b*sin(d*x+c))^2+7/4*a*b*sqrt(e*cos(d*x+c))/(a^2-b^2)^2/d/e/(a+b*sin(d*x+c)),1],
[1/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^3,x,15,5/8*b^(3/2)*(7*a^2+2*b^2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(13/4)/d/e^(3/2)-5/8*b^(3/2)*(7*a^2+2*b^2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(13/4)/d/e^(3/2)-1/4*a*(8*a^2+37*b^2)*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/(a^2-b^2)^3/d/e^2/sqrt(cos(d*x+c))-5/8*a*b*(7*a^2+2*b^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^3/(b-sqrt(-a^2+b^2))/d/e/sqrt(e*cos(d*x+c))-5/8*a*b*(7*a^2+2*b^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^3/(b+sqrt(-a^2+b^2))/d/e/sqrt(e*cos(d*x+c))+1/2*b/(a^2-b^2)/d/e/sqrt(e*cos(d*x+c))/(a+b*sin(d*x+c))^2+9/4*a*b/(a^2-b^2)^2/d/e/sqrt(e*cos(d*x+c))/(a+b*sin(d*x+c))-1/4*(5*b*(7*a^2+2*b^2)-a*(8*a^2+37*b^2)*sin(d*x+c))/(a^2-b^2)^3/d/e/sqrt(e*cos(d*x+c)),1],
[1/(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^3,x,15,-7/8*b^(5/2)*(9*a^2+2*b^2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(15/4)/d/e^(5/2)-7/8*b^(5/2)*(9*a^2+2*b^2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(15/4)/d/e^(5/2)+1/12*a*(8*a^2+69*b^2)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/(a^2-b^2)^3/d/e^2/sqrt(e*cos(d*x+c))-7/8*a*b^2*(9*a^2+2*b^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^3/(a^2-b*(b-sqrt(-a^2+b^2)))/d/e^2/sqrt(e*cos(d*x+c))-7/8*a*b^2*(9*a^2+2*b^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^3/(a^2-b*(b+sqrt(-a^2+b^2)))/d/e^2/sqrt(e*cos(d*x+c))+1/2*b/(a^2-b^2)/d/e/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^2+11/4*a*b/(a^2-b^2)^2/d/e/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))-1/12*(7*b*(9*a^2+2*b^2)-a*(8*a^2+69*b^2)*sin(d*x+c))/(a^2-b^2)^3/d/e/(e*cos(d*x+c))^(3/2),1],
[1/(e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^3,x,16,9/8*b^(7/2)*(11*a^2+2*b^2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(17/4)/d/e^(7/2)-9/8*b^(7/2)*(11*a^2+2*b^2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(17/4)/d/e^(7/2)-3/20*a*(8*a^4-64*a^2*b^2-139*b^4)*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/(a^2-b^2)^4/d/e^4/sqrt(cos(d*x+c))+9/8*a*b^3*(11*a^2+2*b^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^4/(b-sqrt(-a^2+b^2))/d/e^3/sqrt(e*cos(d*x+c))+9/8*a*b^3*(11*a^2+2*b^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^4/(b+sqrt(-a^2+b^2))/d/e^3/sqrt(e*cos(d*x+c))+1/2*b/(a^2-b^2)/d/e/(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^2+13/4*a*b/(a^2-b^2)^2/d/e/(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))-1/20*(9*b*(11*a^2+2*b^2)-a*(8*a^2+109*b^2)*sin(d*x+c))/(a^2-b^2)^3/d/e/(e*cos(d*x+c))^(5/2)+3/20*(15*b^3*(11*a^2+2*b^2)+a*(8*a^4-64*a^2*b^2-139*b^4)*sin(d*x+c))/(a^2-b^2)^4/d/e^3/sqrt(e*cos(d*x+c)),1],
[(e*cos(d*x+c))^(15/2)/(a+b*sin(d*x+c))^4,x,16,39/16*a*(11*a^4-17*a^2*b^2+6*b^4)*e^(15/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(15/2)/(-a^2+b^2)^(3/4)/d+39/16*a*(11*a^4-17*a^2*b^2+6*b^4)*e^(15/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(15/2)/(-a^2+b^2)^(3/4)/d+13/56*(231*a^4-203*a^2*b^2+20*b^4)*e^8*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^8/d/sqrt(e*cos(d*x+c))-39/16*a^2*(11*a^4-17*a^2*b^2+6*b^4)*e^8*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^8/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))-39/16*a^2*(11*a^4-17*a^2*b^2+6*b^4)*e^8*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^8/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))-1/3*e*(e*cos(d*x+c))^(13/2)/b/d/(a+b*sin(d*x+c))^3-13/84*e^3*(e*cos(d*x+c))^(9/2)*(11*a+4*b*sin(d*x+c))/b^3/d/(a+b*sin(d*x+c))^2-39/280*e^5*(e*cos(d*x+c))^(5/2)*(77*a^2-20*b^2+22*a*b*sin(d*x+c))/b^5/d/(a+b*sin(d*x+c))+13/56*e^7*sqrt(e*cos(d*x+c))*(21*a*(11*a^2-6*b^2)-b*(77*a^2-20*b^2)*sin(d*x+c))/b^7/d,1],
[(e*cos(d*x+c))^(13/2)/(a+b*sin(d*x+c))^4,x,15,77/16*a*(3*a^2-2*b^2)*e^(13/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(13/2)/(-a^2+b^2)^(1/4)/d-77/16*a*(3*a^2-2*b^2)*e^(13/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(13/2)/(-a^2+b^2)^(1/4)/d-77/40*(15*a^2-4*b^2)*e^6*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^6/d/sqrt(cos(d*x+c))+77/16*a^2*(3*a^2-2*b^2)*e^7*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^7/(b-sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))+77/16*a^2*(3*a^2-2*b^2)*e^7*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^7/(b+sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))-1/3*e*(e*cos(d*x+c))^(11/2)/b/d/(a+b*sin(d*x+c))^3-11/60*e^3*(e*cos(d*x+c))^(7/2)*(9*a+4*b*sin(d*x+c))/b^3/d/(a+b*sin(d*x+c))^2-77/120*e^5*(e*cos(d*x+c))^(3/2)*(15*a^2-4*b^2+6*a*b*sin(d*x+c))/b^5/d/(a+b*sin(d*x+c)),1],
[(e*cos(d*x+c))^(11/2)/(a+b*sin(d*x+c))^4,x,15,-15/16*a*(7*a^2-6*b^2)*e^(11/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(11/2)/(-a^2+b^2)^(3/4)/d-15/16*a*(7*a^2-6*b^2)*e^(11/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(11/2)/(-a^2+b^2)^(3/4)/d-5/8*(21*a^2-4*b^2)*e^6*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^6/d/sqrt(e*cos(d*x+c))+15/16*a^2*(7*a^2-6*b^2)*e^6*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^6/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))+15/16*a^2*(7*a^2-6*b^2)*e^6*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^6/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))-1/3*e*(e*cos(d*x+c))^(9/2)/b/d/(a+b*sin(d*x+c))^3-1/4*e^3*(e*cos(d*x+c))^(5/2)*(7*a+4*b*sin(d*x+c))/b^3/d/(a+b*sin(d*x+c))^2-5/8*e^5*sqrt(e*cos(d*x+c))*(21*a^2-4*b^2+14*a*b*sin(d*x+c))/b^5/d/(a+b*sin(d*x+c)),1],
[(e*cos(d*x+c))^(9/2)/(a+b*sin(d*x+c))^4,x,15,7/16*a*(5*a^2-6*b^2)*e^(9/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(9/2)/(-a^2+b^2)^(5/4)/d-7/16*a*(5*a^2-6*b^2)*e^(9/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(9/2)/(-a^2+b^2)^(5/4)/d+7/8*(5*a^2-4*b^2)*e^4*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^4/(a^2-b^2)/d/sqrt(cos(d*x+c))-7/16*a^2*(5*a^2-6*b^2)*e^5*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^5/(a^2-b^2)/(b-sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))-7/16*a^2*(5*a^2-6*b^2)*e^5*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^5/(a^2-b^2)/(b+sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))-1/3*e*(e*cos(d*x+c))^(7/2)/b/d/(a+b*sin(d*x+c))^3+7/8*(5*a^2-4*b^2)*e^3*(e*cos(d*x+c))^(3/2)/b^3/(a^2-b^2)/d/(a+b*sin(d*x+c))-7/12*e^3*(e*cos(d*x+c))^(3/2)*(5*a+4*b*sin(d*x+c))/b^3/d/(a+b*sin(d*x+c))^2,1],
[(e*cos(d*x+c))^(7/2)/(a+b*sin(d*x+c))^4,x,15,-5/16*a*(a^2-2*b^2)*e^(7/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(7/2)/(-a^2+b^2)^(7/4)/d-5/16*a*(a^2-2*b^2)*e^(7/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(7/2)/(-a^2+b^2)^(7/4)/d+5/24*(3*a^2-4*b^2)*e^4*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^4/(a^2-b^2)/d/sqrt(e*cos(d*x+c))-5/16*a^2*(a^2-2*b^2)*e^4*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^4/(a^2-b^2)/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))-5/16*a^2*(a^2-2*b^2)*e^4*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^4/(a^2-b^2)/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))-1/3*e*(e*cos(d*x+c))^(5/2)/b/d/(a+b*sin(d*x+c))^3-5/24*(3*a^2-4*b^2)*e^3*sqrt(e*cos(d*x+c))/b^3/(a^2-b^2)/d/(a+b*sin(d*x+c))+5/12*e^3*sqrt(e*cos(d*x+c))*(3*a+4*b*sin(d*x+c))/b^3/d/(a+b*sin(d*x+c))^2,1],
[(e*cos(d*x+c))^(5/2)/(a+b*sin(d*x+c))^4,x,15,-1/16*a*(a^2-6*b^2)*e^(5/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(5/2)/(-a^2+b^2)^(9/4)/d+1/16*a*(a^2-6*b^2)*e^(5/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(5/2)/(-a^2+b^2)^(9/4)/d+1/8*(a^2+4*b^2)*e^2*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/b^2/(a^2-b^2)^2/d/sqrt(cos(d*x+c))-1/16*a^2*(a^2-6*b^2)*e^3*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^3/(a^2-b^2)^2/(b-sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))-1/16*a^2*(a^2-6*b^2)*e^3*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^3/(a^2-b^2)^2/(b+sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))-1/3*e*(e*cos(d*x+c))^(3/2)/b/d/(a+b*sin(d*x+c))^3+1/4*a*e*(e*cos(d*x+c))^(3/2)/b/(a^2-b^2)/d/(a+b*sin(d*x+c))^2+1/8*(a^2+4*b^2)*e*(e*cos(d*x+c))^(3/2)/b/(a^2-b^2)^2/d/(a+b*sin(d*x+c)),1],
[(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^4,x,15,-1/16*a*(a^2+6*b^2)*e^(3/2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(3/2)/(-a^2+b^2)^(11/4)/d-1/16*a*(a^2+6*b^2)*e^(3/2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/b^(3/2)/(-a^2+b^2)^(11/4)/d-1/24*(3*a^2+4*b^2)*e^2*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/b^2/(a^2-b^2)^2/d/sqrt(e*cos(d*x+c))+1/16*a^2*(a^2+6*b^2)*e^2*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b^2/(a^2-b^2)^2/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))+1/16*a^2*(a^2+6*b^2)*e^2*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b^2/(a^2-b^2)^2/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))-1/3*e*sqrt(e*cos(d*x+c))/b/d/(a+b*sin(d*x+c))^3+1/12*a*e*sqrt(e*cos(d*x+c))/b/(a^2-b^2)/d/(a+b*sin(d*x+c))^2+1/24*(3*a^2+4*b^2)*e*sqrt(e*cos(d*x+c))/b/(a^2-b^2)^2/d/(a+b*sin(d*x+c)),1],
[sqrt(e*cos(d*x+c))/(a+b*sin(d*x+c))^4,x,15,-5/16*a*(a^2+2*b^2)*sqrt(e)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/sqrt(b)/(-a^2+b^2)^(13/4)/d+5/16*a*(a^2+2*b^2)*sqrt(e)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/sqrt(b)/(-a^2+b^2)^(13/4)/d+1/8*(11*a^2+4*b^2)*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/(a^2-b^2)^3/d/sqrt(cos(d*x+c))+5/16*a^2*(a^2+2*b^2)*e*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/b/(a^2-b^2)^3/(b-sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))+5/16*a^2*(a^2+2*b^2)*e*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/b/(a^2-b^2)^3/(b+sqrt(-a^2+b^2))/d/sqrt(e*cos(d*x+c))+1/3*b*(e*cos(d*x+c))^(3/2)/(a^2-b^2)/d/e/(a+b*sin(d*x+c))^3+3/4*a*b*(e*cos(d*x+c))^(3/2)/(a^2-b^2)^2/d/e/(a+b*sin(d*x+c))^2+1/8*b*(11*a^2+4*b^2)*(e*cos(d*x+c))^(3/2)/(a^2-b^2)^3/d/e/(a+b*sin(d*x+c)),1],
[1/sqrt(e*cos(d*x+c))/(a+b*sin(d*x+c))^4,x,15,7/16*a*sqrt(b)*(5*a^2+6*b^2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(15/4)/d/sqrt(e)+7/16*a*sqrt(b)*(5*a^2+6*b^2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(15/4)/d/sqrt(e)-1/24*(57*a^2+20*b^2)*sqrt(cos(d*x+c))*InverseJacobiAM(1/2*d*x+1/2*c,sqrt(2))/(a^2-b^2)^3/d/sqrt(e*cos(d*x+c))+7/16*a^2*(5*a^2+6*b^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^3/(a^2-b*(b-sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))+7/16*a^2*(5*a^2+6*b^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^3/(a^2-b*(b+sqrt(-a^2+b^2)))/d/sqrt(e*cos(d*x+c))+1/3*b*sqrt(e*cos(d*x+c))/(a^2-b^2)/d/e/(a+b*sin(d*x+c))^3+11/12*a*b*sqrt(e*cos(d*x+c))/(a^2-b^2)^2/d/e/(a+b*sin(d*x+c))^2+1/24*b*(57*a^2+20*b^2)*sqrt(e*cos(d*x+c))/(a^2-b^2)^3/d/e/(a+b*sin(d*x+c)),1],
[1/(e*cos(d*x+c))^(3/2)/(a+b*sin(d*x+c))^4,x,16,-15/16*a*b^(3/2)*(7*a^2+6*b^2)*arctan(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(17/4)/d/e^(3/2)+15/16*a*b^(3/2)*(7*a^2+6*b^2)*arctanh(sqrt(b)*sqrt(e*cos(d*x+c))/(-a^2+b^2)^(1/4)/sqrt(e))/(-a^2+b^2)^(17/4)/d/e^(3/2)-1/8*(16*a^4+151*a^2*b^2+28*b^4)*sqrt(e*cos(d*x+c))*EllipticE(sin(1/2*d*x+1/2*c),sqrt(2))/(a^2-b^2)^4/d/e^2/sqrt(cos(d*x+c))-15/16*a^2*b*(7*a^2+6*b^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b-sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^4/(b-sqrt(-a^2+b^2))/d/e/sqrt(e*cos(d*x+c))-15/16*a^2*b*(7*a^2+6*b^2)*sqrt(cos(d*x+c))*EllipticPi(sin(1/2*d*x+1/2*c),2*b/(b+sqrt(-a^2+b^2)),sqrt(2))/(a^2-b^2)^4/(b+sqrt(-a^2+b^2))/d/e/sqrt(e*cos(d*x+c))+1/3*b/(a^2-b^2)/d/e/sqrt(e*cos(d*x+c))/(a+b*sin(d*x+c))^3+13/12*a*b/(a^2-b^2)^2/d/e/sqrt(e*cos(d*x+c))/(a+b*sin(d*x+c))^2+1/24*b*(89*a^2+28*b^2)/(a^2-b^2)^3/d/e/sqrt(e*cos(d*x+c))/(a+b*sin(d*x+c))-1/8*(15*a*b*(7*a^2+6*b^2)-(16*a^4+151*a^2*b^2+28*b^4)*sin(d*x+c))/(a^2-b^2)^4/d/e/sqrt(e*cos(d*x+c)),1],
[1/sqrt(c*cos(f*x+e))/sqrt(a+b*sin(f*x+e)),x,2,2*sqrt(2)*(-a+b)^(1/4)*sqrt(c*cos(f*x+e))*InverseJacobiAM(arcsin((a+b)^(1/4)*sqrt((1+cos(f*x+e)+sin(f*x+e))/(1+cos(f*x+e)-sin(f*x+e)))/(-a+b)^(1/4)),sqrt(-1))*sqrt((a+b*sin(f*x+e))/(a-b)/(1-sin(f*x+e)))/(a+b)^(1/4)/c/f/sqrt((1+cos(f*x+e)+sin(f*x+e))/(1+cos(f*x+e)-sin(f*x+e)))/sqrt(a+b*sin(f*x+e)),1],
[(e*cos(d*x+c))^p*(a+b*sin(d*x+c))^3,x,4,-b*(2*b^2*(2+p)+a^2*(p^2+6*p+11))*(e*cos(d*x+c))^(p+1)/d/e/(p+1)/(2+p)/(3+p)-a*(3*b^2+a^2*(2+p))*(e*cos(d*x+c))^(p+1)*hypergeom([1/2, 1/2*p+1/2],[3/2+1/2*p],cos(d*x+c)^2)*sin(d*x+c)/d/e/(p+1)/(2+p)/sqrt(sin(d*x+c)^2)-a*b*(5+p)*(e*cos(d*x+c))^(p+1)*(a+b*sin(d*x+c))/d/e/(2+p)/(3+p)-b*(e*cos(d*x+c))^(p+1)*(a+b*sin(d*x+c))^2/d/e/(3+p),1],
[(e*cos(d*x+c))^p*(a+b*sin(d*x+c))^2,x,3,-a*b*(3+p)*(e*cos(d*x+c))^(p+1)/d/e/(p+1)/(2+p)-(b^2+a^2*(2+p))*(e*cos(d*x+c))^(p+1)*hypergeom([1/2, 1/2*p+1/2],[3/2+1/2*p],cos(d*x+c)^2)*sin(d*x+c)/d/e/(p+1)/(2+p)/sqrt(sin(d*x+c)^2)-b*(e*cos(d*x+c))^(p+1)*(a+b*sin(d*x+c))/d/e/(2+p),1],
[(e*cos(d*x+c))^p*(a+b*sin(d*x+c)),x,2,-b*(e*cos(d*x+c))^(p+1)/d/e/(p+1)-a*(e*cos(d*x+c))^(p+1)*hypergeom([1/2, 1/2*p+1/2],[3/2+1/2*p],cos(d*x+c)^2)*sin(d*x+c)/d/e/(p+1)/sqrt(sin(d*x+c)^2),1],
[(e*cos(d*x+c))^p/(a+b*sin(d*x+c)),x,1,-e*AppellF1(1-p,1/2-1/2*p,1/2-1/2*p,2-p,(a+b)/(a+b*sin(d*x+c)),(a-b)/(a+b*sin(d*x+c)))*(e*cos(d*x+c))^(-1+p)*(-b*(1-sin(d*x+c))/(a+b*sin(d*x+c)))^(1/2-1/2*p)*(b*(1+sin(d*x+c))/(a+b*sin(d*x+c)))^(1/2-1/2*p)/b/d/(1-p),1],
[(e*cos(d*x+c))^p/(a+b*sin(d*x+c))^2,x,1,-e*AppellF1(2-p,1/2-1/2*p,1/2-1/2*p,3-p,(a+b)/(a+b*sin(d*x+c)),(a-b)/(a+b*sin(d*x+c)))*(e*cos(d*x+c))^(-1+p)*(-b*(1-sin(d*x+c))/(a+b*sin(d*x+c)))^(1/2-1/2*p)*(b*(1+sin(d*x+c))/(a+b*sin(d*x+c)))^(1/2-1/2*p)/b/d/(2-p)/(a+b*sin(d*x+c)),1],
[(e*cos(d*x+c))^p/(a+b*sin(d*x+c))^3,x,1,-e*AppellF1(3-p,1/2-1/2*p,1/2-1/2*p,4-p,(a+b)/(a+b*sin(d*x+c)),(a-b)/(a+b*sin(d*x+c)))*(e*cos(d*x+c))^(-1+p)*(-b*(1-sin(d*x+c))/(a+b*sin(d*x+c)))^(1/2-1/2*p)*(b*(1+sin(d*x+c))/(a+b*sin(d*x+c)))^(1/2-1/2*p)/b/d/(3-p)/(a+b*sin(d*x+c))^2,1],
[(e*cos(d*x+c))^p*(a+b*sin(d*x+c))^(3/2),x,2,2/5*e*AppellF1(5/2,1/2-1/2*p,1/2-1/2*p,7/2,(a+b*sin(d*x+c))/(a-b),(a+b*sin(d*x+c))/(a+b))*(e*cos(d*x+c))^(-1+p)*(a+b*sin(d*x+c))^(5/2)*(1-(a+b*sin(d*x+c))/(a-b))^(1/2-1/2*p)*(1-(a+b*sin(d*x+c))/(a+b))^(1/2-1/2*p)/b/d,1],
[(e*cos(d*x+c))^p*sqrt(a+b*sin(d*x+c)),x,2,2/3*e*AppellF1(3/2,1/2-1/2*p,1/2-1/2*p,5/2,(a+b*sin(d*x+c))/(a-b),(a+b*sin(d*x+c))/(a+b))*(e*cos(d*x+c))^(-1+p)*(a+b*sin(d*x+c))^(3/2)*(1-(a+b*sin(d*x+c))/(a-b))^(1/2-1/2*p)*(1-(a+b*sin(d*x+c))/(a+b))^(1/2-1/2*p)/b/d,1],
[(e*cos(d*x+c))^p/sqrt(a+b*sin(d*x+c)),x,2,2*e*AppellF1(1/2,1/2-1/2*p,1/2-1/2*p,3/2,(a+b*sin(d*x+c))/(a-b),(a+b*sin(d*x+c))/(a+b))*(e*cos(d*x+c))^(-1+p)*sqrt(a+b*sin(d*x+c))*(1-(a+b*sin(d*x+c))/(a-b))^(1/2-1/2*p)*(1-(a+b*sin(d*x+c))/(a+b))^(1/2-1/2*p)/b/d,1],
[(e*cos(d*x+c))^p/(a+b*sin(d*x+c))^(3/2),x,2,-2*e*AppellF1(-1/2,1/2-1/2*p,1/2-1/2*p,1/2,(a+b*sin(d*x+c))/(a-b),(a+b*sin(d*x+c))/(a+b))*(e*cos(d*x+c))^(-1+p)*(1-(a+b*sin(d*x+c))/(a-b))^(1/2-1/2*p)*(1-(a+b*sin(d*x+c))/(a+b))^(1/2-1/2*p)/b/d/sqrt(a+b*sin(d*x+c)),1],
[(e*cos(d*x+c))^p/(a+b*sin(d*x+c))^(5/2),x,2,-2/3*e*AppellF1(-3/2,1/2-1/2*p,1/2-1/2*p,-1/2,(a+b*sin(d*x+c))/(a-b),(a+b*sin(d*x+c))/(a+b))*(e*cos(d*x+c))^(-1+p)*(1-(a+b*sin(d*x+c))/(a-b))^(1/2-1/2*p)*(1-(a+b*sin(d*x+c))/(a+b))^(1/2-1/2*p)/b/d/(a+b*sin(d*x+c))^(3/2),1],
[cos(d*x+c)^7*(a+b*sin(d*x+c))^m,x,3,-(a^2-b^2)^3*(a+b*sin(d*x+c))^(1+m)/b^7/d/(1+m)+6*a*(a^2-b^2)^2*(a+b*sin(d*x+c))^(2+m)/b^7/d/(2+m)-3*(5*a^4-6*a^2*b^2+b^4)*(a+b*sin(d*x+c))^(3+m)/b^7/d/(3+m)+4*a*(5*a^2-3*b^2)*(a+b*sin(d*x+c))^(4+m)/b^7/d/(4+m)-3*(5*a^2-b^2)*(a+b*sin(d*x+c))^(5+m)/b^7/d/(5+m)+6*a*(a+b*sin(d*x+c))^(6+m)/b^7/d/(6+m)-(a+b*sin(d*x+c))^(7+m)/b^7/d/(7+m),1],
[cos(d*x+c)^5*(a+b*sin(d*x+c))^m,x,3,(a^2-b^2)^2*(a+b*sin(d*x+c))^(1+m)/b^5/d/(1+m)-4*a*(a^2-b^2)*(a+b*sin(d*x+c))^(2+m)/b^5/d/(2+m)+2*(3*a^2-b^2)*(a+b*sin(d*x+c))^(3+m)/b^5/d/(3+m)-4*a*(a+b*sin(d*x+c))^(4+m)/b^5/d/(4+m)+(a+b*sin(d*x+c))^(5+m)/b^5/d/(5+m),1],
[cos(d*x+c)^3*(a+b*sin(d*x+c))^m,x,3,-(a^2-b^2)*(a+b*sin(d*x+c))^(1+m)/b^3/d/(1+m)+2*a*(a+b*sin(d*x+c))^(2+m)/b^3/d/(2+m)-(a+b*sin(d*x+c))^(3+m)/b^3/d/(3+m),1],
[cos(d*x+c)*(a+b*sin(d*x+c))^m,x,2,(a+b*sin(d*x+c))^(1+m)/b/d/(1+m),1],
[sec(d*x+c)*(a+b*sin(d*x+c))^m,x,5,-1/2*hypergeom([1, 1+m],[2+m],(a+b*sin(d*x+c))/(a-b))*(a+b*sin(d*x+c))^(1+m)/(a-b)/d/(1+m)+1/2*hypergeom([1, 1+m],[2+m],(a+b*sin(d*x+c))/(a+b))*(a+b*sin(d*x+c))^(1+m)/(a+b)/d/(1+m),1],
[sec(d*x+c)^3*(a+b*sin(d*x+c))^m,x,6,-1/4*(a-b*(1-m))*hypergeom([1, 1+m],[2+m],(a+b*sin(d*x+c))/(a-b))*(a+b*sin(d*x+c))^(1+m)/(a-b)^2/d/(1+m)+1/4*(-b*m+a+b)*hypergeom([1, 1+m],[2+m],(a+b*sin(d*x+c))/(a+b))*(a+b*sin(d*x+c))^(1+m)/(a+b)^2/d/(1+m)-1/2*sec(d*x+c)^2*(b-a*sin(d*x+c))*(a+b*sin(d*x+c))^(1+m)/(a^2-b^2)/d,1],
[sec(d*x+c)^5*(a+b*sin(d*x+c))^m,x,7,-1/16*(3*a^2-3*a*b*(2-m)+b^2*(m^2-4*m+3))*hypergeom([1, 1+m],[2+m],(a+b*sin(d*x+c))/(a-b))*(a+b*sin(d*x+c))^(1+m)/(a-b)^3/d/(1+m)+1/16*(3*a^2+3*a*b*(2-m)+b^2*(m^2-4*m+3))*hypergeom([1, 1+m],[2+m],(a+b*sin(d*x+c))/(a+b))*(a+b*sin(d*x+c))^(1+m)/(a+b)^3/d/(1+m)-1/4*sec(d*x+c)^4*(b-a*sin(d*x+c))*(a+b*sin(d*x+c))^(1+m)/(a^2-b^2)/d+1/8*sec(d*x+c)^2*(a+b*sin(d*x+c))^(1+m)*(b*(b^2*(3-m)-a^2*(1+m))+a*(3*a^2-b^2*(5-2*m))*sin(d*x+c))/(a^2-b^2)^2/d,1],
[cos(d*x+c)^4*(a+b*sin(d*x+c))^m,x,2,-4/5*sqrt(2)*AppellF1(5/2,-3/2,-m,7/2,1/2-1/2*sin(d*x+c),b*(1-sin(d*x+c))/(a+b))*cos(d*x+c)^3*(1-sin(d*x+c))*(a+b*sin(d*x+c))^m/d/(1+sin(d*x+c))^(3/2)/(((a+b*sin(d*x+c))/(a+b))^m),1],
[cos(d*x+c)^2*(a+b*sin(d*x+c))^m,x,2,-2/3*sqrt(2)*AppellF1(3/2,-1/2,-m,5/2,1/2-1/2*sin(d*x+c),b*(1-sin(d*x+c))/(a+b))*cos(d*x+c)*(1-sin(d*x+c))*(a+b*sin(d*x+c))^m/d/sqrt(1+sin(d*x+c))/(((a+b*sin(d*x+c))/(a+b))^m),1],
[sec(d*x+c)^2*(a+b*sin(d*x+c))^m,x,2,AppellF1(-1/2,3/2,-m,1/2,1/2-1/2*sin(d*x+c),b*(1-sin(d*x+c))/(a+b))*sec(d*x+c)^3*(1-sin(d*x+c))*(1+sin(d*x+c))^(3/2)*(a+b*sin(d*x+c))^m/sqrt(2)/d/(((a+b*sin(d*x+c))/(a+b))^m),1],
[sec(d*x+c)^4*(a+b*sin(d*x+c))^m,x,2,1/6*AppellF1(-3/2,5/2,-m,-1/2,1/2-1/2*sin(d*x+c),b*(1-sin(d*x+c))/(a+b))*sec(d*x+c)^5*(1-sin(d*x+c))*(1+sin(d*x+c))^(5/2)*(a+b*sin(d*x+c))^m/sqrt(2)/d/(((a+b*sin(d*x+c))/(a+b))^m),1],
[(e*cos(d*x+c))^(5/2)*(a+b*sin(d*x+c))^m,x,2,-4/7*2^(3/4)*e*AppellF1(7/4,-3/4,-m,11/4,1/2-1/2*sin(d*x+c),b*(1-sin(d*x+c))/(a+b))*(e*cos(d*x+c))^(3/2)*(1-sin(d*x+c))*(a+b*sin(d*x+c))^m/d/(1+sin(d*x+c))^(3/4)/(((a+b*sin(d*x+c))/(a+b))^m),1],
[(e*cos(d*x+c))^(3/2)*(a+b*sin(d*x+c))^m,x,2,-4/5*2^(1/4)*e*AppellF1(5/4,-1/4,-m,9/4,1/2-1/2*sin(d*x+c),b*(1-sin(d*x+c))/(a+b))*sqrt(e*cos(d*x+c))*(1-sin(d*x+c))*(a+b*sin(d*x+c))^m/d/(1+sin(d*x+c))^(1/4)/(((a+b*sin(d*x+c))/(a+b))^m),1],
[sqrt(e*cos(d*x+c))*(a+b*sin(d*x+c))^m,x,2,-2/3*2^(3/4)*e*AppellF1(3/4,1/4,-m,7/4,1/2-1/2*sin(d*x+c),b*(1-sin(d*x+c))/(a+b))*(1-sin(d*x+c))*(1+sin(d*x+c))^(1/4)*(a+b*sin(d*x+c))^m/d/sqrt(e*cos(d*x+c))/(((a+b*sin(d*x+c))/(a+b))^m),1],
[(a+b*sin(d*x+c))^m/sqrt(e*cos(d*x+c)),x,2,-2*2^(1/4)*e*AppellF1(1/4,3/4,-m,5/4,1/2-1/2*sin(d*x+c),b*(1-sin(d*x+c))/(a+b))*(1-sin(d*x+c))*(1+sin(d*x+c))^(3/4)*(a+b*sin(d*x+c))^m/d/(e*cos(d*x+c))^(3/2)/(((a+b*sin(d*x+c))/(a+b))^m),1],
[(a+b*sin(d*x+c))^m/(e*cos(d*x+c))^(3/2),x,2,2^(3/4)*e*AppellF1(-1/4,5/4,-m,3/4,1/2-1/2*sin(d*x+c),b*(1-sin(d*x+c))/(a+b))*(1-sin(d*x+c))*(1+sin(d*x+c))^(5/4)*(a+b*sin(d*x+c))^m/d/(e*cos(d*x+c))^(5/2)/(((a+b*sin(d*x+c))/(a+b))^m),1],
[(e*cos(d*x+c))^p*(a+b*sin(d*x+c))^m,x,2,e*AppellF1(1+m,1/2-1/2*p,1/2-1/2*p,2+m,(a+b*sin(d*x+c))/(a-b),(a+b*sin(d*x+c))/(a+b))*(e*cos(d*x+c))^(-1+p)*(a+b*sin(d*x+c))^(1+m)*(1-(a+b*sin(d*x+c))/(a-b))^(1/2-1/2*p)*(1-(a+b*sin(d*x+c))/(a+b))^(1/2-1/2*p)/b/d/(1+m),1],
[(e*cos(d*x+c))^(-3-m)*(a+b*sin(d*x+c))^m,x,-8,-(e*cos(d*x+c))^(-2-m)*(a+b*sin(d*x+c))^(1+m)/(a-b)/d/e/(2+m)+(-b^2+a^2*(1+m))*hypergeom([1+m, 1+1/2*m],[2+m],2*(a+b*sin(d*x+c))/(a+b)/(1+sin(d*x+c)))*((a-b)*(-1+sin(d*x+c))/(a+b)/(1+sin(d*x+c)))^(1/2*m)*(a+b*sin(d*x+c))^(1+m)/(a-b)/(a+b)^2/d/e^3/(1+m)/(2+m)/((e*cos(d*x+c))^m)/(cos(1/2*d*x+1/2*c)+sin(1/2*d*x+1/2*c))^2+a*(e*cos(d*x+c))^(-2-m)*(1+sin(d*x+c))*(a+b*sin(d*x+c))^(1+m)/(a^2-b^2)/d/e/(2+m),1],
[(e*cos(d*x+c))^(-2-m)*(a+b*sin(d*x+c))^m,x,-4,-(e*cos(d*x+c))^(-1-m)*(a+b*sin(d*x+c))^(1+m)/(a-b)/d/e/(1+m)+2^(1/2-1/2*m)*a*(e*cos(d*x+c))^(-1-m)*hypergeom([-1/2-1/2*m, 1/2+1/2*m],[1/2-1/2*m],(a-b)*(1-sin(d*x+c))/(2*a+2*b*sin(d*x+c)))*((a+b)*(1+sin(d*x+c))/(a+b*sin(d*x+c)))^(1/2+1/2*m)*(a+b*sin(d*x+c))^(1+m)/(a^2-b^2)/d/e/(1+m),1],
[(e*cos(d*x+c))^(-1-m)*(a+b*sin(d*x+c))^m,x,1,e*(e*cos(d*x+c))^(-2-m)*hypergeom([1+m, 1+1/2*m],[2+m],2*(a+b*sin(d*x+c))/(a+b)/(1+sin(d*x+c)))*(1-sin(d*x+c))*(-(a-b)*(1-sin(d*x+c))/(a+b)/(1+sin(d*x+c)))^(1/2*m)*(a+b*sin(d*x+c))^(1+m)/(a+b)/d/(1+m),1],
[(a+b*sin(d*x+c))^m/((e*cos(d*x+c))^m),x,2,e*AppellF1(1+m,1/2+1/2*m,1/2+1/2*m,2+m,(a+b*sin(d*x+c))/(a-b),(a+b*sin(d*x+c))/(a+b))*(e*cos(d*x+c))^(-1-m)*(a+b*sin(d*x+c))^(1+m)*(1-(a+b*sin(d*x+c))/(a-b))^(1/2+1/2*m)*(1-(a+b*sin(d*x+c))/(a+b))^(1/2+1/2*m)/b/d/(1+m),1],
[(e*cos(d*x+c))^(1-m)*(a+b*sin(d*x+c))^m,x,2,e*AppellF1(1+m,1/2*m,1/2*m,2+m,(a+b*sin(d*x+c))/(a-b),(a+b*sin(d*x+c))/(a+b))*(a+b*sin(d*x+c))^(1+m)*(1-(a+b*sin(d*x+c))/(a-b))^(1/2*m)*(1-(a+b*sin(d*x+c))/(a+b))^(1/2*m)/b/d/(1+m)/((e*cos(d*x+c))^m),1],
[(e*cos(d*x+c))^(2-m)*(a+b*sin(d*x+c))^m,x,2,e*AppellF1(1+m,-1/2+1/2*m,-1/2+1/2*m,2+m,(a+b*sin(d*x+c))/(a-b),(a+b*sin(d*x+c))/(a+b))*(e*cos(d*x+c))^(1-m)*(a+b*sin(d*x+c))^(1+m)*(1-(a+b*sin(d*x+c))/(a-b))^(-1/2+1/2*m)*(1-(a+b*sin(d*x+c))/(a+b))^(-1/2+1/2*m)/b/d/(1+m),1]]: