# Maple integration test file: "4 Trig functions\4.7 Miscellaneous\4.7.3 (c+d x)^m trig^n trig^p.txt"

lst:=[

# Integrands of the form (c+d x)^m Cos[a+b x]^n Sin[a+b x]^p

# Integrands of the form (c+d x)^m Cos[a+b x]^1 Sin[a+b x]^p

# Integrands of the form (c+d x)^m Cos[a+b x] Sin[a+b x]^p

# p>0
[(c+d*x)^m*cos(a+b*x)*sin(a+b*x),x,5,-2^(-3-m)*exp(2*I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-2*I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)-2^(-3-m)*(c+d*x)^m*GAMMA(1+m,2*I*b*(c+d*x)/d)/(b*exp(2*I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)],
[(c+d*x)^4*cos(a+b*x)*sin(a+b*x),x,5,3/2*c*d^3*x/b^3+3/4*d^4*x^2/b^3-1/4*(c+d*x)^4/b-3/2*d^3*(c+d*x)*cos(a+b*x)*sin(a+b*x)/b^4+d*(c+d*x)^3*cos(a+b*x)*sin(a+b*x)/b^2+3/4*d^4*sin(a+b*x)^2/b^5-3/2*d^2*(c+d*x)^2*sin(a+b*x)^2/b^3+1/2*(c+d*x)^4*sin(a+b*x)^2/b],
[(c+d*x)^3*cos(a+b*x)*sin(a+b*x),x,5,3/8*d^3*x/b^3-1/4*(c+d*x)^3/b-3/8*d^3*cos(a+b*x)*sin(a+b*x)/b^4+3/4*d*(c+d*x)^2*cos(a+b*x)*sin(a+b*x)/b^2-3/4*d^2*(c+d*x)*sin(a+b*x)^2/b^3+1/2*(c+d*x)^3*sin(a+b*x)^2/b],
[(c+d*x)^2*cos(a+b*x)*sin(a+b*x),x,3,-1/2*c*d*x/b-1/4*d^2*x^2/b+1/2*d*(c+d*x)*cos(a+b*x)*sin(a+b*x)/b^2-1/4*d^2*sin(a+b*x)^2/b^3+1/2*(c+d*x)^2*sin(a+b*x)^2/b],
[(c+d*x)*cos(a+b*x)*sin(a+b*x),x,3,-1/4*d*x/b+1/4*d*cos(a+b*x)*sin(a+b*x)/b^2+1/2*(c+d*x)*sin(a+b*x)^2/b],
[cos(a+b*x)*sin(a+b*x)/(c+d*x),x,5,1/2*cos(2*a-2*b*c/d)*Si(2*b*c/d+2*b*x)/d+1/2*Ci(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d],
[cos(a+b*x)*sin(a+b*x)/(c+d*x)^2,x,6,b*Ci(2*b*c/d+2*b*x)*cos(2*a-2*b*c/d)/d^2-b*Si(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^2-1/2*sin(2*a+2*b*x)/(d*(c+d*x))],
[cos(a+b*x)*sin(a+b*x)/(c+d*x)^3,x,7,-1/2*b*cos(2*a+2*b*x)/(d^2*(c+d*x))-b^2*cos(2*a-2*b*c/d)*Si(2*b*c/d+2*b*x)/d^3-b^2*Ci(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^3-1/4*sin(2*a+2*b*x)/(d*(c+d*x)^2)],
[cos(a+b*x)*sin(a+b*x)/(c+d*x)^4,x,8,-2/3*b^3*Ci(2*b*c/d+2*b*x)*cos(2*a-2*b*c/d)/d^4-1/6*b*cos(2*a+2*b*x)/(d^2*(c+d*x)^2)+2/3*b^3*Si(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^4-1/6*sin(2*a+2*b*x)/(d*(c+d*x)^3)+1/3*b^2*sin(2*a+2*b*x)/(d^3*(c+d*x))],
[cos(x)*sin(x)/x,x,3,1/2*Si(2*x)],
[cos(x)*sin(x)/x^2,x,4,Ci(2*x)-1/2*sin(2*x)/x],
[cos(x)*sin(x)/x^3,x,5,-1/2*cos(2*x)/x-Si(2*x)-1/4*sin(2*x)/x^2],
[(c+d*x)^m*cos(a+b*x)*sin(a+b*x)^2,x,8,-1/8*I*exp(I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)+1/8*I*(c+d*x)^m*GAMMA(1+m,I*b*(c+d*x)/d)/(b*exp(I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)+1/8*I*3^(-1-m)*exp(3*I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-3*I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)-1/8*I*3^(-1-m)*(c+d*x)^m*GAMMA(1+m,3*I*b*(c+d*x)/d)/(b*exp(3*I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)],
[(c+d*x)^4*cos(a+b*x)*sin(a+b*x)^2,x,9,-160/27*d^3*(c+d*x)*cos(a+b*x)/b^4+8/9*d*(c+d*x)^3*cos(a+b*x)/b^2+160/27*d^4*sin(a+b*x)/b^5-8/3*d^2*(c+d*x)^2*sin(a+b*x)/b^3-8/27*d^3*(c+d*x)*cos(a+b*x)*sin(a+b*x)^2/b^4+4/9*d*(c+d*x)^3*cos(a+b*x)*sin(a+b*x)^2/b^2+8/81*d^4*sin(a+b*x)^3/b^5-4/9*d^2*(c+d*x)^2*sin(a+b*x)^3/b^3+1/3*(c+d*x)^4*sin(a+b*x)^3/b],
[(c+d*x)^3*cos(a+b*x)*sin(a+b*x)^2,x,7,-14/9*d^3*cos(a+b*x)/b^4+2/3*d*(c+d*x)^2*cos(a+b*x)/b^2+2/27*d^3*cos(a+b*x)^3/b^4-4/3*d^2*(c+d*x)*sin(a+b*x)/b^3+1/3*d*(c+d*x)^2*cos(a+b*x)*sin(a+b*x)^2/b^2-2/9*d^2*(c+d*x)*sin(a+b*x)^3/b^3+1/3*(c+d*x)^3*sin(a+b*x)^3/b],
[(c+d*x)^2*cos(a+b*x)*sin(a+b*x)^2,x,4,4/9*d*(c+d*x)*cos(a+b*x)/b^2-4/9*d^2*sin(a+b*x)/b^3+2/9*d*(c+d*x)*cos(a+b*x)*sin(a+b*x)^2/b^2-2/27*d^2*sin(a+b*x)^3/b^3+1/3*(c+d*x)^2*sin(a+b*x)^3/b],
[(c+d*x)*cos(a+b*x)*sin(a+b*x)^2,x,3,1/3*d*cos(a+b*x)/b^2-1/9*d*cos(a+b*x)^3/b^2+1/3*(c+d*x)*sin(a+b*x)^3/b],
[cos(a+b*x)*sin(a+b*x)^2/(c+d*x),x,8,-1/4*Ci(3*b*c/d+3*b*x)*cos(3*a-3*b*c/d)/d+1/4*Ci(b*c/d+b*x)*cos(a-b*c/d)/d+1/4*Si(3*b*c/d+3*b*x)*sin(3*a-3*b*c/d)/d-1/4*Si(b*c/d+b*x)*sin(a-b*c/d)/d],
[cos(a+b*x)*sin(a+b*x)^2/(c+d*x)^2,x,10,-1/4*cos(a+b*x)/(d*(c+d*x))+1/4*cos(3*a+3*b*x)/(d*(c+d*x))-1/4*b*cos(a-b*c/d)*Si(b*c/d+b*x)/d^2+3/4*b*cos(3*a-3*b*c/d)*Si(3*b*c/d+3*b*x)/d^2+3/4*b*Ci(3*b*c/d+3*b*x)*sin(3*a-3*b*c/d)/d^2-1/4*b*Ci(b*c/d+b*x)*sin(a-b*c/d)/d^2],
[cos(a+b*x)*sin(a+b*x)^2/(c+d*x)^3,x,12,9/8*b^2*Ci(3*b*c/d+3*b*x)*cos(3*a-3*b*c/d)/d^3-1/8*b^2*Ci(b*c/d+b*x)*cos(a-b*c/d)/d^3-1/8*cos(a+b*x)/(d*(c+d*x)^2)+1/8*cos(3*a+3*b*x)/(d*(c+d*x)^2)-9/8*b^2*Si(3*b*c/d+3*b*x)*sin(3*a-3*b*c/d)/d^3+1/8*b^2*Si(b*c/d+b*x)*sin(a-b*c/d)/d^3+1/8*b*sin(a+b*x)/(d^2*(c+d*x))-3/8*b*sin(3*a+3*b*x)/(d^2*(c+d*x))],
[cos(a+b*x)*sin(a+b*x)^2/(c+d*x)^4,x,14,-1/12*cos(a+b*x)/(d*(c+d*x)^3)+1/24*b^2*cos(a+b*x)/(d^3*(c+d*x))+1/12*cos(3*a+3*b*x)/(d*(c+d*x)^3)-3/8*b^2*cos(3*a+3*b*x)/(d^3*(c+d*x))+1/24*b^3*cos(a-b*c/d)*Si(b*c/d+b*x)/d^4-9/8*b^3*cos(3*a-3*b*c/d)*Si(3*b*c/d+3*b*x)/d^4-9/8*b^3*Ci(3*b*c/d+3*b*x)*sin(3*a-3*b*c/d)/d^4+1/24*b^3*Ci(b*c/d+b*x)*sin(a-b*c/d)/d^4+1/24*b*sin(a+b*x)/(d^2*(c+d*x)^2)-1/8*b*sin(3*a+3*b*x)/(d^2*(c+d*x)^2)],
[(c+d*x)^m*cos(a+b*x)*sin(a+b*x)^3,x,8,-2^(-4-m)*exp(2*I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-2*I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)-2^(-4-m)*(c+d*x)^m*GAMMA(1+m,2*I*b*(c+d*x)/d)/(b*exp(2*I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)+exp(4*I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-4*I*b*(c+d*x)/d)/(2^(2*(3+m))*b*(-I*b*(c+d*x)/d)^m)+(c+d*x)^m*GAMMA(1+m,4*I*b*(c+d*x)/d)/(2^(2*(3+m))*b*exp(4*I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)],
[(c+d*x)^4*cos(a+b*x)*sin(a+b*x)^3,x,9,45/64*c*d^3*x/b^3+45/128*d^4*x^2/b^3-3/32*(c+d*x)^4/b-45/64*d^3*(c+d*x)*cos(a+b*x)*sin(a+b*x)/b^4+3/8*d*(c+d*x)^3*cos(a+b*x)*sin(a+b*x)/b^2+45/128*d^4*sin(a+b*x)^2/b^5-9/16*d^2*(c+d*x)^2*sin(a+b*x)^2/b^3-3/32*d^3*(c+d*x)*cos(a+b*x)*sin(a+b*x)^3/b^4+1/4*d*(c+d*x)^3*cos(a+b*x)*sin(a+b*x)^3/b^2+3/128*d^4*sin(a+b*x)^4/b^5-3/16*d^2*(c+d*x)^2*sin(a+b*x)^4/b^3+1/4*(c+d*x)^4*sin(a+b*x)^4/b],
[(c+d*x)^3*cos(a+b*x)*sin(a+b*x)^3,x,9,45/256*d^3*x/b^3-3/32*(c+d*x)^3/b-45/256*d^3*cos(a+b*x)*sin(a+b*x)/b^4+9/32*d*(c+d*x)^2*cos(a+b*x)*sin(a+b*x)/b^2-9/32*d^2*(c+d*x)*sin(a+b*x)^2/b^3-3/128*d^3*cos(a+b*x)*sin(a+b*x)^3/b^4+3/16*d*(c+d*x)^2*cos(a+b*x)*sin(a+b*x)^3/b^2-3/32*d^2*(c+d*x)*sin(a+b*x)^4/b^3+1/4*(c+d*x)^3*sin(a+b*x)^4/b],
[(c+d*x)^2*cos(a+b*x)*sin(a+b*x)^3,x,4,-3/16*c*d*x/b-3/32*d^2*x^2/b+3/16*d*(c+d*x)*cos(a+b*x)*sin(a+b*x)/b^2-3/32*d^2*sin(a+b*x)^2/b^3+1/8*d*(c+d*x)*cos(a+b*x)*sin(a+b*x)^3/b^2-1/32*d^2*sin(a+b*x)^4/b^3+1/4*(c+d*x)^2*sin(a+b*x)^4/b],
[(c+d*x)*cos(a+b*x)*sin(a+b*x)^3,x,4,-3/32*d*x/b+3/32*d*cos(a+b*x)*sin(a+b*x)/b^2+1/16*d*cos(a+b*x)*sin(a+b*x)^3/b^2+1/4*(c+d*x)*sin(a+b*x)^4/b],
[cos(a+b*x)*sin(a+b*x)^3/(c+d*x),x,8,1/4*cos(2*a-2*b*c/d)*Si(2*b*c/d+2*b*x)/d-1/8*cos(4*a-4*b*c/d)*Si(4*b*c/d+4*b*x)/d-1/8*Ci(4*b*c/d+4*b*x)*sin(4*a-4*b*c/d)/d+1/4*Ci(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d],
[cos(a+b*x)*sin(a+b*x)^3/(c+d*x)^2,x,10,-1/2*b*Ci(4*b*c/d+4*b*x)*cos(4*a-4*b*c/d)/d^2+1/2*b*Ci(2*b*c/d+2*b*x)*cos(2*a-2*b*c/d)/d^2+1/2*b*Si(4*b*c/d+4*b*x)*sin(4*a-4*b*c/d)/d^2-1/2*b*Si(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^2-1/4*sin(2*a+2*b*x)/(d*(c+d*x))+1/8*sin(4*a+4*b*x)/(d*(c+d*x))],
[cos(a+b*x)*sin(a+b*x)^3/(c+d*x)^3,x,12,-1/4*b*cos(2*a+2*b*x)/(d^2*(c+d*x))+1/4*b*cos(4*a+4*b*x)/(d^2*(c+d*x))-1/2*b^2*cos(2*a-2*b*c/d)*Si(2*b*c/d+2*b*x)/d^3+b^2*cos(4*a-4*b*c/d)*Si(4*b*c/d+4*b*x)/d^3+b^2*Ci(4*b*c/d+4*b*x)*sin(4*a-4*b*c/d)/d^3-1/2*b^2*Ci(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^3-1/8*sin(2*a+2*b*x)/(d*(c+d*x)^2)+1/16*sin(4*a+4*b*x)/(d*(c+d*x)^2)],
[cos(a+b*x)*sin(a+b*x)^3/(c+d*x)^4,x,14,4/3*b^3*Ci(4*b*c/d+4*b*x)*cos(4*a-4*b*c/d)/d^4-1/3*b^3*Ci(2*b*c/d+2*b*x)*cos(2*a-2*b*c/d)/d^4-1/12*b*cos(2*a+2*b*x)/(d^2*(c+d*x)^2)+1/12*b*cos(4*a+4*b*x)/(d^2*(c+d*x)^2)-4/3*b^3*Si(4*b*c/d+4*b*x)*sin(4*a-4*b*c/d)/d^4+1/3*b^3*Si(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^4-1/12*sin(2*a+2*b*x)/(d*(c+d*x)^3)+1/6*b^2*sin(2*a+2*b*x)/(d^3*(c+d*x))+1/24*sin(4*a+4*b*x)/(d*(c+d*x)^3)-1/3*b^2*sin(4*a+4*b*x)/(d^3*(c+d*x))],

# p<0
[(c+d*x)^m*cos(a+b*x)*csc(a+b*x),x,0,Unintegrable((c+d*x)^m*cot(a+b*x),x)],
[(c+d*x)^4*cos(a+b*x)*csc(a+b*x),x,7,-1/5*I*(c+d*x)^5/d+(c+d*x)^4*log(1-exp(2*I*(a+b*x)))/b-2*I*d*(c+d*x)^3*polylog(2,exp(2*I*(a+b*x)))/b^2+3*d^2*(c+d*x)^2*polylog(3,exp(2*I*(a+b*x)))/b^3+3*I*d^3*(c+d*x)*polylog(4,exp(2*I*(a+b*x)))/b^4-3/2*d^4*polylog(5,exp(2*I*(a+b*x)))/b^5],
[(c+d*x)^3*cos(a+b*x)*csc(a+b*x),x,6,-1/4*I*(c+d*x)^4/d+(c+d*x)^3*log(1-exp(2*I*(a+b*x)))/b-3/2*I*d*(c+d*x)^2*polylog(2,exp(2*I*(a+b*x)))/b^2+3/2*d^2*(c+d*x)*polylog(3,exp(2*I*(a+b*x)))/b^3+3/4*I*d^3*polylog(4,exp(2*I*(a+b*x)))/b^4],
[(c+d*x)^2*cos(a+b*x)*csc(a+b*x),x,5,-1/3*I*(c+d*x)^3/d+(c+d*x)^2*log(1-exp(2*I*(a+b*x)))/b-I*d*(c+d*x)*polylog(2,exp(2*I*(a+b*x)))/b^2+1/2*d^2*polylog(3,exp(2*I*(a+b*x)))/b^3],
[(c+d*x)*cos(a+b*x)*csc(a+b*x),x,4,-1/2*I*(c+d*x)^2/d+(c+d*x)*log(1-exp(2*I*(a+b*x)))/b-1/2*I*d*polylog(2,exp(2*I*(a+b*x)))/b^2],
[cos(a+b*x)*csc(a+b*x)/(c+d*x),x,0,Unintegrable(cot(a+b*x)/(c+d*x),x)],
[cos(a+b*x)*csc(a+b*x)/(c+d*x)^2,x,0,Unintegrable(cot(a+b*x)/(c+d*x)^2,x)],
[(c+d*x)^m*cos(a+b*x)*csc(a+b*x)^2,x,0,CannotIntegrate((c+d*x)^m*cot(a+b*x)*csc(a+b*x),x)],
[(c+d*x)^4*cos(a+b*x)*csc(a+b*x)^2,x,10,-8*d*(c+d*x)^3*arctanh(exp(I*(a+b*x)))/b^2-(c+d*x)^4*csc(a+b*x)/b+12*I*d^2*(c+d*x)^2*polylog(2,-exp(I*(a+b*x)))/b^3-12*I*d^2*(c+d*x)^2*polylog(2,exp(I*(a+b*x)))/b^3-24*d^3*(c+d*x)*polylog(3,-exp(I*(a+b*x)))/b^4+24*d^3*(c+d*x)*polylog(3,exp(I*(a+b*x)))/b^4-24*I*d^4*polylog(4,-exp(I*(a+b*x)))/b^5+24*I*d^4*polylog(4,exp(I*(a+b*x)))/b^5],
[(c+d*x)^3*cos(a+b*x)*csc(a+b*x)^2,x,8,-6*d*(c+d*x)^2*arctanh(exp(I*(a+b*x)))/b^2-(c+d*x)^3*csc(a+b*x)/b+6*I*d^2*(c+d*x)*polylog(2,-exp(I*(a+b*x)))/b^3-6*I*d^2*(c+d*x)*polylog(2,exp(I*(a+b*x)))/b^3-6*d^3*polylog(3,-exp(I*(a+b*x)))/b^4+6*d^3*polylog(3,exp(I*(a+b*x)))/b^4],
[(c+d*x)^2*cos(a+b*x)*csc(a+b*x)^2,x,6,-4*d*(c+d*x)*arctanh(exp(I*(a+b*x)))/b^2-(c+d*x)^2*csc(a+b*x)/b+2*I*d^2*polylog(2,-exp(I*(a+b*x)))/b^3-2*I*d^2*polylog(2,exp(I*(a+b*x)))/b^3],
[(c+d*x)*cos(a+b*x)*csc(a+b*x)^2,x,2,-d*arctanh(cos(a+b*x))/b^2-(c+d*x)*csc(a+b*x)/b],
[cos(a+b*x)*csc(a+b*x)^2/(c+d*x),x,0,CannotIntegrate(cot(a+b*x)*csc(a+b*x)/(c+d*x),x)],
[cos(a+b*x)*csc(a+b*x)^2/(c+d*x)^2,x,0,CannotIntegrate(cot(a+b*x)*csc(a+b*x)/(c+d*x)^2,x)],
[(c+d*x)^m*cos(a+b*x)*csc(a+b*x)^3,x,0,CannotIntegrate((c+d*x)^m*cot(a+b*x)*csc(a+b*x)^2,x)],
[(c+d*x)^4*cos(a+b*x)*csc(a+b*x)^3,x,7,-2*I*d*(c+d*x)^3/b^2-2*d*(c+d*x)^3*cot(a+b*x)/b^2-1/2*(c+d*x)^4*csc(a+b*x)^2/b+6*d^2*(c+d*x)^2*log(1-exp(2*I*(a+b*x)))/b^3-6*I*d^3*(c+d*x)*polylog(2,exp(2*I*(a+b*x)))/b^4+3*d^4*polylog(3,exp(2*I*(a+b*x)))/b^5],
[(c+d*x)^3*cos(a+b*x)*csc(a+b*x)^3,x,6,-3/2*I*d*(c+d*x)^2/b^2-3/2*d*(c+d*x)^2*cot(a+b*x)/b^2-1/2*(c+d*x)^3*csc(a+b*x)^2/b+3*d^2*(c+d*x)*log(1-exp(2*I*(a+b*x)))/b^3-3/2*I*d^3*polylog(2,exp(2*I*(a+b*x)))/b^4],
[(c+d*x)^2*cos(a+b*x)*csc(a+b*x)^3,x,3,-d*(c+d*x)*cot(a+b*x)/b^2-1/2*(c+d*x)^2*csc(a+b*x)^2/b+d^2*log(sin(a+b*x))/b^3],
[(c+d*x)*cos(a+b*x)*csc(a+b*x)^3,x,3,-1/2*d*cot(a+b*x)/b^2-1/2*(c+d*x)*csc(a+b*x)^2/b],
[cos(a+b*x)*csc(a+b*x)^3/(c+d*x),x,0,CannotIntegrate(cot(a+b*x)*csc(a+b*x)^2/(c+d*x),x)],
[cos(a+b*x)*csc(a+b*x)^3/(c+d*x)^2,x,0,CannotIntegrate(cot(a+b*x)*csc(a+b*x)^2/(c+d*x)^2,x)],

# Integrands of the form (c+d x)^(m/2) Cos[a+b x] Sin[a+b x]^p

# p>0
[(c+d*x)^(5/2)*cos(a+b*x)*sin(a+b*x),x,10,-1/4*(c+d*x)^(5/2)*cos(2*a+2*b*x)/b+5/16*d*(c+d*x)^(3/2)*sin(2*a+2*b*x)/b^2-15/128*d^(5/2)*cos(2*a-2*b*c/d)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(Pi)/b^(7/2)+15/128*d^(5/2)*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(Pi)/b^(7/2)+15/64*d^2*cos(2*a+2*b*x)*sqrt(c+d*x)/b^3],
[(c+d*x)^(3/2)*cos(a+b*x)*sin(a+b*x),x,9,-1/4*(c+d*x)^(3/2)*cos(2*a+2*b*x)/b-3/32*d^(3/2)*cos(2*a-2*b*c/d)*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(Pi)/b^(5/2)-3/32*d^(3/2)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(Pi)/b^(5/2)+3/16*d*sin(2*a+2*b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(1/2)*cos(a+b*x)*sin(a+b*x),x,8,1/8*cos(2*a-2*b*c/d)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(d)*sqrt(Pi)/b^(3/2)-1/8*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(d)*sqrt(Pi)/b^(3/2)-1/4*cos(2*a+2*b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(1/2)*cos(a+b*x)*sin(a+b*x),x,8,1/8*cos(2*a-2*b*c/d)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(d)*sqrt(Pi)/b^(3/2)-1/8*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(d)*sqrt(Pi)/b^(3/2)-1/4*cos(2*a+2*b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(3/2)*cos(a+b*x)*sin(a+b*x),x,9,-1/4*(c+d*x)^(3/2)*cos(2*a+2*b*x)/b-3/32*d^(3/2)*cos(2*a-2*b*c/d)*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(Pi)/b^(5/2)-3/32*d^(3/2)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(Pi)/b^(5/2)+3/16*d*sin(2*a+2*b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(5/2)*cos(a+b*x)*sin(a+b*x),x,10,-1/4*(c+d*x)^(5/2)*cos(2*a+2*b*x)/b+5/16*d*(c+d*x)^(3/2)*sin(2*a+2*b*x)/b^2-15/128*d^(5/2)*cos(2*a-2*b*c/d)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(Pi)/b^(7/2)+15/128*d^(5/2)*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(Pi)/b^(7/2)+15/64*d^2*cos(2*a+2*b*x)*sqrt(c+d*x)/b^3],
[(c+d*x)^(5/2)*cos(a+b*x)*sin(a+b*x)^2,x,18,5/8*d*(c+d*x)^(3/2)*cos(a+b*x)/b^2-5/72*d*(c+d*x)^(3/2)*cos(3*a+3*b*x)/b^2+1/4*(c+d*x)^(5/2)*sin(a+b*x)/b-1/12*(c+d*x)^(5/2)*sin(3*a+3*b*x)/b-5/144*d^(5/2)*cos(3*a-3*b*c/d)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/6*Pi)/b^(7/2)-5/144*d^(5/2)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(1/6*Pi)/b^(7/2)+15/16*d^(5/2)*cos(a-b*c/d)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(7/2)+15/16*d^(5/2)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(1/2*Pi)/b^(7/2)-15/16*d^2*sin(a+b*x)*sqrt(c+d*x)/b^3+5/144*d^2*sin(3*a+3*b*x)*sqrt(c+d*x)/b^3],
[(c+d*x)^(3/2)*cos(a+b*x)*sin(a+b*x)^2,x,16,1/4*(c+d*x)^(3/2)*sin(a+b*x)/b-1/12*(c+d*x)^(3/2)*sin(3*a+3*b*x)/b+1/24*d^(3/2)*cos(3*a-3*b*c/d)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/6*Pi)/b^(5/2)-1/24*d^(3/2)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(1/6*Pi)/b^(5/2)-3/8*d^(3/2)*cos(a-b*c/d)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(5/2)+3/8*d^(3/2)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(1/2*Pi)/b^(5/2)+3/8*d*cos(a+b*x)*sqrt(c+d*x)/b^2-1/24*d*cos(3*a+3*b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(1/2)*cos(a+b*x)*sin(a+b*x)^2,x,14,1/12*cos(3*a-3*b*c/d)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/6*Pi)/b^(3/2)+1/12*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(d)*sqrt(1/6*Pi)/b^(3/2)-1/4*cos(a-b*c/d)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)-1/4*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)+1/4*sin(a+b*x)*sqrt(c+d*x)/b-1/12*sin(3*a+3*b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(1/2)*cos(a+b*x)*sin(a+b*x)^2,x,14,1/12*cos(3*a-3*b*c/d)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/6*Pi)/b^(3/2)+1/12*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(d)*sqrt(1/6*Pi)/b^(3/2)-1/4*cos(a-b*c/d)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)-1/4*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)+1/4*sin(a+b*x)*sqrt(c+d*x)/b-1/12*sin(3*a+3*b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(3/2)*cos(a+b*x)*sin(a+b*x)^2,x,16,1/4*(c+d*x)^(3/2)*sin(a+b*x)/b-1/12*(c+d*x)^(3/2)*sin(3*a+3*b*x)/b+1/24*d^(3/2)*cos(3*a-3*b*c/d)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/6*Pi)/b^(5/2)-1/24*d^(3/2)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(1/6*Pi)/b^(5/2)-3/8*d^(3/2)*cos(a-b*c/d)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(5/2)+3/8*d^(3/2)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(1/2*Pi)/b^(5/2)+3/8*d*cos(a+b*x)*sqrt(c+d*x)/b^2-1/24*d*cos(3*a+3*b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(5/2)*cos(a+b*x)*sin(a+b*x)^2,x,18,5/8*d*(c+d*x)^(3/2)*cos(a+b*x)/b^2-5/72*d*(c+d*x)^(3/2)*cos(3*a+3*b*x)/b^2+1/4*(c+d*x)^(5/2)*sin(a+b*x)/b-1/12*(c+d*x)^(5/2)*sin(3*a+3*b*x)/b-5/144*d^(5/2)*cos(3*a-3*b*c/d)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/6*Pi)/b^(7/2)-5/144*d^(5/2)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(1/6*Pi)/b^(7/2)+15/16*d^(5/2)*cos(a-b*c/d)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(7/2)+15/16*d^(5/2)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(1/2*Pi)/b^(7/2)-15/16*d^2*sin(a+b*x)*sqrt(c+d*x)/b^3+5/144*d^2*sin(3*a+3*b*x)*sqrt(c+d*x)/b^3],
[(c+d*x)^(5/2)*cos(a+b*x)*sin(a+b*x)^3,x,18,-1/8*(c+d*x)^(5/2)*cos(2*a+2*b*x)/b+1/32*(c+d*x)^(5/2)*cos(4*a+4*b*x)/b+5/32*d*(c+d*x)^(3/2)*sin(2*a+2*b*x)/b^2-5/256*d*(c+d*x)^(3/2)*sin(4*a+4*b*x)/b^2+15/4096*d^(5/2)*cos(4*a-4*b*c/d)*FresnelC(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(7/2)-15/4096*d^(5/2)*FresnelS(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(4*a-4*b*c/d)*sqrt(1/2*Pi)/b^(7/2)-15/256*d^(5/2)*cos(2*a-2*b*c/d)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(Pi)/b^(7/2)+15/256*d^(5/2)*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(Pi)/b^(7/2)+15/128*d^2*cos(2*a+2*b*x)*sqrt(c+d*x)/b^3-15/2048*d^2*cos(4*a+4*b*x)*sqrt(c+d*x)/b^3],
[(c+d*x)^(3/2)*cos(a+b*x)*sin(a+b*x)^3,x,16,-1/8*(c+d*x)^(3/2)*cos(2*a+2*b*x)/b+1/32*(c+d*x)^(3/2)*cos(4*a+4*b*x)/b+3/512*d^(3/2)*cos(4*a-4*b*c/d)*FresnelS(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(5/2)+3/512*d^(3/2)*FresnelC(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(4*a-4*b*c/d)*sqrt(1/2*Pi)/b^(5/2)-3/64*d^(3/2)*cos(2*a-2*b*c/d)*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(Pi)/b^(5/2)-3/64*d^(3/2)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(Pi)/b^(5/2)+3/32*d*sin(2*a+2*b*x)*sqrt(c+d*x)/b^2-3/256*d*sin(4*a+4*b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(1/2)*cos(a+b*x)*sin(a+b*x)^3,x,14,-1/64*cos(4*a-4*b*c/d)*FresnelC(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)+1/64*FresnelS(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(4*a-4*b*c/d)*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)+1/16*cos(2*a-2*b*c/d)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(d)*sqrt(Pi)/b^(3/2)-1/16*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(d)*sqrt(Pi)/b^(3/2)-1/8*cos(2*a+2*b*x)*sqrt(c+d*x)/b+1/32*cos(4*a+4*b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(1/2)*cos(a+b*x)*sin(a+b*x)^3,x,14,-1/64*cos(4*a-4*b*c/d)*FresnelC(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)+1/64*FresnelS(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(4*a-4*b*c/d)*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)+1/16*cos(2*a-2*b*c/d)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(d)*sqrt(Pi)/b^(3/2)-1/16*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(d)*sqrt(Pi)/b^(3/2)-1/8*cos(2*a+2*b*x)*sqrt(c+d*x)/b+1/32*cos(4*a+4*b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(3/2)*cos(a+b*x)*sin(a+b*x)^3,x,16,-1/8*(c+d*x)^(3/2)*cos(2*a+2*b*x)/b+1/32*(c+d*x)^(3/2)*cos(4*a+4*b*x)/b+3/512*d^(3/2)*cos(4*a-4*b*c/d)*FresnelS(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(5/2)+3/512*d^(3/2)*FresnelC(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(4*a-4*b*c/d)*sqrt(1/2*Pi)/b^(5/2)-3/64*d^(3/2)*cos(2*a-2*b*c/d)*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(Pi)/b^(5/2)-3/64*d^(3/2)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(Pi)/b^(5/2)+3/32*d*sin(2*a+2*b*x)*sqrt(c+d*x)/b^2-3/256*d*sin(4*a+4*b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(5/2)*cos(a+b*x)*sin(a+b*x)^3,x,18,-1/8*(c+d*x)^(5/2)*cos(2*a+2*b*x)/b+1/32*(c+d*x)^(5/2)*cos(4*a+4*b*x)/b+5/32*d*(c+d*x)^(3/2)*sin(2*a+2*b*x)/b^2-5/256*d*(c+d*x)^(3/2)*sin(4*a+4*b*x)/b^2+15/4096*d^(5/2)*cos(4*a-4*b*c/d)*FresnelC(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(7/2)-15/4096*d^(5/2)*FresnelS(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(4*a-4*b*c/d)*sqrt(1/2*Pi)/b^(7/2)-15/256*d^(5/2)*cos(2*a-2*b*c/d)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(Pi)/b^(7/2)+15/256*d^(5/2)*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(Pi)/b^(7/2)+15/128*d^2*cos(2*a+2*b*x)*sqrt(c+d*x)/b^3-15/2048*d^2*cos(4*a+4*b*x)*sqrt(c+d*x)/b^3],

# p<0

# Integrands of the form (c+d x)^m Cos[a+b x]^2 Sin[a+b x]^p

# Integrands of the form (c+d x)^m Cos[a+b x]^2 Sin[a+b x]^p

# p>0
[(c+d*x)^m*cos(a+b*x)^2*sin(a+b*x),x,8,-1/8*exp(I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)-1/8*(c+d*x)^m*GAMMA(1+m,I*b*(c+d*x)/d)/(b*exp(I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)-1/8*3^(-1-m)*exp(3*I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-3*I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)-1/8*3^(-1-m)*(c+d*x)^m*GAMMA(1+m,3*I*b*(c+d*x)/d)/(b*exp(3*I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)],
[(c+d*x)^4*cos(a+b*x)^2*sin(a+b*x),x,9,-160/27*d^4*cos(a+b*x)/b^5+8/3*d^2*(c+d*x)^2*cos(a+b*x)/b^3-8/81*d^4*cos(a+b*x)^3/b^5+4/9*d^2*(c+d*x)^2*cos(a+b*x)^3/b^3-1/3*(c+d*x)^4*cos(a+b*x)^3/b-160/27*d^3*(c+d*x)*sin(a+b*x)/b^4+8/9*d*(c+d*x)^3*sin(a+b*x)/b^2-8/27*d^3*(c+d*x)*cos(a+b*x)^2*sin(a+b*x)/b^4+4/9*d*(c+d*x)^3*cos(a+b*x)^2*sin(a+b*x)/b^2],
[(c+d*x)^3*cos(a+b*x)^2*sin(a+b*x),x,7,4/3*d^2*(c+d*x)*cos(a+b*x)/b^3+2/9*d^2*(c+d*x)*cos(a+b*x)^3/b^3-1/3*(c+d*x)^3*cos(a+b*x)^3/b-14/9*d^3*sin(a+b*x)/b^4+2/3*d*(c+d*x)^2*sin(a+b*x)/b^2+1/3*d*(c+d*x)^2*cos(a+b*x)^2*sin(a+b*x)/b^2+2/27*d^3*sin(a+b*x)^3/b^4],
[(c+d*x)^2*cos(a+b*x)^2*sin(a+b*x),x,4,4/9*d^2*cos(a+b*x)/b^3+2/27*d^2*cos(a+b*x)^3/b^3-1/3*(c+d*x)^2*cos(a+b*x)^3/b+4/9*d*(c+d*x)*sin(a+b*x)/b^2+2/9*d*(c+d*x)*cos(a+b*x)^2*sin(a+b*x)/b^2],
[(c+d*x)*cos(a+b*x)^2*sin(a+b*x),x,3,-1/3*(c+d*x)*cos(a+b*x)^3/b+1/3*d*sin(a+b*x)/b^2-1/9*d*sin(a+b*x)^3/b^2],
[cos(a+b*x)^2*sin(a+b*x)/(c+d*x),x,8,1/4*cos(a-b*c/d)*Si(b*c/d+b*x)/d+1/4*cos(3*a-3*b*c/d)*Si(3*b*c/d+3*b*x)/d+1/4*Ci(3*b*c/d+3*b*x)*sin(3*a-3*b*c/d)/d+1/4*Ci(b*c/d+b*x)*sin(a-b*c/d)/d],
[cos(a+b*x)^2*sin(a+b*x)/(c+d*x)^2,x,10,3/4*b*Ci(3*b*c/d+3*b*x)*cos(3*a-3*b*c/d)/d^2+1/4*b*Ci(b*c/d+b*x)*cos(a-b*c/d)/d^2-3/4*b*Si(3*b*c/d+3*b*x)*sin(3*a-3*b*c/d)/d^2-1/4*b*Si(b*c/d+b*x)*sin(a-b*c/d)/d^2-1/4*sin(a+b*x)/(d*(c+d*x))-1/4*sin(3*a+3*b*x)/(d*(c+d*x))],
[cos(a+b*x)^2*sin(a+b*x)/(c+d*x)^3,x,12,-1/8*b*cos(a+b*x)/(d^2*(c+d*x))-3/8*b*cos(3*a+3*b*x)/(d^2*(c+d*x))-1/8*b^2*cos(a-b*c/d)*Si(b*c/d+b*x)/d^3-9/8*b^2*cos(3*a-3*b*c/d)*Si(3*b*c/d+3*b*x)/d^3-9/8*b^2*Ci(3*b*c/d+3*b*x)*sin(3*a-3*b*c/d)/d^3-1/8*b^2*Ci(b*c/d+b*x)*sin(a-b*c/d)/d^3-1/8*sin(a+b*x)/(d*(c+d*x)^2)-1/8*sin(3*a+3*b*x)/(d*(c+d*x)^2)],
[cos(a+b*x)^2*sin(a+b*x)/(c+d*x)^4,x,14,-9/8*b^3*Ci(3*b*c/d+3*b*x)*cos(3*a-3*b*c/d)/d^4-1/24*b^3*Ci(b*c/d+b*x)*cos(a-b*c/d)/d^4-1/24*b*cos(a+b*x)/(d^2*(c+d*x)^2)-1/8*b*cos(3*a+3*b*x)/(d^2*(c+d*x)^2)+9/8*b^3*Si(3*b*c/d+3*b*x)*sin(3*a-3*b*c/d)/d^4+1/24*b^3*Si(b*c/d+b*x)*sin(a-b*c/d)/d^4-1/12*sin(a+b*x)/(d*(c+d*x)^3)+1/24*b^2*sin(a+b*x)/(d^3*(c+d*x))-1/12*sin(3*a+3*b*x)/(d*(c+d*x)^3)+3/8*b^2*sin(3*a+3*b*x)/(d^3*(c+d*x))],
[(c+d*x)^m*cos(a+b*x)^2*sin(a+b*x)^2,x,5,1/8*(c+d*x)^(1+m)/(d*(1+m))+I*exp(4*I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-4*I*b*(c+d*x)/d)/(2^(2*(3+m))*b*(-I*b*(c+d*x)/d)^m)-I*(c+d*x)^m*GAMMA(1+m,4*I*b*(c+d*x)/d)/(2^(2*(3+m))*b*exp(4*I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)],
[(c+d*x)^4*cos(a+b*x)^2*sin(a+b*x)^2,x,7,1/40*(c+d*x)^5/d+3/256*d^3*(c+d*x)*cos(4*a+4*b*x)/b^4-1/32*d*(c+d*x)^3*cos(4*a+4*b*x)/b^2-3/1024*d^4*sin(4*a+4*b*x)/b^5+3/128*d^2*(c+d*x)^2*sin(4*a+4*b*x)/b^3-1/32*(c+d*x)^4*sin(4*a+4*b*x)/b],
[(c+d*x)^3*cos(a+b*x)^2*sin(a+b*x)^2,x,6,1/32*(c+d*x)^4/d+3/1024*d^3*cos(4*a+4*b*x)/b^4-3/128*d*(c+d*x)^2*cos(4*a+4*b*x)/b^2+3/256*d^2*(c+d*x)*sin(4*a+4*b*x)/b^3-1/32*(c+d*x)^3*sin(4*a+4*b*x)/b],
[(c+d*x)^2*cos(a+b*x)^2*sin(a+b*x)^2,x,5,1/24*(c+d*x)^3/d-1/64*d*(c+d*x)*cos(4*a+4*b*x)/b^2+1/256*d^2*sin(4*a+4*b*x)/b^3-1/32*(c+d*x)^2*sin(4*a+4*b*x)/b],
[(c+d*x)*cos(a+b*x)^2*sin(a+b*x)^2,x,4,1/16*(c+d*x)^2/d-1/128*d*cos(4*a+4*b*x)/b^2-1/32*(c+d*x)*sin(4*a+4*b*x)/b],
[cos(a+b*x)^2*sin(a+b*x)^2/(c+d*x),x,5,-1/8*Ci(4*b*c/d+4*b*x)*cos(4*a-4*b*c/d)/d+1/8*log(c+d*x)/d+1/8*Si(4*b*c/d+4*b*x)*sin(4*a-4*b*c/d)/d],
[cos(a+b*x)^2*sin(a+b*x)^2/(c+d*x)^2,x,6,(-1/8)/(d*(c+d*x))+1/8*cos(4*a+4*b*x)/(d*(c+d*x))+1/2*b*cos(4*a-4*b*c/d)*Si(4*b*c/d+4*b*x)/d^2+1/2*b*Ci(4*b*c/d+4*b*x)*sin(4*a-4*b*c/d)/d^2],
[cos(a+b*x)^2*sin(a+b*x)^2/(c+d*x)^3,x,7,(-1/16)/(d*(c+d*x)^2)+b^2*Ci(4*b*c/d+4*b*x)*cos(4*a-4*b*c/d)/d^3+1/16*cos(4*a+4*b*x)/(d*(c+d*x)^2)-b^2*Si(4*b*c/d+4*b*x)*sin(4*a-4*b*c/d)/d^3-1/4*b*sin(4*a+4*b*x)/(d^2*(c+d*x))],
[cos(a+b*x)^2*sin(a+b*x)^2/(c+d*x)^4,x,8,(-1/24)/(d*(c+d*x)^3)+1/24*cos(4*a+4*b*x)/(d*(c+d*x)^3)-1/3*b^2*cos(4*a+4*b*x)/(d^3*(c+d*x))-4/3*b^3*cos(4*a-4*b*c/d)*Si(4*b*c/d+4*b*x)/d^4-4/3*b^3*Ci(4*b*c/d+4*b*x)*sin(4*a-4*b*c/d)/d^4-1/12*b*sin(4*a+4*b*x)/(d^2*(c+d*x)^2)],
[(c+d*x)^m*cos(a+b*x)^2*sin(a+b*x)^3,x,11,-1/16*exp(I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)-1/16*(c+d*x)^m*GAMMA(1+m,I*b*(c+d*x)/d)/(b*exp(I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)-1/32*3^(-1-m)*exp(3*I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-3*I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)-1/32*3^(-1-m)*(c+d*x)^m*GAMMA(1+m,3*I*b*(c+d*x)/d)/(b*exp(3*I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)+1/32*5^(-1-m)*exp(5*I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-5*I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)+1/32*5^(-1-m)*(c+d*x)^m*GAMMA(1+m,5*I*b*(c+d*x)/d)/(b*exp(5*I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)],
[(c+d*x)^4*cos(a+b*x)^2*sin(a+b*x)^3,x,17,-3*d^4*cos(a+b*x)/b^5+3/2*d^2*(c+d*x)^2*cos(a+b*x)/b^3-1/8*(c+d*x)^4*cos(a+b*x)/b-1/162*d^4*cos(3*a+3*b*x)/b^5+1/36*d^2*(c+d*x)^2*cos(3*a+3*b*x)/b^3-1/48*(c+d*x)^4*cos(3*a+3*b*x)/b+3/6250*d^4*cos(5*a+5*b*x)/b^5-3/500*d^2*(c+d*x)^2*cos(5*a+5*b*x)/b^3+1/80*(c+d*x)^4*cos(5*a+5*b*x)/b-3*d^3*(c+d*x)*sin(a+b*x)/b^4+1/2*d*(c+d*x)^3*sin(a+b*x)/b^2-1/54*d^3*(c+d*x)*sin(3*a+3*b*x)/b^4+1/36*d*(c+d*x)^3*sin(3*a+3*b*x)/b^2+3/1250*d^3*(c+d*x)*sin(5*a+5*b*x)/b^4-1/100*d*(c+d*x)^3*sin(5*a+5*b*x)/b^2],
[(c+d*x)^3*cos(a+b*x)^2*sin(a+b*x)^3,x,14,3/4*d^2*(c+d*x)*cos(a+b*x)/b^3-1/8*(c+d*x)^3*cos(a+b*x)/b+1/72*d^2*(c+d*x)*cos(3*a+3*b*x)/b^3-1/48*(c+d*x)^3*cos(3*a+3*b*x)/b-3/1000*d^2*(c+d*x)*cos(5*a+5*b*x)/b^3+1/80*(c+d*x)^3*cos(5*a+5*b*x)/b-3/4*d^3*sin(a+b*x)/b^4+3/8*d*(c+d*x)^2*sin(a+b*x)/b^2-1/216*d^3*sin(3*a+3*b*x)/b^4+1/48*d*(c+d*x)^2*sin(3*a+3*b*x)/b^2+3/5000*d^3*sin(5*a+5*b*x)/b^4-3/400*d*(c+d*x)^2*sin(5*a+5*b*x)/b^2],
[(c+d*x)^2*cos(a+b*x)^2*sin(a+b*x)^3,x,11,1/4*d^2*cos(a+b*x)/b^3-1/8*(c+d*x)^2*cos(a+b*x)/b+1/216*d^2*cos(3*a+3*b*x)/b^3-1/48*(c+d*x)^2*cos(3*a+3*b*x)/b-1/1000*d^2*cos(5*a+5*b*x)/b^3+1/80*(c+d*x)^2*cos(5*a+5*b*x)/b+1/4*d*(c+d*x)*sin(a+b*x)/b^2+1/72*d*(c+d*x)*sin(3*a+3*b*x)/b^2-1/200*d*(c+d*x)*sin(5*a+5*b*x)/b^2],
[(c+d*x)*cos(a+b*x)^2*sin(a+b*x)^3,x,8,-1/8*(c+d*x)*cos(a+b*x)/b-1/48*(c+d*x)*cos(3*a+3*b*x)/b+1/80*(c+d*x)*cos(5*a+5*b*x)/b+1/8*d*sin(a+b*x)/b^2+1/144*d*sin(3*a+3*b*x)/b^2-1/400*d*sin(5*a+5*b*x)/b^2],
[cos(a+b*x)^2*sin(a+b*x)^3/(c+d*x),x,11,1/8*cos(a-b*c/d)*Si(b*c/d+b*x)/d+1/16*cos(3*a-3*b*c/d)*Si(3*b*c/d+3*b*x)/d-1/16*cos(5*a-5*b*c/d)*Si(5*b*c/d+5*b*x)/d-1/16*Ci(5*b*c/d+5*b*x)*sin(5*a-5*b*c/d)/d+1/16*Ci(3*b*c/d+3*b*x)*sin(3*a-3*b*c/d)/d+1/8*Ci(b*c/d+b*x)*sin(a-b*c/d)/d],
[cos(a+b*x)^2*sin(a+b*x)^3/(c+d*x)^2,x,14,-5/16*b*Ci(5*b*c/d+5*b*x)*cos(5*a-5*b*c/d)/d^2+3/16*b*Ci(3*b*c/d+3*b*x)*cos(3*a-3*b*c/d)/d^2+1/8*b*Ci(b*c/d+b*x)*cos(a-b*c/d)/d^2+5/16*b*Si(5*b*c/d+5*b*x)*sin(5*a-5*b*c/d)/d^2-3/16*b*Si(3*b*c/d+3*b*x)*sin(3*a-3*b*c/d)/d^2-1/8*b*Si(b*c/d+b*x)*sin(a-b*c/d)/d^2-1/8*sin(a+b*x)/(d*(c+d*x))-1/16*sin(3*a+3*b*x)/(d*(c+d*x))+1/16*sin(5*a+5*b*x)/(d*(c+d*x))],
[cos(a+b*x)^2*sin(a+b*x)^3/(c+d*x)^3,x,17,-1/16*b*cos(a+b*x)/(d^2*(c+d*x))-3/32*b*cos(3*a+3*b*x)/(d^2*(c+d*x))+5/32*b*cos(5*a+5*b*x)/(d^2*(c+d*x))-1/16*b^2*cos(a-b*c/d)*Si(b*c/d+b*x)/d^3-9/32*b^2*cos(3*a-3*b*c/d)*Si(3*b*c/d+3*b*x)/d^3+25/32*b^2*cos(5*a-5*b*c/d)*Si(5*b*c/d+5*b*x)/d^3+25/32*b^2*Ci(5*b*c/d+5*b*x)*sin(5*a-5*b*c/d)/d^3-9/32*b^2*Ci(3*b*c/d+3*b*x)*sin(3*a-3*b*c/d)/d^3-1/16*b^2*Ci(b*c/d+b*x)*sin(a-b*c/d)/d^3-1/16*sin(a+b*x)/(d*(c+d*x)^2)-1/32*sin(3*a+3*b*x)/(d*(c+d*x)^2)+1/32*sin(5*a+5*b*x)/(d*(c+d*x)^2)],
[cos(a+b*x)^2*sin(a+b*x)^3/(c+d*x)^4,x,20,125/96*b^3*Ci(5*b*c/d+5*b*x)*cos(5*a-5*b*c/d)/d^4-9/32*b^3*Ci(3*b*c/d+3*b*x)*cos(3*a-3*b*c/d)/d^4-1/48*b^3*Ci(b*c/d+b*x)*cos(a-b*c/d)/d^4-1/48*b*cos(a+b*x)/(d^2*(c+d*x)^2)-1/32*b*cos(3*a+3*b*x)/(d^2*(c+d*x)^2)+5/96*b*cos(5*a+5*b*x)/(d^2*(c+d*x)^2)-125/96*b^3*Si(5*b*c/d+5*b*x)*sin(5*a-5*b*c/d)/d^4+9/32*b^3*Si(3*b*c/d+3*b*x)*sin(3*a-3*b*c/d)/d^4+1/48*b^3*Si(b*c/d+b*x)*sin(a-b*c/d)/d^4-1/24*sin(a+b*x)/(d*(c+d*x)^3)+1/48*b^2*sin(a+b*x)/(d^3*(c+d*x))-1/48*sin(3*a+3*b*x)/(d*(c+d*x)^3)+3/32*b^2*sin(3*a+3*b*x)/(d^3*(c+d*x))+1/48*sin(5*a+5*b*x)/(d*(c+d*x)^3)-25/96*b^2*sin(5*a+5*b*x)/(d^3*(c+d*x))],

# p<0
[(c+d*x)^m*cos(a+b*x)*cot(a+b*x),x,4,1/2*exp(I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)+1/2*(c+d*x)^m*GAMMA(1+m,I*b*(c+d*x)/d)/(b*exp(I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)+Unintegrable((c+d*x)^m*csc(a+b*x),x)],
[(c+d*x)^4*cos(a+b*x)*cot(a+b*x),x,17,-2*(c+d*x)^4*arctanh(exp(I*(a+b*x)))/b+24*d^4*cos(a+b*x)/b^5-12*d^2*(c+d*x)^2*cos(a+b*x)/b^3+(c+d*x)^4*cos(a+b*x)/b+4*I*d*(c+d*x)^3*polylog(2,-exp(I*(a+b*x)))/b^2-4*I*d*(c+d*x)^3*polylog(2,exp(I*(a+b*x)))/b^2-12*d^2*(c+d*x)^2*polylog(3,-exp(I*(a+b*x)))/b^3+12*d^2*(c+d*x)^2*polylog(3,exp(I*(a+b*x)))/b^3-24*I*d^3*(c+d*x)*polylog(4,-exp(I*(a+b*x)))/b^4+24*I*d^3*(c+d*x)*polylog(4,exp(I*(a+b*x)))/b^4+24*d^4*polylog(5,-exp(I*(a+b*x)))/b^5-24*d^4*polylog(5,exp(I*(a+b*x)))/b^5+24*d^3*(c+d*x)*sin(a+b*x)/b^4-4*d*(c+d*x)^3*sin(a+b*x)/b^2],
[(c+d*x)^3*cos(a+b*x)*cot(a+b*x),x,14,-2*(c+d*x)^3*arctanh(exp(I*(a+b*x)))/b-6*d^2*(c+d*x)*cos(a+b*x)/b^3+(c+d*x)^3*cos(a+b*x)/b+3*I*d*(c+d*x)^2*polylog(2,-exp(I*(a+b*x)))/b^2-3*I*d*(c+d*x)^2*polylog(2,exp(I*(a+b*x)))/b^2-6*d^2*(c+d*x)*polylog(3,-exp(I*(a+b*x)))/b^3+6*d^2*(c+d*x)*polylog(3,exp(I*(a+b*x)))/b^3-6*I*d^3*polylog(4,-exp(I*(a+b*x)))/b^4+6*I*d^3*polylog(4,exp(I*(a+b*x)))/b^4+6*d^3*sin(a+b*x)/b^4-3*d*(c+d*x)^2*sin(a+b*x)/b^2],
[(c+d*x)^2*cos(a+b*x)*cot(a+b*x),x,11,-2*(c+d*x)^2*arctanh(exp(I*(a+b*x)))/b-2*d^2*cos(a+b*x)/b^3+(c+d*x)^2*cos(a+b*x)/b+2*I*d*(c+d*x)*polylog(2,-exp(I*(a+b*x)))/b^2-2*I*d*(c+d*x)*polylog(2,exp(I*(a+b*x)))/b^2-2*d^2*polylog(3,-exp(I*(a+b*x)))/b^3+2*d^2*polylog(3,exp(I*(a+b*x)))/b^3-2*d*(c+d*x)*sin(a+b*x)/b^2],
[(c+d*x)*cos(a+b*x)*cot(a+b*x),x,8,-2*(c+d*x)*arctanh(exp(I*(a+b*x)))/b+(c+d*x)*cos(a+b*x)/b+I*d*polylog(2,-exp(I*(a+b*x)))/b^2-I*d*polylog(2,exp(I*(a+b*x)))/b^2-d*sin(a+b*x)/b^2],
[cos(a+b*x)*cot(a+b*x)/(c+d*x),x,4,-cos(a-b*c/d)*Si(b*c/d+b*x)/d-Ci(b*c/d+b*x)*sin(a-b*c/d)/d+Unintegrable(csc(a+b*x)/(c+d*x),x)],
[cos(a+b*x)*cot(a+b*x)/(c+d*x)^2,x,5,-b*Ci(b*c/d+b*x)*cos(a-b*c/d)/d^2+b*Si(b*c/d+b*x)*sin(a-b*c/d)/d^2+sin(a+b*x)/(d*(c+d*x))+Unintegrable(csc(a+b*x)/(c+d*x)^2,x)],
[(c+d*x)^m*cot(a+b*x)^2,x,0,Unintegrable((c+d*x)^m*cot(a+b*x)^2,x)],
[(c+d*x)^4*cot(a+b*x)^2,x,8,-I*(c+d*x)^4/b-1/5*(c+d*x)^5/d-(c+d*x)^4*cot(a+b*x)/b+4*d*(c+d*x)^3*log(1-exp(2*I*(a+b*x)))/b^2-6*I*d^2*(c+d*x)^2*polylog(2,exp(2*I*(a+b*x)))/b^3+6*d^3*(c+d*x)*polylog(3,exp(2*I*(a+b*x)))/b^4+3*I*d^4*polylog(4,exp(2*I*(a+b*x)))/b^5],
[(c+d*x)^3*cot(a+b*x)^2,x,7,-I*(c+d*x)^3/b-1/4*(c+d*x)^4/d-(c+d*x)^3*cot(a+b*x)/b+3*d*(c+d*x)^2*log(1-exp(2*I*(a+b*x)))/b^2-3*I*d^2*(c+d*x)*polylog(2,exp(2*I*(a+b*x)))/b^3+3/2*d^3*polylog(3,exp(2*I*(a+b*x)))/b^4],
[(c+d*x)^2*cot(a+b*x)^2,x,6,-I*(c+d*x)^2/b-1/3*(c+d*x)^3/d-(c+d*x)^2*cot(a+b*x)/b+2*d*(c+d*x)*log(1-exp(2*I*(a+b*x)))/b^2-I*d^2*polylog(2,exp(2*I*(a+b*x)))/b^3],
[(c+d*x)*cot(a+b*x)^2,x,3,-c*x-1/2*d*x^2-(c+d*x)*cot(a+b*x)/b+d*log(sin(a+b*x))/b^2],
[cot(a+b*x)^2/(c+d*x),x,0,Unintegrable(cot(a+b*x)^2/(c+d*x),x)],
[cot(a+b*x)^2/(c+d*x)^2,x,0,Unintegrable(cot(a+b*x)^2/(c+d*x)^2,x)],
[(c+d*x)^m*cot(a+b*x)^2*csc(a+b*x),x,1,-Unintegrable((c+d*x)^m*csc(a+b*x),x)+Unintegrable((c+d*x)^m*csc(a+b*x)^3,x)],
[(c+d*x)^4*cot(a+b*x)^2*csc(a+b*x),x,31,-12*d^2*(c+d*x)^2*arctanh(exp(I*(a+b*x)))/b^3+(c+d*x)^4*arctanh(exp(I*(a+b*x)))/b-2*d*(c+d*x)^3*csc(a+b*x)/b^2-1/2*(c+d*x)^4*cot(a+b*x)*csc(a+b*x)/b+12*I*d^3*(c+d*x)*polylog(2,-exp(I*(a+b*x)))/b^4-2*I*d*(c+d*x)^3*polylog(2,-exp(I*(a+b*x)))/b^2-12*I*d^3*(c+d*x)*polylog(2,exp(I*(a+b*x)))/b^4+2*I*d*(c+d*x)^3*polylog(2,exp(I*(a+b*x)))/b^2-12*d^4*polylog(3,-exp(I*(a+b*x)))/b^5+6*d^2*(c+d*x)^2*polylog(3,-exp(I*(a+b*x)))/b^3+12*d^4*polylog(3,exp(I*(a+b*x)))/b^5-6*d^2*(c+d*x)^2*polylog(3,exp(I*(a+b*x)))/b^3+12*I*d^3*(c+d*x)*polylog(4,-exp(I*(a+b*x)))/b^4-12*I*d^3*(c+d*x)*polylog(4,exp(I*(a+b*x)))/b^4-12*d^4*polylog(5,-exp(I*(a+b*x)))/b^5+12*d^4*polylog(5,exp(I*(a+b*x)))/b^5],
[(c+d*x)^3*cot(a+b*x)^2*csc(a+b*x),x,25,-6*d^2*(c+d*x)*arctanh(exp(I*(a+b*x)))/b^3+(c+d*x)^3*arctanh(exp(I*(a+b*x)))/b-3/2*d*(c+d*x)^2*csc(a+b*x)/b^2-1/2*(c+d*x)^3*cot(a+b*x)*csc(a+b*x)/b+3*I*d^3*polylog(2,-exp(I*(a+b*x)))/b^4-3/2*I*d*(c+d*x)^2*polylog(2,-exp(I*(a+b*x)))/b^2-3*I*d^3*polylog(2,exp(I*(a+b*x)))/b^4+3/2*I*d*(c+d*x)^2*polylog(2,exp(I*(a+b*x)))/b^2+3*d^2*(c+d*x)*polylog(3,-exp(I*(a+b*x)))/b^3-3*d^2*(c+d*x)*polylog(3,exp(I*(a+b*x)))/b^3+3*I*d^3*polylog(4,-exp(I*(a+b*x)))/b^4-3*I*d^3*polylog(4,exp(I*(a+b*x)))/b^4],
[(c+d*x)^2*cot(a+b*x)^2*csc(a+b*x),x,17,(c+d*x)^2*arctanh(exp(I*(a+b*x)))/b-d^2*arctanh(cos(a+b*x))/b^3-d*(c+d*x)*csc(a+b*x)/b^2-1/2*(c+d*x)^2*cot(a+b*x)*csc(a+b*x)/b-I*d*(c+d*x)*polylog(2,-exp(I*(a+b*x)))/b^2+I*d*(c+d*x)*polylog(2,exp(I*(a+b*x)))/b^2+d^2*polylog(3,-exp(I*(a+b*x)))/b^3-d^2*polylog(3,exp(I*(a+b*x)))/b^3],
[(c+d*x)*cot(a+b*x)^2*csc(a+b*x),x,12,(c+d*x)*arctanh(exp(I*(a+b*x)))/b-1/2*d*csc(a+b*x)/b^2-1/2*(c+d*x)*cot(a+b*x)*csc(a+b*x)/b-1/2*I*d*polylog(2,-exp(I*(a+b*x)))/b^2+1/2*I*d*polylog(2,exp(I*(a+b*x)))/b^2],
[cot(a+b*x)^2*csc(a+b*x)/(c+d*x),x,1,-Unintegrable(csc(a+b*x)/(c+d*x),x)+Unintegrable(csc(a+b*x)^3/(c+d*x),x)],
[cot(a+b*x)^2*csc(a+b*x)/(c+d*x)^2,x,1,-Unintegrable(csc(a+b*x)/(c+d*x)^2,x)+Unintegrable(csc(a+b*x)^3/(c+d*x)^2,x)],

# Integrands of the form (c+d x)^(m/2) Cos[a+b x]^2 Sin[a+b x]^p

# p>0
[(c+d*x)^(5/2)*cos(a+b*x)^2*sin(a+b*x),x,18,-1/4*(c+d*x)^(5/2)*cos(a+b*x)/b-1/12*(c+d*x)^(5/2)*cos(3*a+3*b*x)/b+5/8*d*(c+d*x)^(3/2)*sin(a+b*x)/b^2+5/72*d*(c+d*x)^(3/2)*sin(3*a+3*b*x)/b^2-5/144*d^(5/2)*cos(3*a-3*b*c/d)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/6*Pi)/b^(7/2)+5/144*d^(5/2)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(1/6*Pi)/b^(7/2)-15/16*d^(5/2)*cos(a-b*c/d)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(7/2)+15/16*d^(5/2)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(1/2*Pi)/b^(7/2)+15/16*d^2*cos(a+b*x)*sqrt(c+d*x)/b^3+5/144*d^2*cos(3*a+3*b*x)*sqrt(c+d*x)/b^3],
[(c+d*x)^(3/2)*cos(a+b*x)^2*sin(a+b*x),x,16,-1/4*(c+d*x)^(3/2)*cos(a+b*x)/b-1/12*(c+d*x)^(3/2)*cos(3*a+3*b*x)/b-1/24*d^(3/2)*cos(3*a-3*b*c/d)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/6*Pi)/b^(5/2)-1/24*d^(3/2)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(1/6*Pi)/b^(5/2)-3/8*d^(3/2)*cos(a-b*c/d)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(5/2)-3/8*d^(3/2)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(1/2*Pi)/b^(5/2)+3/8*d*sin(a+b*x)*sqrt(c+d*x)/b^2+1/24*d*sin(3*a+3*b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(1/2)*cos(a+b*x)^2*sin(a+b*x),x,14,1/12*cos(3*a-3*b*c/d)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/6*Pi)/b^(3/2)-1/12*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(d)*sqrt(1/6*Pi)/b^(3/2)+1/4*cos(a-b*c/d)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)-1/4*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)-1/4*cos(a+b*x)*sqrt(c+d*x)/b-1/12*cos(3*a+3*b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(1/2)*cos(a+b*x)^2*sin(a+b*x),x,14,1/12*cos(3*a-3*b*c/d)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/6*Pi)/b^(3/2)-1/12*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(d)*sqrt(1/6*Pi)/b^(3/2)+1/4*cos(a-b*c/d)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)-1/4*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)-1/4*cos(a+b*x)*sqrt(c+d*x)/b-1/12*cos(3*a+3*b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(3/2)*cos(a+b*x)^2*sin(a+b*x),x,16,-1/4*(c+d*x)^(3/2)*cos(a+b*x)/b-1/12*(c+d*x)^(3/2)*cos(3*a+3*b*x)/b-1/24*d^(3/2)*cos(3*a-3*b*c/d)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/6*Pi)/b^(5/2)-1/24*d^(3/2)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(1/6*Pi)/b^(5/2)-3/8*d^(3/2)*cos(a-b*c/d)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(5/2)-3/8*d^(3/2)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(1/2*Pi)/b^(5/2)+3/8*d*sin(a+b*x)*sqrt(c+d*x)/b^2+1/24*d*sin(3*a+3*b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(5/2)*cos(a+b*x)^2*sin(a+b*x),x,18,-1/4*(c+d*x)^(5/2)*cos(a+b*x)/b-1/12*(c+d*x)^(5/2)*cos(3*a+3*b*x)/b+5/8*d*(c+d*x)^(3/2)*sin(a+b*x)/b^2+5/72*d*(c+d*x)^(3/2)*sin(3*a+3*b*x)/b^2-5/144*d^(5/2)*cos(3*a-3*b*c/d)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/6*Pi)/b^(7/2)+5/144*d^(5/2)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(1/6*Pi)/b^(7/2)-15/16*d^(5/2)*cos(a-b*c/d)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(7/2)+15/16*d^(5/2)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(1/2*Pi)/b^(7/2)+15/16*d^2*cos(a+b*x)*sqrt(c+d*x)/b^3+5/144*d^2*cos(3*a+3*b*x)*sqrt(c+d*x)/b^3],
[(c+d*x)^(5/2)*cos(a+b*x)^2*sin(a+b*x)^2,x,10,1/28*(c+d*x)^(7/2)/d-5/256*d*(c+d*x)^(3/2)*cos(4*a+4*b*x)/b^2-1/32*(c+d*x)^(5/2)*sin(4*a+4*b*x)/b-15/4096*d^(5/2)*cos(4*a-4*b*c/d)*FresnelS(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(7/2)-15/4096*d^(5/2)*FresnelC(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(4*a-4*b*c/d)*sqrt(1/2*Pi)/b^(7/2)+15/2048*d^2*sin(4*a+4*b*x)*sqrt(c+d*x)/b^3],
[(c+d*x)^(3/2)*cos(a+b*x)^2*sin(a+b*x)^2,x,9,1/20*(c+d*x)^(5/2)/d-1/32*(c+d*x)^(3/2)*sin(4*a+4*b*x)/b+3/512*d^(3/2)*cos(4*a-4*b*c/d)*FresnelC(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(5/2)-3/512*d^(3/2)*FresnelS(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(4*a-4*b*c/d)*sqrt(1/2*Pi)/b^(5/2)-3/256*d*cos(4*a+4*b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(1/2)*cos(a+b*x)^2*sin(a+b*x)^2,x,8,1/12*(c+d*x)^(3/2)/d+1/64*cos(4*a-4*b*c/d)*FresnelS(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)+1/64*FresnelC(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(4*a-4*b*c/d)*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)-1/32*sin(4*a+4*b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(1/2)*cos(a+b*x)^2*sin(a+b*x)^2,x,8,1/12*(c+d*x)^(3/2)/d+1/64*cos(4*a-4*b*c/d)*FresnelS(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)+1/64*FresnelC(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(4*a-4*b*c/d)*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)-1/32*sin(4*a+4*b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(3/2)*cos(a+b*x)^2*sin(a+b*x)^2,x,9,1/20*(c+d*x)^(5/2)/d-1/32*(c+d*x)^(3/2)*sin(4*a+4*b*x)/b+3/512*d^(3/2)*cos(4*a-4*b*c/d)*FresnelC(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(5/2)-3/512*d^(3/2)*FresnelS(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(4*a-4*b*c/d)*sqrt(1/2*Pi)/b^(5/2)-3/256*d*cos(4*a+4*b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(5/2)*cos(a+b*x)^2*sin(a+b*x)^2,x,10,1/28*(c+d*x)^(7/2)/d-5/256*d*(c+d*x)^(3/2)*cos(4*a+4*b*x)/b^2-1/32*(c+d*x)^(5/2)*sin(4*a+4*b*x)/b-15/4096*d^(5/2)*cos(4*a-4*b*c/d)*FresnelS(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(7/2)-15/4096*d^(5/2)*FresnelC(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(4*a-4*b*c/d)*sqrt(1/2*Pi)/b^(7/2)+15/2048*d^2*sin(4*a+4*b*x)*sqrt(c+d*x)/b^3],
[(c+d*x)^(5/2)*cos(a+b*x)^2*sin(a+b*x)^3,x,26,-1/8*(c+d*x)^(5/2)*cos(a+b*x)/b-1/48*(c+d*x)^(5/2)*cos(3*a+3*b*x)/b+1/80*(c+d*x)^(5/2)*cos(5*a+5*b*x)/b+5/16*d*(c+d*x)^(3/2)*sin(a+b*x)/b^2+5/288*d*(c+d*x)^(3/2)*sin(3*a+3*b*x)/b^2-1/160*d*(c+d*x)^(3/2)*sin(5*a+5*b*x)/b^2+3/1600*d^(5/2)*cos(5*a-5*b*c/d)*FresnelC(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/10*Pi)/b^(7/2)-3/1600*d^(5/2)*FresnelS(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sin(5*a-5*b*c/d)*sqrt(1/10*Pi)/b^(7/2)-5/576*d^(5/2)*cos(3*a-3*b*c/d)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/6*Pi)/b^(7/2)+5/576*d^(5/2)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(1/6*Pi)/b^(7/2)-15/32*d^(5/2)*cos(a-b*c/d)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(7/2)+15/32*d^(5/2)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(1/2*Pi)/b^(7/2)+15/32*d^2*cos(a+b*x)*sqrt(c+d*x)/b^3+5/576*d^2*cos(3*a+3*b*x)*sqrt(c+d*x)/b^3-3/1600*d^2*cos(5*a+5*b*x)*sqrt(c+d*x)/b^3],
[(c+d*x)^(3/2)*cos(a+b*x)^2*sin(a+b*x)^3,x,23,-1/8*(c+d*x)^(3/2)*cos(a+b*x)/b-1/48*(c+d*x)^(3/2)*cos(3*a+3*b*x)/b+1/80*(c+d*x)^(3/2)*cos(5*a+5*b*x)/b+3/800*d^(3/2)*cos(5*a-5*b*c/d)*FresnelS(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/10*Pi)/b^(5/2)+3/800*d^(3/2)*FresnelC(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sin(5*a-5*b*c/d)*sqrt(1/10*Pi)/b^(5/2)-1/96*d^(3/2)*cos(3*a-3*b*c/d)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/6*Pi)/b^(5/2)-1/96*d^(3/2)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(1/6*Pi)/b^(5/2)-3/16*d^(3/2)*cos(a-b*c/d)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(5/2)-3/16*d^(3/2)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(1/2*Pi)/b^(5/2)+3/16*d*sin(a+b*x)*sqrt(c+d*x)/b^2+1/96*d*sin(3*a+3*b*x)*sqrt(c+d*x)/b^2-3/800*d*sin(5*a+5*b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(1/2)*cos(a+b*x)^2*sin(a+b*x)^3,x,20,-1/80*cos(5*a-5*b*c/d)*FresnelC(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/10*Pi)/b^(3/2)+1/80*FresnelS(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sin(5*a-5*b*c/d)*sqrt(d)*sqrt(1/10*Pi)/b^(3/2)+1/48*cos(3*a-3*b*c/d)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/6*Pi)/b^(3/2)-1/48*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(d)*sqrt(1/6*Pi)/b^(3/2)+1/8*cos(a-b*c/d)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)-1/8*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)-1/8*cos(a+b*x)*sqrt(c+d*x)/b-1/48*cos(3*a+3*b*x)*sqrt(c+d*x)/b+1/80*cos(5*a+5*b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(1/2)*cos(a+b*x)^2*sin(a+b*x)^3,x,20,-1/80*cos(5*a-5*b*c/d)*FresnelC(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/10*Pi)/b^(3/2)+1/80*FresnelS(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sin(5*a-5*b*c/d)*sqrt(d)*sqrt(1/10*Pi)/b^(3/2)+1/48*cos(3*a-3*b*c/d)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/6*Pi)/b^(3/2)-1/48*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(d)*sqrt(1/6*Pi)/b^(3/2)+1/8*cos(a-b*c/d)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)-1/8*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)-1/8*cos(a+b*x)*sqrt(c+d*x)/b-1/48*cos(3*a+3*b*x)*sqrt(c+d*x)/b+1/80*cos(5*a+5*b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(3/2)*cos(a+b*x)^2*sin(a+b*x)^3,x,23,-1/8*(c+d*x)^(3/2)*cos(a+b*x)/b-1/48*(c+d*x)^(3/2)*cos(3*a+3*b*x)/b+1/80*(c+d*x)^(3/2)*cos(5*a+5*b*x)/b+3/800*d^(3/2)*cos(5*a-5*b*c/d)*FresnelS(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/10*Pi)/b^(5/2)+3/800*d^(3/2)*FresnelC(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sin(5*a-5*b*c/d)*sqrt(1/10*Pi)/b^(5/2)-1/96*d^(3/2)*cos(3*a-3*b*c/d)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/6*Pi)/b^(5/2)-1/96*d^(3/2)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(1/6*Pi)/b^(5/2)-3/16*d^(3/2)*cos(a-b*c/d)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(5/2)-3/16*d^(3/2)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(1/2*Pi)/b^(5/2)+3/16*d*sin(a+b*x)*sqrt(c+d*x)/b^2+1/96*d*sin(3*a+3*b*x)*sqrt(c+d*x)/b^2-3/800*d*sin(5*a+5*b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(5/2)*cos(a+b*x)^2*sin(a+b*x)^3,x,26,-1/8*(c+d*x)^(5/2)*cos(a+b*x)/b-1/48*(c+d*x)^(5/2)*cos(3*a+3*b*x)/b+1/80*(c+d*x)^(5/2)*cos(5*a+5*b*x)/b+5/16*d*(c+d*x)^(3/2)*sin(a+b*x)/b^2+5/288*d*(c+d*x)^(3/2)*sin(3*a+3*b*x)/b^2-1/160*d*(c+d*x)^(3/2)*sin(5*a+5*b*x)/b^2+3/1600*d^(5/2)*cos(5*a-5*b*c/d)*FresnelC(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/10*Pi)/b^(7/2)-3/1600*d^(5/2)*FresnelS(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sin(5*a-5*b*c/d)*sqrt(1/10*Pi)/b^(7/2)-5/576*d^(5/2)*cos(3*a-3*b*c/d)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/6*Pi)/b^(7/2)+5/576*d^(5/2)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(1/6*Pi)/b^(7/2)-15/32*d^(5/2)*cos(a-b*c/d)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(7/2)+15/32*d^(5/2)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(1/2*Pi)/b^(7/2)+15/32*d^2*cos(a+b*x)*sqrt(c+d*x)/b^3+5/576*d^2*cos(3*a+3*b*x)*sqrt(c+d*x)/b^3-3/1600*d^2*cos(5*a+5*b*x)*sqrt(c+d*x)/b^3],

# p<0

# Integrands of the form (c+d x)^m Cos[a+b x]^3 Sin[a+b x]^p

# Integrands of the form (c+d x)^m Cos[a+b x]^3 Sin[a+b x]^p

# p>0
[(c+d*x)^m*cos(a+b*x)^3*sin(a+b*x),x,8,-2^(-4-m)*exp(2*I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-2*I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)-2^(-4-m)*(c+d*x)^m*GAMMA(1+m,2*I*b*(c+d*x)/d)/(b*exp(2*I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)-exp(4*I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-4*I*b*(c+d*x)/d)/(2^(2*(3+m))*b*(-I*b*(c+d*x)/d)^m)-(c+d*x)^m*GAMMA(1+m,4*I*b*(c+d*x)/d)/(2^(2*(3+m))*b*exp(4*I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)],
[(c+d*x)^4*cos(a+b*x)^3*sin(a+b*x),x,9,-45/64*c*d^3*x/b^3-45/128*d^4*x^2/b^3+3/32*(c+d*x)^4/b-45/128*d^4*cos(a+b*x)^2/b^5+9/16*d^2*(c+d*x)^2*cos(a+b*x)^2/b^3-3/128*d^4*cos(a+b*x)^4/b^5+3/16*d^2*(c+d*x)^2*cos(a+b*x)^4/b^3-1/4*(c+d*x)^4*cos(a+b*x)^4/b-45/64*d^3*(c+d*x)*cos(a+b*x)*sin(a+b*x)/b^4+3/8*d*(c+d*x)^3*cos(a+b*x)*sin(a+b*x)/b^2-3/32*d^3*(c+d*x)*cos(a+b*x)^3*sin(a+b*x)/b^4+1/4*d*(c+d*x)^3*cos(a+b*x)^3*sin(a+b*x)/b^2],
[(c+d*x)^3*cos(a+b*x)^3*sin(a+b*x),x,9,-45/256*d^3*x/b^3+3/32*(c+d*x)^3/b+9/32*d^2*(c+d*x)*cos(a+b*x)^2/b^3+3/32*d^2*(c+d*x)*cos(a+b*x)^4/b^3-1/4*(c+d*x)^3*cos(a+b*x)^4/b-45/256*d^3*cos(a+b*x)*sin(a+b*x)/b^4+9/32*d*(c+d*x)^2*cos(a+b*x)*sin(a+b*x)/b^2-3/128*d^3*cos(a+b*x)^3*sin(a+b*x)/b^4+3/16*d*(c+d*x)^2*cos(a+b*x)^3*sin(a+b*x)/b^2],
[(c+d*x)^2*cos(a+b*x)^3*sin(a+b*x),x,4,3/16*c*d*x/b+3/32*d^2*x^2/b+3/32*d^2*cos(a+b*x)^2/b^3+1/32*d^2*cos(a+b*x)^4/b^3-1/4*(c+d*x)^2*cos(a+b*x)^4/b+3/16*d*(c+d*x)*cos(a+b*x)*sin(a+b*x)/b^2+1/8*d*(c+d*x)*cos(a+b*x)^3*sin(a+b*x)/b^2],
[(c+d*x)*cos(a+b*x)^3*sin(a+b*x),x,4,3/32*d*x/b-1/4*(c+d*x)*cos(a+b*x)^4/b+3/32*d*cos(a+b*x)*sin(a+b*x)/b^2+1/16*d*cos(a+b*x)^3*sin(a+b*x)/b^2],
[cos(a+b*x)^3*sin(a+b*x)/(c+d*x),x,8,1/4*cos(2*a-2*b*c/d)*Si(2*b*c/d+2*b*x)/d+1/8*cos(4*a-4*b*c/d)*Si(4*b*c/d+4*b*x)/d+1/8*Ci(4*b*c/d+4*b*x)*sin(4*a-4*b*c/d)/d+1/4*Ci(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d],
[cos(a+b*x)^3*sin(a+b*x)/(c+d*x)^2,x,10,1/2*b*Ci(4*b*c/d+4*b*x)*cos(4*a-4*b*c/d)/d^2+1/2*b*Ci(2*b*c/d+2*b*x)*cos(2*a-2*b*c/d)/d^2-1/2*b*Si(4*b*c/d+4*b*x)*sin(4*a-4*b*c/d)/d^2-1/2*b*Si(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^2-1/4*sin(2*a+2*b*x)/(d*(c+d*x))-1/8*sin(4*a+4*b*x)/(d*(c+d*x))],
[cos(a+b*x)^3*sin(a+b*x)/(c+d*x)^3,x,12,-1/4*b*cos(2*a+2*b*x)/(d^2*(c+d*x))-1/4*b*cos(4*a+4*b*x)/(d^2*(c+d*x))-1/2*b^2*cos(2*a-2*b*c/d)*Si(2*b*c/d+2*b*x)/d^3-b^2*cos(4*a-4*b*c/d)*Si(4*b*c/d+4*b*x)/d^3-b^2*Ci(4*b*c/d+4*b*x)*sin(4*a-4*b*c/d)/d^3-1/2*b^2*Ci(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^3-1/8*sin(2*a+2*b*x)/(d*(c+d*x)^2)-1/16*sin(4*a+4*b*x)/(d*(c+d*x)^2)],
[cos(a+b*x)^3*sin(a+b*x)/(c+d*x)^4,x,14,-4/3*b^3*Ci(4*b*c/d+4*b*x)*cos(4*a-4*b*c/d)/d^4-1/3*b^3*Ci(2*b*c/d+2*b*x)*cos(2*a-2*b*c/d)/d^4-1/12*b*cos(2*a+2*b*x)/(d^2*(c+d*x)^2)-1/12*b*cos(4*a+4*b*x)/(d^2*(c+d*x)^2)+4/3*b^3*Si(4*b*c/d+4*b*x)*sin(4*a-4*b*c/d)/d^4+1/3*b^3*Si(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^4-1/12*sin(2*a+2*b*x)/(d*(c+d*x)^3)+1/6*b^2*sin(2*a+2*b*x)/(d^3*(c+d*x))-1/24*sin(4*a+4*b*x)/(d*(c+d*x)^3)+1/3*b^2*sin(4*a+4*b*x)/(d^3*(c+d*x))],
[(c+d*x)^m*cos(a+b*x)^3*sin(a+b*x)^2,x,11,-1/16*I*exp(I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)+1/16*I*(c+d*x)^m*GAMMA(1+m,I*b*(c+d*x)/d)/(b*exp(I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)+1/32*I*3^(-1-m)*exp(3*I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-3*I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)-1/32*I*3^(-1-m)*(c+d*x)^m*GAMMA(1+m,3*I*b*(c+d*x)/d)/(b*exp(3*I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)+1/32*I*5^(-1-m)*exp(5*I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-5*I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)-1/32*I*5^(-1-m)*(c+d*x)^m*GAMMA(1+m,5*I*b*(c+d*x)/d)/(b*exp(5*I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)],
[(c+d*x)^4*cos(a+b*x)^3*sin(a+b*x)^2,x,17,-3*d^3*(c+d*x)*cos(a+b*x)/b^4+1/2*d*(c+d*x)^3*cos(a+b*x)/b^2+1/54*d^3*(c+d*x)*cos(3*a+3*b*x)/b^4-1/36*d*(c+d*x)^3*cos(3*a+3*b*x)/b^2+3/1250*d^3*(c+d*x)*cos(5*a+5*b*x)/b^4-1/100*d*(c+d*x)^3*cos(5*a+5*b*x)/b^2+3*d^4*sin(a+b*x)/b^5-3/2*d^2*(c+d*x)^2*sin(a+b*x)/b^3+1/8*(c+d*x)^4*sin(a+b*x)/b-1/162*d^4*sin(3*a+3*b*x)/b^5+1/36*d^2*(c+d*x)^2*sin(3*a+3*b*x)/b^3-1/48*(c+d*x)^4*sin(3*a+3*b*x)/b-3/6250*d^4*sin(5*a+5*b*x)/b^5+3/500*d^2*(c+d*x)^2*sin(5*a+5*b*x)/b^3-1/80*(c+d*x)^4*sin(5*a+5*b*x)/b],
[(c+d*x)^3*cos(a+b*x)^3*sin(a+b*x)^2,x,14,-3/4*d^3*cos(a+b*x)/b^4+3/8*d*(c+d*x)^2*cos(a+b*x)/b^2+1/216*d^3*cos(3*a+3*b*x)/b^4-1/48*d*(c+d*x)^2*cos(3*a+3*b*x)/b^2+3/5000*d^3*cos(5*a+5*b*x)/b^4-3/400*d*(c+d*x)^2*cos(5*a+5*b*x)/b^2-3/4*d^2*(c+d*x)*sin(a+b*x)/b^3+1/8*(c+d*x)^3*sin(a+b*x)/b+1/72*d^2*(c+d*x)*sin(3*a+3*b*x)/b^3-1/48*(c+d*x)^3*sin(3*a+3*b*x)/b+3/1000*d^2*(c+d*x)*sin(5*a+5*b*x)/b^3-1/80*(c+d*x)^3*sin(5*a+5*b*x)/b],
[(c+d*x)^2*cos(a+b*x)^3*sin(a+b*x)^2,x,11,1/4*d*(c+d*x)*cos(a+b*x)/b^2-1/72*d*(c+d*x)*cos(3*a+3*b*x)/b^2-1/200*d*(c+d*x)*cos(5*a+5*b*x)/b^2-1/4*d^2*sin(a+b*x)/b^3+1/8*(c+d*x)^2*sin(a+b*x)/b+1/216*d^2*sin(3*a+3*b*x)/b^3-1/48*(c+d*x)^2*sin(3*a+3*b*x)/b+1/1000*d^2*sin(5*a+5*b*x)/b^3-1/80*(c+d*x)^2*sin(5*a+5*b*x)/b],
[(c+d*x)*cos(a+b*x)^3*sin(a+b*x)^2,x,8,1/8*d*cos(a+b*x)/b^2-1/144*d*cos(3*a+3*b*x)/b^2-1/400*d*cos(5*a+5*b*x)/b^2+1/8*(c+d*x)*sin(a+b*x)/b-1/48*(c+d*x)*sin(3*a+3*b*x)/b-1/80*(c+d*x)*sin(5*a+5*b*x)/b],
[cos(a+b*x)^3*sin(a+b*x)^2/(c+d*x),x,11,-1/16*Ci(5*b*c/d+5*b*x)*cos(5*a-5*b*c/d)/d-1/16*Ci(3*b*c/d+3*b*x)*cos(3*a-3*b*c/d)/d+1/8*Ci(b*c/d+b*x)*cos(a-b*c/d)/d+1/16*Si(5*b*c/d+5*b*x)*sin(5*a-5*b*c/d)/d+1/16*Si(3*b*c/d+3*b*x)*sin(3*a-3*b*c/d)/d-1/8*Si(b*c/d+b*x)*sin(a-b*c/d)/d],
[cos(a+b*x)^3*sin(a+b*x)^2/(c+d*x)^2,x,14,-1/8*cos(a+b*x)/(d*(c+d*x))+1/16*cos(3*a+3*b*x)/(d*(c+d*x))+1/16*cos(5*a+5*b*x)/(d*(c+d*x))-1/8*b*cos(a-b*c/d)*Si(b*c/d+b*x)/d^2+3/16*b*cos(3*a-3*b*c/d)*Si(3*b*c/d+3*b*x)/d^2+5/16*b*cos(5*a-5*b*c/d)*Si(5*b*c/d+5*b*x)/d^2+5/16*b*Ci(5*b*c/d+5*b*x)*sin(5*a-5*b*c/d)/d^2+3/16*b*Ci(3*b*c/d+3*b*x)*sin(3*a-3*b*c/d)/d^2-1/8*b*Ci(b*c/d+b*x)*sin(a-b*c/d)/d^2],
[cos(a+b*x)^3*sin(a+b*x)^2/(c+d*x)^3,x,17,25/32*b^2*Ci(5*b*c/d+5*b*x)*cos(5*a-5*b*c/d)/d^3+9/32*b^2*Ci(3*b*c/d+3*b*x)*cos(3*a-3*b*c/d)/d^3-1/16*b^2*Ci(b*c/d+b*x)*cos(a-b*c/d)/d^3-1/16*cos(a+b*x)/(d*(c+d*x)^2)+1/32*cos(3*a+3*b*x)/(d*(c+d*x)^2)+1/32*cos(5*a+5*b*x)/(d*(c+d*x)^2)-25/32*b^2*Si(5*b*c/d+5*b*x)*sin(5*a-5*b*c/d)/d^3-9/32*b^2*Si(3*b*c/d+3*b*x)*sin(3*a-3*b*c/d)/d^3+1/16*b^2*Si(b*c/d+b*x)*sin(a-b*c/d)/d^3+1/16*b*sin(a+b*x)/(d^2*(c+d*x))-3/32*b*sin(3*a+3*b*x)/(d^2*(c+d*x))-5/32*b*sin(5*a+5*b*x)/(d^2*(c+d*x))],
[cos(a+b*x)^3*sin(a+b*x)^2/(c+d*x)^4,x,20,-1/24*cos(a+b*x)/(d*(c+d*x)^3)+1/48*b^2*cos(a+b*x)/(d^3*(c+d*x))+1/48*cos(3*a+3*b*x)/(d*(c+d*x)^3)-3/32*b^2*cos(3*a+3*b*x)/(d^3*(c+d*x))+1/48*cos(5*a+5*b*x)/(d*(c+d*x)^3)-25/96*b^2*cos(5*a+5*b*x)/(d^3*(c+d*x))+1/48*b^3*cos(a-b*c/d)*Si(b*c/d+b*x)/d^4-9/32*b^3*cos(3*a-3*b*c/d)*Si(3*b*c/d+3*b*x)/d^4-125/96*b^3*cos(5*a-5*b*c/d)*Si(5*b*c/d+5*b*x)/d^4-125/96*b^3*Ci(5*b*c/d+5*b*x)*sin(5*a-5*b*c/d)/d^4-9/32*b^3*Ci(3*b*c/d+3*b*x)*sin(3*a-3*b*c/d)/d^4+1/48*b^3*Ci(b*c/d+b*x)*sin(a-b*c/d)/d^4+1/48*b*sin(a+b*x)/(d^2*(c+d*x)^2)-1/32*b*sin(3*a+3*b*x)/(d^2*(c+d*x)^2)-5/96*b*sin(5*a+5*b*x)/(d^2*(c+d*x)^2)],
[(c+d*x)^m*cos(a+b*x)^3*sin(a+b*x)^3,x,8,-3*2^(-7-m)*exp(2*I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-2*I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)-3*2^(-7-m)*(c+d*x)^m*GAMMA(1+m,2*I*b*(c+d*x)/d)/(b*exp(2*I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)+2^(-7-m)*3^(-1-m)*exp(6*I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-6*I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)+2^(-7-m)*3^(-1-m)*(c+d*x)^m*GAMMA(1+m,6*I*b*(c+d*x)/d)/(b*exp(6*I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)],
[(c+d*x)^4*cos(a+b*x)^3*sin(a+b*x)^3,x,12,-9/128*d^4*cos(2*a+2*b*x)/b^5+9/64*d^2*(c+d*x)^2*cos(2*a+2*b*x)/b^3-3/64*(c+d*x)^4*cos(2*a+2*b*x)/b+1/10368*d^4*cos(6*a+6*b*x)/b^5-1/576*d^2*(c+d*x)^2*cos(6*a+6*b*x)/b^3+1/192*(c+d*x)^4*cos(6*a+6*b*x)/b-9/64*d^3*(c+d*x)*sin(2*a+2*b*x)/b^4+3/32*d*(c+d*x)^3*sin(2*a+2*b*x)/b^2+1/1728*d^3*(c+d*x)*sin(6*a+6*b*x)/b^4-1/288*d*(c+d*x)^3*sin(6*a+6*b*x)/b^2],
[(c+d*x)^3*cos(a+b*x)^3*sin(a+b*x)^3,x,10,9/128*d^2*(c+d*x)*cos(2*a+2*b*x)/b^3-3/64*(c+d*x)^3*cos(2*a+2*b*x)/b-1/1152*d^2*(c+d*x)*cos(6*a+6*b*x)/b^3+1/192*(c+d*x)^3*cos(6*a+6*b*x)/b-9/256*d^3*sin(2*a+2*b*x)/b^4+9/128*d*(c+d*x)^2*sin(2*a+2*b*x)/b^2+1/6912*d^3*sin(6*a+6*b*x)/b^4-1/384*d*(c+d*x)^2*sin(6*a+6*b*x)/b^2],
[(c+d*x)^2*cos(a+b*x)^3*sin(a+b*x)^3,x,8,3/128*d^2*cos(2*a+2*b*x)/b^3-3/64*(c+d*x)^2*cos(2*a+2*b*x)/b-1/3456*d^2*cos(6*a+6*b*x)/b^3+1/192*(c+d*x)^2*cos(6*a+6*b*x)/b+3/64*d*(c+d*x)*sin(2*a+2*b*x)/b^2-1/576*d*(c+d*x)*sin(6*a+6*b*x)/b^2],
[(c+d*x)*cos(a+b*x)^3*sin(a+b*x)^3,x,6,-3/64*(c+d*x)*cos(2*a+2*b*x)/b+1/192*(c+d*x)*cos(6*a+6*b*x)/b+3/128*d*sin(2*a+2*b*x)/b^2-1/1152*d*sin(6*a+6*b*x)/b^2],
[cos(a+b*x)^3*sin(a+b*x)^3/(c+d*x),x,8,3/32*cos(2*a-2*b*c/d)*Si(2*b*c/d+2*b*x)/d-1/32*cos(6*a-6*b*c/d)*Si(6*b*c/d+6*b*x)/d-1/32*Ci(6*b*c/d+6*b*x)*sin(6*a-6*b*c/d)/d+3/32*Ci(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d],
[cos(a+b*x)^3*sin(a+b*x)^3/(c+d*x)^2,x,10,-3/16*b*Ci(6*b*c/d+6*b*x)*cos(6*a-6*b*c/d)/d^2+3/16*b*Ci(2*b*c/d+2*b*x)*cos(2*a-2*b*c/d)/d^2+3/16*b*Si(6*b*c/d+6*b*x)*sin(6*a-6*b*c/d)/d^2-3/16*b*Si(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^2-3/32*sin(2*a+2*b*x)/(d*(c+d*x))+1/32*sin(6*a+6*b*x)/(d*(c+d*x))],
[cos(a+b*x)^3*sin(a+b*x)^3/(c+d*x)^3,x,12,-3/32*b*cos(2*a+2*b*x)/(d^2*(c+d*x))+3/32*b*cos(6*a+6*b*x)/(d^2*(c+d*x))-3/16*b^2*cos(2*a-2*b*c/d)*Si(2*b*c/d+2*b*x)/d^3+9/16*b^2*cos(6*a-6*b*c/d)*Si(6*b*c/d+6*b*x)/d^3+9/16*b^2*Ci(6*b*c/d+6*b*x)*sin(6*a-6*b*c/d)/d^3-3/16*b^2*Ci(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^3-3/64*sin(2*a+2*b*x)/(d*(c+d*x)^2)+1/64*sin(6*a+6*b*x)/(d*(c+d*x)^2)],
[cos(a+b*x)^3*sin(a+b*x)^3/(c+d*x)^4,x,14,9/8*b^3*Ci(6*b*c/d+6*b*x)*cos(6*a-6*b*c/d)/d^4-1/8*b^3*Ci(2*b*c/d+2*b*x)*cos(2*a-2*b*c/d)/d^4-1/32*b*cos(2*a+2*b*x)/(d^2*(c+d*x)^2)+1/32*b*cos(6*a+6*b*x)/(d^2*(c+d*x)^2)-9/8*b^3*Si(6*b*c/d+6*b*x)*sin(6*a-6*b*c/d)/d^4+1/8*b^3*Si(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^4-1/32*sin(2*a+2*b*x)/(d*(c+d*x)^3)+1/16*b^2*sin(2*a+2*b*x)/(d^3*(c+d*x))+1/96*sin(6*a+6*b*x)/(d*(c+d*x)^3)-3/16*b^2*sin(6*a+6*b*x)/(d^3*(c+d*x))],

# p<0
[(c+d*x)^m*cos(a+b*x)^2*cot(a+b*x),x,6,2^(-3-m)*exp(2*I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-2*I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)+2^(-3-m)*(c+d*x)^m*GAMMA(1+m,2*I*b*(c+d*x)/d)/(b*exp(2*I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)+Unintegrable((c+d*x)^m*cot(a+b*x),x)],
[(c+d*x)^4*cos(a+b*x)^2*cot(a+b*x),x,13,-3/2*c*d^3*x/b^3-3/4*d^4*x^2/b^3+1/4*(c+d*x)^4/b-1/5*I*(c+d*x)^5/d+(c+d*x)^4*log(1-exp(2*I*(a+b*x)))/b-2*I*d*(c+d*x)^3*polylog(2,exp(2*I*(a+b*x)))/b^2+3*d^2*(c+d*x)^2*polylog(3,exp(2*I*(a+b*x)))/b^3+3*I*d^3*(c+d*x)*polylog(4,exp(2*I*(a+b*x)))/b^4-3/2*d^4*polylog(5,exp(2*I*(a+b*x)))/b^5+3/2*d^3*(c+d*x)*cos(a+b*x)*sin(a+b*x)/b^4-d*(c+d*x)^3*cos(a+b*x)*sin(a+b*x)/b^2-3/4*d^4*sin(a+b*x)^2/b^5+3/2*d^2*(c+d*x)^2*sin(a+b*x)^2/b^3-1/2*(c+d*x)^4*sin(a+b*x)^2/b],
[(c+d*x)^3*cos(a+b*x)^2*cot(a+b*x),x,12,-3/8*d^3*x/b^3+1/4*(c+d*x)^3/b-1/4*I*(c+d*x)^4/d+(c+d*x)^3*log(1-exp(2*I*(a+b*x)))/b-3/2*I*d*(c+d*x)^2*polylog(2,exp(2*I*(a+b*x)))/b^2+3/2*d^2*(c+d*x)*polylog(3,exp(2*I*(a+b*x)))/b^3+3/4*I*d^3*polylog(4,exp(2*I*(a+b*x)))/b^4+3/8*d^3*cos(a+b*x)*sin(a+b*x)/b^4-3/4*d*(c+d*x)^2*cos(a+b*x)*sin(a+b*x)/b^2+3/4*d^2*(c+d*x)*sin(a+b*x)^2/b^3-1/2*(c+d*x)^3*sin(a+b*x)^2/b],
[(c+d*x)^2*cos(a+b*x)^2*cot(a+b*x),x,9,1/2*c*d*x/b+1/4*d^2*x^2/b-1/3*I*(c+d*x)^3/d+(c+d*x)^2*log(1-exp(2*I*(a+b*x)))/b-I*d*(c+d*x)*polylog(2,exp(2*I*(a+b*x)))/b^2+1/2*d^2*polylog(3,exp(2*I*(a+b*x)))/b^3-1/2*d*(c+d*x)*cos(a+b*x)*sin(a+b*x)/b^2+1/4*d^2*sin(a+b*x)^2/b^3-1/2*(c+d*x)^2*sin(a+b*x)^2/b],
[(c+d*x)*cos(a+b*x)^2*cot(a+b*x),x,8,1/4*d*x/b-1/2*I*(c+d*x)^2/d+(c+d*x)*log(1-exp(2*I*(a+b*x)))/b-1/2*I*d*polylog(2,exp(2*I*(a+b*x)))/b^2-1/4*d*cos(a+b*x)*sin(a+b*x)/b^2-1/2*(c+d*x)*sin(a+b*x)^2/b],
[cos(a+b*x)^2*cot(a+b*x)/(c+d*x),x,6,-1/2*cos(2*a-2*b*c/d)*Si(2*b*c/d+2*b*x)/d-1/2*Ci(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d+Unintegrable(cot(a+b*x)/(c+d*x),x)],
[cos(a+b*x)^2*cot(a+b*x)/(c+d*x)^2,x,7,-b*Ci(2*b*c/d+2*b*x)*cos(2*a-2*b*c/d)/d^2+b*Si(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^2+1/2*sin(2*a+2*b*x)/(d*(c+d*x))+Unintegrable(cot(a+b*x)/(c+d*x)^2,x)],
[(c+d*x)^m*cos(a+b*x)*cot(a+b*x)^2,x,4,CannotIntegrate((c+d*x)^m*cot(a+b*x)*csc(a+b*x),x)+1/2*I*exp(I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)-1/2*I*(c+d*x)^m*GAMMA(1+m,I*b*(c+d*x)/d)/(b*exp(I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)],
[(c+d*x)^4*cos(a+b*x)*cot(a+b*x)^2,x,16,-8*d*(c+d*x)^3*arctanh(exp(I*(a+b*x)))/b^2+24*d^3*(c+d*x)*cos(a+b*x)/b^4-4*d*(c+d*x)^3*cos(a+b*x)/b^2-(c+d*x)^4*csc(a+b*x)/b+12*I*d^2*(c+d*x)^2*polylog(2,-exp(I*(a+b*x)))/b^3-12*I*d^2*(c+d*x)^2*polylog(2,exp(I*(a+b*x)))/b^3-24*d^3*(c+d*x)*polylog(3,-exp(I*(a+b*x)))/b^4+24*d^3*(c+d*x)*polylog(3,exp(I*(a+b*x)))/b^4-24*I*d^4*polylog(4,-exp(I*(a+b*x)))/b^5+24*I*d^4*polylog(4,exp(I*(a+b*x)))/b^5-24*d^4*sin(a+b*x)/b^5+12*d^2*(c+d*x)^2*sin(a+b*x)/b^3-(c+d*x)^4*sin(a+b*x)/b],
[(c+d*x)^3*cos(a+b*x)*cot(a+b*x)^2,x,13,-6*d*(c+d*x)^2*arctanh(exp(I*(a+b*x)))/b^2+6*d^3*cos(a+b*x)/b^4-3*d*(c+d*x)^2*cos(a+b*x)/b^2-(c+d*x)^3*csc(a+b*x)/b+6*I*d^2*(c+d*x)*polylog(2,-exp(I*(a+b*x)))/b^3-6*I*d^2*(c+d*x)*polylog(2,exp(I*(a+b*x)))/b^3-6*d^3*polylog(3,-exp(I*(a+b*x)))/b^4+6*d^3*polylog(3,exp(I*(a+b*x)))/b^4+6*d^2*(c+d*x)*sin(a+b*x)/b^3-(c+d*x)^3*sin(a+b*x)/b],
[(c+d*x)^2*cos(a+b*x)*cot(a+b*x)^2,x,10,-4*d*(c+d*x)*arctanh(exp(I*(a+b*x)))/b^2-2*d*(c+d*x)*cos(a+b*x)/b^2-(c+d*x)^2*csc(a+b*x)/b+2*I*d^2*polylog(2,-exp(I*(a+b*x)))/b^3-2*I*d^2*polylog(2,exp(I*(a+b*x)))/b^3+2*d^2*sin(a+b*x)/b^3-(c+d*x)^2*sin(a+b*x)/b],
[(c+d*x)*cos(a+b*x)*cot(a+b*x)^2,x,5,-d*arctanh(cos(a+b*x))/b^2-d*cos(a+b*x)/b^2-(c+d*x)*csc(a+b*x)/b-(c+d*x)*sin(a+b*x)/b],
[cos(a+b*x)*cot(a+b*x)^2/(c+d*x),x,4,CannotIntegrate(cot(a+b*x)*csc(a+b*x)/(c+d*x),x)-Ci(b*c/d+b*x)*cos(a-b*c/d)/d+Si(b*c/d+b*x)*sin(a-b*c/d)/d],
[cos(a+b*x)*cot(a+b*x)^2/(c+d*x)^2,x,5,CannotIntegrate(cot(a+b*x)*csc(a+b*x)/(c+d*x)^2,x)+cos(a+b*x)/(d*(c+d*x))+b*cos(a-b*c/d)*Si(b*c/d+b*x)/d^2+b*Ci(b*c/d+b*x)*sin(a-b*c/d)/d^2],
[(c+d*x)^m*cot(a+b*x)^3,x,0,Unintegrable((c+d*x)^m*cot(a+b*x)^3,x)],
[(c+d*x)^4*cot(a+b*x)^3,x,15,-2*I*d*(c+d*x)^3/b^2-1/2*(c+d*x)^4/b+1/5*I*(c+d*x)^5/d-2*d*(c+d*x)^3*cot(a+b*x)/b^2-1/2*(c+d*x)^4*cot(a+b*x)^2/b+6*d^2*(c+d*x)^2*log(1-exp(2*I*(a+b*x)))/b^3-(c+d*x)^4*log(1-exp(2*I*(a+b*x)))/b-6*I*d^3*(c+d*x)*polylog(2,exp(2*I*(a+b*x)))/b^4+2*I*d*(c+d*x)^3*polylog(2,exp(2*I*(a+b*x)))/b^2+3*d^4*polylog(3,exp(2*I*(a+b*x)))/b^5-3*d^2*(c+d*x)^2*polylog(3,exp(2*I*(a+b*x)))/b^3-3*I*d^3*(c+d*x)*polylog(4,exp(2*I*(a+b*x)))/b^4+3/2*d^4*polylog(5,exp(2*I*(a+b*x)))/b^5],
[(c+d*x)^3*cot(a+b*x)^3,x,13,-3/2*I*d*(c+d*x)^2/b^2-1/2*(c+d*x)^3/b+1/4*I*(c+d*x)^4/d-3/2*d*(c+d*x)^2*cot(a+b*x)/b^2-1/2*(c+d*x)^3*cot(a+b*x)^2/b+3*d^2*(c+d*x)*log(1-exp(2*I*(a+b*x)))/b^3-(c+d*x)^3*log(1-exp(2*I*(a+b*x)))/b-3/2*I*d^3*polylog(2,exp(2*I*(a+b*x)))/b^4+3/2*I*d*(c+d*x)^2*polylog(2,exp(2*I*(a+b*x)))/b^2-3/2*d^2*(c+d*x)*polylog(3,exp(2*I*(a+b*x)))/b^3-3/4*I*d^3*polylog(4,exp(2*I*(a+b*x)))/b^4],
[(c+d*x)^2*cot(a+b*x)^3,x,9,-c*d*x/b-1/2*d^2*x^2/b+1/3*I*(c+d*x)^3/d-d*(c+d*x)*cot(a+b*x)/b^2-1/2*(c+d*x)^2*cot(a+b*x)^2/b-(c+d*x)^2*log(1-exp(2*I*(a+b*x)))/b+d^2*log(sin(a+b*x))/b^3+I*d*(c+d*x)*polylog(2,exp(2*I*(a+b*x)))/b^2-1/2*d^2*polylog(3,exp(2*I*(a+b*x)))/b^3],
[(c+d*x)*cot(a+b*x)^3,x,7,-1/2*d*x/b+1/2*I*(c+d*x)^2/d-1/2*d*cot(a+b*x)/b^2-1/2*(c+d*x)*cot(a+b*x)^2/b-(c+d*x)*log(1-exp(2*I*(a+b*x)))/b+1/2*I*d*polylog(2,exp(2*I*(a+b*x)))/b^2],
[cot(a+b*x)^3/(c+d*x),x,0,Unintegrable(cot(a+b*x)^3/(c+d*x),x)],
[cot(a+b*x)^3/(c+d*x)^2,x,0,Unintegrable(cot(a+b*x)^3/(c+d*x)^2,x)],

# Integrands of the form (c+d x)^(m/2) Cos[a+b x]^3 Sin[a+b x]^p

# p>0
[(c+d*x)^(5/2)*cos(a+b*x)^3*sin(a+b*x),x,18,-1/8*(c+d*x)^(5/2)*cos(2*a+2*b*x)/b-1/32*(c+d*x)^(5/2)*cos(4*a+4*b*x)/b+5/32*d*(c+d*x)^(3/2)*sin(2*a+2*b*x)/b^2+5/256*d*(c+d*x)^(3/2)*sin(4*a+4*b*x)/b^2-15/4096*d^(5/2)*cos(4*a-4*b*c/d)*FresnelC(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(7/2)+15/4096*d^(5/2)*FresnelS(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(4*a-4*b*c/d)*sqrt(1/2*Pi)/b^(7/2)-15/256*d^(5/2)*cos(2*a-2*b*c/d)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(Pi)/b^(7/2)+15/256*d^(5/2)*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(Pi)/b^(7/2)+15/128*d^2*cos(2*a+2*b*x)*sqrt(c+d*x)/b^3+15/2048*d^2*cos(4*a+4*b*x)*sqrt(c+d*x)/b^3],
[(c+d*x)^(3/2)*cos(a+b*x)^3*sin(a+b*x),x,16,-1/8*(c+d*x)^(3/2)*cos(2*a+2*b*x)/b-1/32*(c+d*x)^(3/2)*cos(4*a+4*b*x)/b-3/512*d^(3/2)*cos(4*a-4*b*c/d)*FresnelS(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(5/2)-3/512*d^(3/2)*FresnelC(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(4*a-4*b*c/d)*sqrt(1/2*Pi)/b^(5/2)-3/64*d^(3/2)*cos(2*a-2*b*c/d)*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(Pi)/b^(5/2)-3/64*d^(3/2)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(Pi)/b^(5/2)+3/32*d*sin(2*a+2*b*x)*sqrt(c+d*x)/b^2+3/256*d*sin(4*a+4*b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(1/2)*cos(a+b*x)^3*sin(a+b*x),x,14,1/64*cos(4*a-4*b*c/d)*FresnelC(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)-1/64*FresnelS(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(4*a-4*b*c/d)*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)+1/16*cos(2*a-2*b*c/d)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(d)*sqrt(Pi)/b^(3/2)-1/16*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(d)*sqrt(Pi)/b^(3/2)-1/8*cos(2*a+2*b*x)*sqrt(c+d*x)/b-1/32*cos(4*a+4*b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(1/2)*cos(a+b*x)^3*sin(a+b*x),x,14,1/64*cos(4*a-4*b*c/d)*FresnelC(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)-1/64*FresnelS(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(4*a-4*b*c/d)*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)+1/16*cos(2*a-2*b*c/d)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(d)*sqrt(Pi)/b^(3/2)-1/16*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(d)*sqrt(Pi)/b^(3/2)-1/8*cos(2*a+2*b*x)*sqrt(c+d*x)/b-1/32*cos(4*a+4*b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(3/2)*cos(a+b*x)^3*sin(a+b*x),x,16,-1/8*(c+d*x)^(3/2)*cos(2*a+2*b*x)/b-1/32*(c+d*x)^(3/2)*cos(4*a+4*b*x)/b-3/512*d^(3/2)*cos(4*a-4*b*c/d)*FresnelS(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(5/2)-3/512*d^(3/2)*FresnelC(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(4*a-4*b*c/d)*sqrt(1/2*Pi)/b^(5/2)-3/64*d^(3/2)*cos(2*a-2*b*c/d)*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(Pi)/b^(5/2)-3/64*d^(3/2)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(Pi)/b^(5/2)+3/32*d*sin(2*a+2*b*x)*sqrt(c+d*x)/b^2+3/256*d*sin(4*a+4*b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(5/2)*cos(a+b*x)^3*sin(a+b*x),x,18,-1/8*(c+d*x)^(5/2)*cos(2*a+2*b*x)/b-1/32*(c+d*x)^(5/2)*cos(4*a+4*b*x)/b+5/32*d*(c+d*x)^(3/2)*sin(2*a+2*b*x)/b^2+5/256*d*(c+d*x)^(3/2)*sin(4*a+4*b*x)/b^2-15/4096*d^(5/2)*cos(4*a-4*b*c/d)*FresnelC(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(7/2)+15/4096*d^(5/2)*FresnelS(2*sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(4*a-4*b*c/d)*sqrt(1/2*Pi)/b^(7/2)-15/256*d^(5/2)*cos(2*a-2*b*c/d)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(Pi)/b^(7/2)+15/256*d^(5/2)*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(Pi)/b^(7/2)+15/128*d^2*cos(2*a+2*b*x)*sqrt(c+d*x)/b^3+15/2048*d^2*cos(4*a+4*b*x)*sqrt(c+d*x)/b^3],
[(c+d*x)^(5/2)*cos(a+b*x)^3*sin(a+b*x)^2,x,26,5/16*d*(c+d*x)^(3/2)*cos(a+b*x)/b^2-5/288*d*(c+d*x)^(3/2)*cos(3*a+3*b*x)/b^2-1/160*d*(c+d*x)^(3/2)*cos(5*a+5*b*x)/b^2+1/8*(c+d*x)^(5/2)*sin(a+b*x)/b-1/48*(c+d*x)^(5/2)*sin(3*a+3*b*x)/b-1/80*(c+d*x)^(5/2)*sin(5*a+5*b*x)/b-3/1600*d^(5/2)*cos(5*a-5*b*c/d)*FresnelS(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/10*Pi)/b^(7/2)-3/1600*d^(5/2)*FresnelC(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sin(5*a-5*b*c/d)*sqrt(1/10*Pi)/b^(7/2)-5/576*d^(5/2)*cos(3*a-3*b*c/d)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/6*Pi)/b^(7/2)-5/576*d^(5/2)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(1/6*Pi)/b^(7/2)+15/32*d^(5/2)*cos(a-b*c/d)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(7/2)+15/32*d^(5/2)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(1/2*Pi)/b^(7/2)-15/32*d^2*sin(a+b*x)*sqrt(c+d*x)/b^3+5/576*d^2*sin(3*a+3*b*x)*sqrt(c+d*x)/b^3+3/1600*d^2*sin(5*a+5*b*x)*sqrt(c+d*x)/b^3],
[(c+d*x)^(3/2)*cos(a+b*x)^3*sin(a+b*x)^2,x,23,1/8*(c+d*x)^(3/2)*sin(a+b*x)/b-1/48*(c+d*x)^(3/2)*sin(3*a+3*b*x)/b-1/80*(c+d*x)^(3/2)*sin(5*a+5*b*x)/b+3/800*d^(3/2)*cos(5*a-5*b*c/d)*FresnelC(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/10*Pi)/b^(5/2)-3/800*d^(3/2)*FresnelS(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sin(5*a-5*b*c/d)*sqrt(1/10*Pi)/b^(5/2)+1/96*d^(3/2)*cos(3*a-3*b*c/d)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/6*Pi)/b^(5/2)-1/96*d^(3/2)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(1/6*Pi)/b^(5/2)-3/16*d^(3/2)*cos(a-b*c/d)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(5/2)+3/16*d^(3/2)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(1/2*Pi)/b^(5/2)+3/16*d*cos(a+b*x)*sqrt(c+d*x)/b^2-1/96*d*cos(3*a+3*b*x)*sqrt(c+d*x)/b^2-3/800*d*cos(5*a+5*b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(1/2)*cos(a+b*x)^3*sin(a+b*x)^2,x,20,1/80*cos(5*a-5*b*c/d)*FresnelS(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/10*Pi)/b^(3/2)+1/80*FresnelC(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sin(5*a-5*b*c/d)*sqrt(d)*sqrt(1/10*Pi)/b^(3/2)+1/48*cos(3*a-3*b*c/d)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/6*Pi)/b^(3/2)+1/48*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(d)*sqrt(1/6*Pi)/b^(3/2)-1/8*cos(a-b*c/d)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)-1/8*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)+1/8*sin(a+b*x)*sqrt(c+d*x)/b-1/48*sin(3*a+3*b*x)*sqrt(c+d*x)/b-1/80*sin(5*a+5*b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(1/2)*cos(a+b*x)^3*sin(a+b*x)^2,x,20,1/80*cos(5*a-5*b*c/d)*FresnelS(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/10*Pi)/b^(3/2)+1/80*FresnelC(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sin(5*a-5*b*c/d)*sqrt(d)*sqrt(1/10*Pi)/b^(3/2)+1/48*cos(3*a-3*b*c/d)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/6*Pi)/b^(3/2)+1/48*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(d)*sqrt(1/6*Pi)/b^(3/2)-1/8*cos(a-b*c/d)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)-1/8*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(d)*sqrt(1/2*Pi)/b^(3/2)+1/8*sin(a+b*x)*sqrt(c+d*x)/b-1/48*sin(3*a+3*b*x)*sqrt(c+d*x)/b-1/80*sin(5*a+5*b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(3/2)*cos(a+b*x)^3*sin(a+b*x)^2,x,23,1/8*(c+d*x)^(3/2)*sin(a+b*x)/b-1/48*(c+d*x)^(3/2)*sin(3*a+3*b*x)/b-1/80*(c+d*x)^(3/2)*sin(5*a+5*b*x)/b+3/800*d^(3/2)*cos(5*a-5*b*c/d)*FresnelC(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/10*Pi)/b^(5/2)-3/800*d^(3/2)*FresnelS(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sin(5*a-5*b*c/d)*sqrt(1/10*Pi)/b^(5/2)+1/96*d^(3/2)*cos(3*a-3*b*c/d)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/6*Pi)/b^(5/2)-1/96*d^(3/2)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(1/6*Pi)/b^(5/2)-3/16*d^(3/2)*cos(a-b*c/d)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(5/2)+3/16*d^(3/2)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(1/2*Pi)/b^(5/2)+3/16*d*cos(a+b*x)*sqrt(c+d*x)/b^2-1/96*d*cos(3*a+3*b*x)*sqrt(c+d*x)/b^2-3/800*d*cos(5*a+5*b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(5/2)*cos(a+b*x)^3*sin(a+b*x)^2,x,26,5/16*d*(c+d*x)^(3/2)*cos(a+b*x)/b^2-5/288*d*(c+d*x)^(3/2)*cos(3*a+3*b*x)/b^2-1/160*d*(c+d*x)^(3/2)*cos(5*a+5*b*x)/b^2+1/8*(c+d*x)^(5/2)*sin(a+b*x)/b-1/48*(c+d*x)^(5/2)*sin(3*a+3*b*x)/b-1/80*(c+d*x)^(5/2)*sin(5*a+5*b*x)/b-3/1600*d^(5/2)*cos(5*a-5*b*c/d)*FresnelS(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/10*Pi)/b^(7/2)-3/1600*d^(5/2)*FresnelC(sqrt(b)*sqrt(10/Pi)*sqrt(c+d*x)/sqrt(d))*sin(5*a-5*b*c/d)*sqrt(1/10*Pi)/b^(7/2)-5/576*d^(5/2)*cos(3*a-3*b*c/d)*FresnelS(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/6*Pi)/b^(7/2)-5/576*d^(5/2)*FresnelC(sqrt(b)*sqrt(6/Pi)*sqrt(c+d*x)/sqrt(d))*sin(3*a-3*b*c/d)*sqrt(1/6*Pi)/b^(7/2)+15/32*d^(5/2)*cos(a-b*c/d)*FresnelS(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/2*Pi)/b^(7/2)+15/32*d^(5/2)*FresnelC(sqrt(b)*sqrt(2/Pi)*sqrt(c+d*x)/sqrt(d))*sin(a-b*c/d)*sqrt(1/2*Pi)/b^(7/2)-15/32*d^2*sin(a+b*x)*sqrt(c+d*x)/b^3+5/576*d^2*sin(3*a+3*b*x)*sqrt(c+d*x)/b^3+3/1600*d^2*sin(5*a+5*b*x)*sqrt(c+d*x)/b^3],
[(c+d*x)^(5/2)*cos(a+b*x)^3*sin(a+b*x)^3,x,18,-3/64*(c+d*x)^(5/2)*cos(2*a+2*b*x)/b+1/192*(c+d*x)^(5/2)*cos(6*a+6*b*x)/b+15/256*d*(c+d*x)^(3/2)*sin(2*a+2*b*x)/b^2-5/2304*d*(c+d*x)^(3/2)*sin(6*a+6*b*x)/b^2+5/18432*d^(5/2)*cos(6*a-6*b*c/d)*FresnelC(2*sqrt(b)*sqrt(3/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/3*Pi)/b^(7/2)-5/18432*d^(5/2)*FresnelS(2*sqrt(b)*sqrt(3/Pi)*sqrt(c+d*x)/sqrt(d))*sin(6*a-6*b*c/d)*sqrt(1/3*Pi)/b^(7/2)-45/2048*d^(5/2)*cos(2*a-2*b*c/d)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(Pi)/b^(7/2)+45/2048*d^(5/2)*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(Pi)/b^(7/2)+45/1024*d^2*cos(2*a+2*b*x)*sqrt(c+d*x)/b^3-5/9216*d^2*cos(6*a+6*b*x)*sqrt(c+d*x)/b^3],
[(c+d*x)^(3/2)*cos(a+b*x)^3*sin(a+b*x)^3,x,16,-3/64*(c+d*x)^(3/2)*cos(2*a+2*b*x)/b+1/192*(c+d*x)^(3/2)*cos(6*a+6*b*x)/b+1/1536*d^(3/2)*cos(6*a-6*b*c/d)*FresnelS(2*sqrt(b)*sqrt(3/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/3*Pi)/b^(5/2)+1/1536*d^(3/2)*FresnelC(2*sqrt(b)*sqrt(3/Pi)*sqrt(c+d*x)/sqrt(d))*sin(6*a-6*b*c/d)*sqrt(1/3*Pi)/b^(5/2)-9/512*d^(3/2)*cos(2*a-2*b*c/d)*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(Pi)/b^(5/2)-9/512*d^(3/2)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(Pi)/b^(5/2)+9/256*d*sin(2*a+2*b*x)*sqrt(c+d*x)/b^2-1/768*d*sin(6*a+6*b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(1/2)*cos(a+b*x)^3*sin(a+b*x)^3,x,14,-1/384*cos(6*a-6*b*c/d)*FresnelC(2*sqrt(b)*sqrt(3/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/3*Pi)/b^(3/2)+1/384*FresnelS(2*sqrt(b)*sqrt(3/Pi)*sqrt(c+d*x)/sqrt(d))*sin(6*a-6*b*c/d)*sqrt(d)*sqrt(1/3*Pi)/b^(3/2)+3/128*cos(2*a-2*b*c/d)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(d)*sqrt(Pi)/b^(3/2)-3/128*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(d)*sqrt(Pi)/b^(3/2)-3/64*cos(2*a+2*b*x)*sqrt(c+d*x)/b+1/192*cos(6*a+6*b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(1/2)*cos(a+b*x)^3*sin(a+b*x)^3,x,14,-1/384*cos(6*a-6*b*c/d)*FresnelC(2*sqrt(b)*sqrt(3/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(d)*sqrt(1/3*Pi)/b^(3/2)+1/384*FresnelS(2*sqrt(b)*sqrt(3/Pi)*sqrt(c+d*x)/sqrt(d))*sin(6*a-6*b*c/d)*sqrt(d)*sqrt(1/3*Pi)/b^(3/2)+3/128*cos(2*a-2*b*c/d)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(d)*sqrt(Pi)/b^(3/2)-3/128*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(d)*sqrt(Pi)/b^(3/2)-3/64*cos(2*a+2*b*x)*sqrt(c+d*x)/b+1/192*cos(6*a+6*b*x)*sqrt(c+d*x)/b],
[(c+d*x)^(3/2)*cos(a+b*x)^3*sin(a+b*x)^3,x,16,-3/64*(c+d*x)^(3/2)*cos(2*a+2*b*x)/b+1/192*(c+d*x)^(3/2)*cos(6*a+6*b*x)/b+1/1536*d^(3/2)*cos(6*a-6*b*c/d)*FresnelS(2*sqrt(b)*sqrt(3/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/3*Pi)/b^(5/2)+1/1536*d^(3/2)*FresnelC(2*sqrt(b)*sqrt(3/Pi)*sqrt(c+d*x)/sqrt(d))*sin(6*a-6*b*c/d)*sqrt(1/3*Pi)/b^(5/2)-9/512*d^(3/2)*cos(2*a-2*b*c/d)*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(Pi)/b^(5/2)-9/512*d^(3/2)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(Pi)/b^(5/2)+9/256*d*sin(2*a+2*b*x)*sqrt(c+d*x)/b^2-1/768*d*sin(6*a+6*b*x)*sqrt(c+d*x)/b^2],
[(c+d*x)^(5/2)*cos(a+b*x)^3*sin(a+b*x)^3,x,18,-3/64*(c+d*x)^(5/2)*cos(2*a+2*b*x)/b+1/192*(c+d*x)^(5/2)*cos(6*a+6*b*x)/b+15/256*d*(c+d*x)^(3/2)*sin(2*a+2*b*x)/b^2-5/2304*d*(c+d*x)^(3/2)*sin(6*a+6*b*x)/b^2+5/18432*d^(5/2)*cos(6*a-6*b*c/d)*FresnelC(2*sqrt(b)*sqrt(3/Pi)*sqrt(c+d*x)/sqrt(d))*sqrt(1/3*Pi)/b^(7/2)-5/18432*d^(5/2)*FresnelS(2*sqrt(b)*sqrt(3/Pi)*sqrt(c+d*x)/sqrt(d))*sin(6*a-6*b*c/d)*sqrt(1/3*Pi)/b^(7/2)-45/2048*d^(5/2)*cos(2*a-2*b*c/d)*FresnelC(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sqrt(Pi)/b^(7/2)+45/2048*d^(5/2)*FresnelS(2*sqrt(b)*sqrt(c+d*x)/(sqrt(d)*sqrt(Pi)))*sin(2*a-2*b*c/d)*sqrt(Pi)/b^(7/2)+45/1024*d^2*cos(2*a+2*b*x)*sqrt(c+d*x)/b^3-5/9216*d^2*cos(6*a+6*b*x)*sqrt(c+d*x)/b^3],

# p<0

# Integrands of the form (c+d x)^m Cos[a+b x]^4 Sin[a+b x]^p
[x^3*cos(x)^2*cot(x)^2,x,12,3/8*x^2-I*x^3-3/8*x^4+3/8*cos(x)^2-3/4*x^2*cos(x)^2-x^3*cot(x)+3*x^2*log(1-exp(2*I*x))-3*I*x*polylog(2,exp(2*I*x))+3/2*polylog(3,exp(2*I*x))+3/4*x*cos(x)*sin(x)-1/2*x^3*cos(x)*sin(x)],
[x^2*cos(x)^2*cot(x)^2,x,11,1/4*x-I*x^2-1/2*x^3-1/2*x*cos(x)^2-x^2*cot(x)+2*x*log(1-exp(2*I*x))-I*polylog(2,exp(2*I*x))+1/4*cos(x)*sin(x)-1/2*x^2*cos(x)*sin(x)],
[x*cos(x)^2*cot(x)^2,x,6,-3/4*x^2-1/4*cos(x)^2-x*cot(x)+log(sin(x))-1/2*x*cos(x)*sin(x)],

# Integrands of the form (c+d x)^m Cos[a+b x]^5 Sin[a+b x]^p
[x^3*cos(x)^2*cot(x)^3,x,26,3/8*x-3/2*I*x^2-3/4*x^3+1/2*I*x^4-3/2*x^2*cot(x)-1/2*x^3*cot(x)^2+3*x*log(1-exp(2*I*x))-2*x^3*log(1-exp(2*I*x))-3/2*I*polylog(2,exp(2*I*x))+3*I*x^2*polylog(2,exp(2*I*x))-3*x*polylog(3,exp(2*I*x))-3/2*I*polylog(4,exp(2*I*x))-3/8*cos(x)*sin(x)+3/4*x^2*cos(x)*sin(x)-3/4*x*sin(x)^2+1/2*x^3*sin(x)^2],
[x^2*cos(x)^2*cot(x)^3,x,19,-3/4*x^2+2/3*I*x^3-x*cot(x)-1/2*x^2*cot(x)^2-2*x^2*log(1-exp(2*I*x))+log(sin(x))+2*I*x*polylog(2,exp(2*I*x))-polylog(3,exp(2*I*x))+1/2*x*cos(x)*sin(x)-1/4*sin(x)^2+1/2*x^2*sin(x)^2],
[x*cos(x)^2*cot(x)^3,x,16,-3/4*x+I*x^2-1/2*cot(x)-1/2*x*cot(x)^2-2*x*log(1-exp(2*I*x))+I*polylog(2,exp(2*I*x))+1/4*cos(x)*sin(x)+1/2*x*sin(x)^2],

# Integrands of the form (c+d x)^m Sec[a+b x]^1 Sin[a+b x]^p

# Integrands of the form (c+d x)^m Sec[a+b x] Sin[a+b x]^p

# p>0
[(c+d*x)^m*sec(a+b*x)*sin(a+b*x),x,0,Unintegrable((c+d*x)^m*tan(a+b*x),x)],
[(c+d*x)^4*sec(a+b*x)*sin(a+b*x),x,7,1/5*I*(c+d*x)^5/d-(c+d*x)^4*log(1+exp(2*I*(a+b*x)))/b+2*I*d*(c+d*x)^3*polylog(2,-exp(2*I*(a+b*x)))/b^2-3*d^2*(c+d*x)^2*polylog(3,-exp(2*I*(a+b*x)))/b^3-3*I*d^3*(c+d*x)*polylog(4,-exp(2*I*(a+b*x)))/b^4+3/2*d^4*polylog(5,-exp(2*I*(a+b*x)))/b^5],
[(c+d*x)^3*sec(a+b*x)*sin(a+b*x),x,6,1/4*I*(c+d*x)^4/d-(c+d*x)^3*log(1+exp(2*I*(a+b*x)))/b+3/2*I*d*(c+d*x)^2*polylog(2,-exp(2*I*(a+b*x)))/b^2-3/2*d^2*(c+d*x)*polylog(3,-exp(2*I*(a+b*x)))/b^3-3/4*I*d^3*polylog(4,-exp(2*I*(a+b*x)))/b^4],
[(c+d*x)^2*sec(a+b*x)*sin(a+b*x),x,5,1/3*I*(c+d*x)^3/d-(c+d*x)^2*log(1+exp(2*I*(a+b*x)))/b+I*d*(c+d*x)*polylog(2,-exp(2*I*(a+b*x)))/b^2-1/2*d^2*polylog(3,-exp(2*I*(a+b*x)))/b^3],
[(c+d*x)*sec(a+b*x)*sin(a+b*x),x,4,1/2*I*(c+d*x)^2/d-(c+d*x)*log(1+exp(2*I*(a+b*x)))/b+1/2*I*d*polylog(2,-exp(2*I*(a+b*x)))/b^2],
[sec(a+b*x)*sin(a+b*x)/(c+d*x),x,0,Unintegrable(tan(a+b*x)/(c+d*x),x)],
[sec(a+b*x)*sin(a+b*x)/(c+d*x)^2,x,0,Unintegrable(tan(a+b*x)/(c+d*x)^2,x)],
[(c+d*x)^m*sec(a+b*x)*sin(a+b*x)^2,x,4,1/2*I*exp(I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)-1/2*I*(c+d*x)^m*GAMMA(1+m,I*b*(c+d*x)/d)/(b*exp(I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)+Unintegrable((c+d*x)^m*sec(a+b*x),x)],
[(c+d*x)^3*sec(a+b*x)*sin(a+b*x)^2,x,14,-2*I*(c+d*x)^3*arctan(exp(I*(a+b*x)))/b+6*d^3*cos(a+b*x)/b^4-3*d*(c+d*x)^2*cos(a+b*x)/b^2+3*I*d*(c+d*x)^2*polylog(2,-I*exp(I*(a+b*x)))/b^2-3*I*d*(c+d*x)^2*polylog(2,I*exp(I*(a+b*x)))/b^2-6*d^2*(c+d*x)*polylog(3,-I*exp(I*(a+b*x)))/b^3+6*d^2*(c+d*x)*polylog(3,I*exp(I*(a+b*x)))/b^3-6*I*d^3*polylog(4,-I*exp(I*(a+b*x)))/b^4+6*I*d^3*polylog(4,I*exp(I*(a+b*x)))/b^4+6*d^2*(c+d*x)*sin(a+b*x)/b^3-(c+d*x)^3*sin(a+b*x)/b],
[(c+d*x)^2*sec(a+b*x)*sin(a+b*x)^2,x,11,-2*I*(c+d*x)^2*arctan(exp(I*(a+b*x)))/b-2*d*(c+d*x)*cos(a+b*x)/b^2+2*I*d*(c+d*x)*polylog(2,-I*exp(I*(a+b*x)))/b^2-2*I*d*(c+d*x)*polylog(2,I*exp(I*(a+b*x)))/b^2-2*d^2*polylog(3,-I*exp(I*(a+b*x)))/b^3+2*d^2*polylog(3,I*exp(I*(a+b*x)))/b^3+2*d^2*sin(a+b*x)/b^3-(c+d*x)^2*sin(a+b*x)/b],
[(c+d*x)*sec(a+b*x)*sin(a+b*x)^2,x,8,-2*I*(c+d*x)*arctan(exp(I*(a+b*x)))/b-d*cos(a+b*x)/b^2+I*d*polylog(2,-I*exp(I*(a+b*x)))/b^2-I*d*polylog(2,I*exp(I*(a+b*x)))/b^2-(c+d*x)*sin(a+b*x)/b],
[sec(a+b*x)*sin(a+b*x)^2/(c+d*x),x,4,-Ci(b*c/d+b*x)*cos(a-b*c/d)/d+Si(b*c/d+b*x)*sin(a-b*c/d)/d+Unintegrable(sec(a+b*x)/(c+d*x),x)],
[sec(a+b*x)*sin(a+b*x)^2/(c+d*x)^2,x,5,cos(a+b*x)/(d*(c+d*x))+b*cos(a-b*c/d)*Si(b*c/d+b*x)/d^2+b*Ci(b*c/d+b*x)*sin(a-b*c/d)/d^2+Unintegrable(sec(a+b*x)/(c+d*x)^2,x)],
[(c+d*x)^m*sec(a+b*x)*sin(a+b*x)^3,x,6,2^(-3-m)*exp(2*I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-2*I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)+2^(-3-m)*(c+d*x)^m*GAMMA(1+m,2*I*b*(c+d*x)/d)/(b*exp(2*I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)+Unintegrable((c+d*x)^m*tan(a+b*x),x)],
[(c+d*x)^3*sec(a+b*x)*sin(a+b*x)^3,x,12,-3/8*d^3*x/b^3+1/4*(c+d*x)^3/b+1/4*I*(c+d*x)^4/d-(c+d*x)^3*log(1+exp(2*I*(a+b*x)))/b+3/2*I*d*(c+d*x)^2*polylog(2,-exp(2*I*(a+b*x)))/b^2-3/2*d^2*(c+d*x)*polylog(3,-exp(2*I*(a+b*x)))/b^3-3/4*I*d^3*polylog(4,-exp(2*I*(a+b*x)))/b^4+3/8*d^3*cos(a+b*x)*sin(a+b*x)/b^4-3/4*d*(c+d*x)^2*cos(a+b*x)*sin(a+b*x)/b^2+3/4*d^2*(c+d*x)*sin(a+b*x)^2/b^3-1/2*(c+d*x)^3*sin(a+b*x)^2/b],
[(c+d*x)^2*sec(a+b*x)*sin(a+b*x)^3,x,9,1/2*c*d*x/b+1/4*d^2*x^2/b+1/3*I*(c+d*x)^3/d-(c+d*x)^2*log(1+exp(2*I*(a+b*x)))/b+I*d*(c+d*x)*polylog(2,-exp(2*I*(a+b*x)))/b^2-1/2*d^2*polylog(3,-exp(2*I*(a+b*x)))/b^3-1/2*d*(c+d*x)*cos(a+b*x)*sin(a+b*x)/b^2+1/4*d^2*sin(a+b*x)^2/b^3-1/2*(c+d*x)^2*sin(a+b*x)^2/b],
[(c+d*x)*sec(a+b*x)*sin(a+b*x)^3,x,8,1/4*d*x/b+1/2*I*(c+d*x)^2/d-(c+d*x)*log(1+exp(2*I*(a+b*x)))/b+1/2*I*d*polylog(2,-exp(2*I*(a+b*x)))/b^2-1/4*d*cos(a+b*x)*sin(a+b*x)/b^2-1/2*(c+d*x)*sin(a+b*x)^2/b],
[sec(a+b*x)*sin(a+b*x)^3/(c+d*x),x,6,-1/2*cos(2*a-2*b*c/d)*Si(2*b*c/d+2*b*x)/d-1/2*Ci(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d+Unintegrable(tan(a+b*x)/(c+d*x),x)],
[sec(a+b*x)*sin(a+b*x)^3/(c+d*x)^2,x,7,-b*Ci(2*b*c/d+2*b*x)*cos(2*a-2*b*c/d)/d^2+b*Si(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^2+1/2*sin(2*a+2*b*x)/(d*(c+d*x))+Unintegrable(tan(a+b*x)/(c+d*x)^2,x)],

# p<0
[(c+d*x)^m*csc(a+b*x)*sec(a+b*x),x,0,CannotIntegrate((c+d*x)^m*csc(a+b*x)*sec(a+b*x),x)],
[(c+d*x)^4*csc(a+b*x)*sec(a+b*x),x,12,-2*(c+d*x)^4*arctanh(exp(2*I*(a+b*x)))/b+2*I*d*(c+d*x)^3*polylog(2,-exp(2*I*(a+b*x)))/b^2-2*I*d*(c+d*x)^3*polylog(2,exp(2*I*(a+b*x)))/b^2-3*d^2*(c+d*x)^2*polylog(3,-exp(2*I*(a+b*x)))/b^3+3*d^2*(c+d*x)^2*polylog(3,exp(2*I*(a+b*x)))/b^3-3*I*d^3*(c+d*x)*polylog(4,-exp(2*I*(a+b*x)))/b^4+3*I*d^3*(c+d*x)*polylog(4,exp(2*I*(a+b*x)))/b^4+3/2*d^4*polylog(5,-exp(2*I*(a+b*x)))/b^5-3/2*d^4*polylog(5,exp(2*I*(a+b*x)))/b^5],
[(c+d*x)^3*csc(a+b*x)*sec(a+b*x),x,10,-2*(c+d*x)^3*arctanh(exp(2*I*(a+b*x)))/b+3/2*I*d*(c+d*x)^2*polylog(2,-exp(2*I*(a+b*x)))/b^2-3/2*I*d*(c+d*x)^2*polylog(2,exp(2*I*(a+b*x)))/b^2-3/2*d^2*(c+d*x)*polylog(3,-exp(2*I*(a+b*x)))/b^3+3/2*d^2*(c+d*x)*polylog(3,exp(2*I*(a+b*x)))/b^3-3/4*I*d^3*polylog(4,-exp(2*I*(a+b*x)))/b^4+3/4*I*d^3*polylog(4,exp(2*I*(a+b*x)))/b^4],
[(c+d*x)^2*csc(a+b*x)*sec(a+b*x),x,8,-2*(c+d*x)^2*arctanh(exp(2*I*(a+b*x)))/b+I*d*(c+d*x)*polylog(2,-exp(2*I*(a+b*x)))/b^2-I*d*(c+d*x)*polylog(2,exp(2*I*(a+b*x)))/b^2-1/2*d^2*polylog(3,-exp(2*I*(a+b*x)))/b^3+1/2*d^2*polylog(3,exp(2*I*(a+b*x)))/b^3],
[(c+d*x)*csc(a+b*x)*sec(a+b*x),x,6,-2*(c+d*x)*arctanh(exp(2*I*(a+b*x)))/b+1/2*I*d*polylog(2,-exp(2*I*(a+b*x)))/b^2-1/2*I*d*polylog(2,exp(2*I*(a+b*x)))/b^2],
[csc(a+b*x)*sec(a+b*x)/(c+d*x),x,1,2*Unintegrable(csc(2*a+2*b*x)/(c+d*x),x)],
[csc(a+b*x)*sec(a+b*x)/(c+d*x)^2,x,1,2*Unintegrable(csc(2*a+2*b*x)/(c+d*x)^2,x)],
[(c+d*x)^m*csc(a+b*x)^2*sec(a+b*x),x,0,CannotIntegrate((c+d*x)^m*csc(a+b*x)^2*sec(a+b*x),x)],
[(c+d*x)^3*csc(a+b*x)^2*sec(a+b*x),x,23,-2*I*(c+d*x)^3*arctan(exp(I*(a+b*x)))/b-6*d*(c+d*x)^2*arctanh(exp(I*(a+b*x)))/b^2-(c+d*x)^3*csc(a+b*x)/b+6*I*d^2*(c+d*x)*polylog(2,-exp(I*(a+b*x)))/b^3+3*I*d*(c+d*x)^2*polylog(2,-I*exp(I*(a+b*x)))/b^2-3*I*d*(c+d*x)^2*polylog(2,I*exp(I*(a+b*x)))/b^2-6*I*d^2*(c+d*x)*polylog(2,exp(I*(a+b*x)))/b^3-6*d^3*polylog(3,-exp(I*(a+b*x)))/b^4-6*d^2*(c+d*x)*polylog(3,-I*exp(I*(a+b*x)))/b^3+6*d^2*(c+d*x)*polylog(3,I*exp(I*(a+b*x)))/b^3+6*d^3*polylog(3,exp(I*(a+b*x)))/b^4-6*I*d^3*polylog(4,-I*exp(I*(a+b*x)))/b^4+6*I*d^3*polylog(4,I*exp(I*(a+b*x)))/b^4],
[(c+d*x)^2*csc(a+b*x)^2*sec(a+b*x),x,19,-2*I*(c+d*x)^2*arctan(exp(I*(a+b*x)))/b-4*d*(c+d*x)*arctanh(exp(I*(a+b*x)))/b^2-(c+d*x)^2*csc(a+b*x)/b+2*I*d^2*polylog(2,-exp(I*(a+b*x)))/b^3+2*I*d*(c+d*x)*polylog(2,-I*exp(I*(a+b*x)))/b^2-2*I*d*(c+d*x)*polylog(2,I*exp(I*(a+b*x)))/b^2-2*I*d^2*polylog(2,exp(I*(a+b*x)))/b^3-2*d^2*polylog(3,-I*exp(I*(a+b*x)))/b^3+2*d^2*polylog(3,I*exp(I*(a+b*x)))/b^3],
[(c+d*x)*csc(a+b*x)^2*sec(a+b*x),x,10,-2*I*d*x*arctan(exp(I*(a+b*x)))/b-d*arctanh(cos(a+b*x))/b^2-d*x*arctanh(sin(a+b*x))/b+(c+d*x)*arctanh(sin(a+b*x))/b-(c+d*x)*csc(a+b*x)/b+I*d*polylog(2,-I*exp(I*(a+b*x)))/b^2-I*d*polylog(2,I*exp(I*(a+b*x)))/b^2],
[csc(a+b*x)^2*sec(a+b*x)/(c+d*x),x,0,CannotIntegrate(csc(a+b*x)^2*sec(a+b*x)/(c+d*x),x)],
[csc(a+b*x)^2*sec(a+b*x)/(c+d*x)^2,x,0,CannotIntegrate(csc(a+b*x)^2*sec(a+b*x)/(c+d*x)^2,x)],
[(c+d*x)^m*csc(a+b*x)^3*sec(a+b*x),x,0,CannotIntegrate((c+d*x)^m*csc(a+b*x)^3*sec(a+b*x),x)],
[(c+d*x)^3*csc(a+b*x)^3*sec(a+b*x),x,22,-3/2*I*d*(c+d*x)^2/b^2-1/2*(c+d*x)^3/b-2*(c+d*x)^3*arctanh(exp(2*I*(a+b*x)))/b-3/2*d*(c+d*x)^2*cot(a+b*x)/b^2-1/2*(c+d*x)^3*cot(a+b*x)^2/b+3*d^2*(c+d*x)*log(1-exp(2*I*(a+b*x)))/b^3+3/2*I*d*(c+d*x)^2*polylog(2,-exp(2*I*(a+b*x)))/b^2-3/2*I*d^3*polylog(2,exp(2*I*(a+b*x)))/b^4-3/2*I*d*(c+d*x)^2*polylog(2,exp(2*I*(a+b*x)))/b^2-3/2*d^2*(c+d*x)*polylog(3,-exp(2*I*(a+b*x)))/b^3+3/2*d^2*(c+d*x)*polylog(3,exp(2*I*(a+b*x)))/b^3-3/4*I*d^3*polylog(4,-exp(2*I*(a+b*x)))/b^4+3/4*I*d^3*polylog(4,exp(2*I*(a+b*x)))/b^4],
[(c+d*x)^2*csc(a+b*x)^3*sec(a+b*x),x,17,-c*d*x/b-1/2*d^2*x^2/b-2*(c+d*x)^2*arctanh(exp(2*I*(a+b*x)))/b-d*(c+d*x)*cot(a+b*x)/b^2-1/2*(c+d*x)^2*cot(a+b*x)^2/b+d^2*log(sin(a+b*x))/b^3+I*d*(c+d*x)*polylog(2,-exp(2*I*(a+b*x)))/b^2-I*d*(c+d*x)*polylog(2,exp(2*I*(a+b*x)))/b^2-1/2*d^2*polylog(3,-exp(2*I*(a+b*x)))/b^3+1/2*d^2*polylog(3,exp(2*I*(a+b*x)))/b^3],
[(c+d*x)*csc(a+b*x)^3*sec(a+b*x),x,11,-1/2*d*x/b-2*d*x*arctanh(exp(2*I*(a+b*x)))/b-1/2*d*cot(a+b*x)/b^2-1/2*(c+d*x)*cot(a+b*x)^2/b-d*x*log(tan(a+b*x))/b+(c+d*x)*log(tan(a+b*x))/b+1/2*I*d*polylog(2,-exp(2*I*(a+b*x)))/b^2-1/2*I*d*polylog(2,exp(2*I*(a+b*x)))/b^2],
[csc(a+b*x)^3*sec(a+b*x)/(c+d*x),x,0,CannotIntegrate(csc(a+b*x)^3*sec(a+b*x)/(c+d*x),x)],
[csc(a+b*x)^3*sec(a+b*x)/(c+d*x)^2,x,0,CannotIntegrate(csc(a+b*x)^3*sec(a+b*x)/(c+d*x)^2,x)],

# Integrands of the form (c+d x)^(m/2) Sec[a+b x] Sin[a+b x]^p

# Integrands of the form (c+d x)^m Sec[a+b x]^2 Sin[a+b x]^p

# Integrands of the form (c+d x)^m Sec[a+b x]^2 Sin[a+b x]^p

# p>0
[(c+d*x)^m*sec(a+b*x)*tan(a+b*x),x,0,CannotIntegrate((c+d*x)^m*sec(a+b*x)*tan(a+b*x),x)],
[(c+d*x)^4*sec(a+b*x)*tan(a+b*x),x,10,8*I*d*(c+d*x)^3*arctan(exp(I*(a+b*x)))/b^2-12*I*d^2*(c+d*x)^2*polylog(2,-I*exp(I*(a+b*x)))/b^3+12*I*d^2*(c+d*x)^2*polylog(2,I*exp(I*(a+b*x)))/b^3+24*d^3*(c+d*x)*polylog(3,-I*exp(I*(a+b*x)))/b^4-24*d^3*(c+d*x)*polylog(3,I*exp(I*(a+b*x)))/b^4+24*I*d^4*polylog(4,-I*exp(I*(a+b*x)))/b^5-24*I*d^4*polylog(4,I*exp(I*(a+b*x)))/b^5+(c+d*x)^4*sec(a+b*x)/b],
[(c+d*x)^3*sec(a+b*x)*tan(a+b*x),x,8,6*I*d*(c+d*x)^2*arctan(exp(I*(a+b*x)))/b^2-6*I*d^2*(c+d*x)*polylog(2,-I*exp(I*(a+b*x)))/b^3+6*I*d^2*(c+d*x)*polylog(2,I*exp(I*(a+b*x)))/b^3+6*d^3*polylog(3,-I*exp(I*(a+b*x)))/b^4-6*d^3*polylog(3,I*exp(I*(a+b*x)))/b^4+(c+d*x)^3*sec(a+b*x)/b],
[(c+d*x)^2*sec(a+b*x)*tan(a+b*x),x,6,4*I*d*(c+d*x)*arctan(exp(I*(a+b*x)))/b^2-2*I*d^2*polylog(2,-I*exp(I*(a+b*x)))/b^3+2*I*d^2*polylog(2,I*exp(I*(a+b*x)))/b^3+(c+d*x)^2*sec(a+b*x)/b],
[(c+d*x)*sec(a+b*x)*tan(a+b*x),x,2,-d*arctanh(sin(a+b*x))/b^2+(c+d*x)*sec(a+b*x)/b],
[sec(a+b*x)*tan(a+b*x)/(c+d*x),x,0,CannotIntegrate(sec(a+b*x)*tan(a+b*x)/(c+d*x),x)],
[sec(a+b*x)*tan(a+b*x)/(c+d*x)^2,x,0,CannotIntegrate(sec(a+b*x)*tan(a+b*x)/(c+d*x)^2,x)],
[(c+d*x)^m*tan(a+b*x)^2,x,0,Unintegrable((c+d*x)^m*tan(a+b*x)^2,x)],
[(c+d*x)^3*tan(a+b*x)^2,x,7,-I*(c+d*x)^3/b-1/4*(c+d*x)^4/d+3*d*(c+d*x)^2*log(1+exp(2*I*(a+b*x)))/b^2-3*I*d^2*(c+d*x)*polylog(2,-exp(2*I*(a+b*x)))/b^3+3/2*d^3*polylog(3,-exp(2*I*(a+b*x)))/b^4+(c+d*x)^3*tan(a+b*x)/b],
[(c+d*x)^2*tan(a+b*x)^2,x,6,-I*(c+d*x)^2/b-1/3*(c+d*x)^3/d+2*d*(c+d*x)*log(1+exp(2*I*(a+b*x)))/b^2-I*d^2*polylog(2,-exp(2*I*(a+b*x)))/b^3+(c+d*x)^2*tan(a+b*x)/b],
[(c+d*x)*tan(a+b*x)^2,x,3,-c*x-1/2*d*x^2+d*log(cos(a+b*x))/b^2+(c+d*x)*tan(a+b*x)/b],
[tan(a+b*x)^2/(c+d*x),x,0,Unintegrable(tan(a+b*x)^2/(c+d*x),x)],
[tan(a+b*x)^2/(c+d*x)^2,x,0,Unintegrable(tan(a+b*x)^2/(c+d*x)^2,x)],
[(c+d*x)^m*sin(a+b*x)*tan(a+b*x)^2,x,4,CannotIntegrate((c+d*x)^m*sec(a+b*x)*tan(a+b*x),x)+1/2*exp(I*(a-b*c/d))*(c+d*x)^m*GAMMA(1+m,-I*b*(c+d*x)/d)/(b*(-I*b*(c+d*x)/d)^m)+1/2*(c+d*x)^m*GAMMA(1+m,I*b*(c+d*x)/d)/(b*exp(I*(a-b*c/d))*(I*b*(c+d*x)/d)^m)],
[(c+d*x)^3*sin(a+b*x)*tan(a+b*x)^2,x,13,6*I*d*(c+d*x)^2*arctan(exp(I*(a+b*x)))/b^2-6*d^2*(c+d*x)*cos(a+b*x)/b^3+(c+d*x)^3*cos(a+b*x)/b-6*I*d^2*(c+d*x)*polylog(2,-I*exp(I*(a+b*x)))/b^3+6*I*d^2*(c+d*x)*polylog(2,I*exp(I*(a+b*x)))/b^3+6*d^3*polylog(3,-I*exp(I*(a+b*x)))/b^4-6*d^3*polylog(3,I*exp(I*(a+b*x)))/b^4+(c+d*x)^3*sec(a+b*x)/b+6*d^3*sin(a+b*x)/b^4-3*d*(c+d*x)^2*sin(a+b*x)/b^2],
[(c+d*x)^2*sin(a+b*x)*tan(a+b*x)^2,x,10,4*I*d*(c+d*x)*arctan(exp(I*(a+b*x)))/b^2-2*d^2*cos(a+b*x)/b^3+(c+d*x)^2*cos(a+b*x)/b-2*I*d^2*polylog(2,-I*exp(I*(a+b*x)))/b^3+2*I*d^2*polylog(2,I*exp(I*(a+b*x)))/b^3+(c+d*x)^2*sec(a+b*x)/b-2*d*(c+d*x)*sin(a+b*x)/b^2],
[(c+d*x)*sin(a+b*x)*tan(a+b*x)^2,x,5,-d*arctanh(sin(a+b*x))/b^2+(c+d*x)*cos(a+b*x)/b+(c+d*x)*sec(a+b*x)/b-d*sin(a+b*x)/b^2],
[sin(a+b*x)*tan(a+b*x)^2/(c+d*x),x,4,CannotIntegrate(sec(a+b*x)*tan(a+b*x)/(c+d*x),x)-cos(a-b*c/d)*Si(b*c/d+b*x)/d-Ci(b*c/d+b*x)*sin(a-b*c/d)/d],
[sin(a+b*x)*tan(a+b*x)^2/(c+d*x)^2,x,5,CannotIntegrate(sec(a+b*x)*tan(a+b*x)/(c+d*x)^2,x)-b*Ci(b*c/d+b*x)*cos(a-b*c/d)/d^2+b*Si(b*c/d+b*x)*sin(a-b*c/d)/d^2+sin(a+b*x)/(d*(c+d*x))],

# p<0
[(c+d*x)^m*csc(a+b*x)*sec(a+b*x)^2,x,0,CannotIntegrate((c+d*x)^m*csc(a+b*x)*sec(a+b*x)^2,x)],
[(c+d*x)^4*csc(a+b*x)*sec(a+b*x)^2,x,27,8*I*d*(c+d*x)^3*arctan(exp(I*(a+b*x)))/b^2-2*(c+d*x)^4*arctanh(exp(I*(a+b*x)))/b+4*I*d*(c+d*x)^3*polylog(2,-exp(I*(a+b*x)))/b^2-12*I*d^2*(c+d*x)^2*polylog(2,-I*exp(I*(a+b*x)))/b^3+12*I*d^2*(c+d*x)^2*polylog(2,I*exp(I*(a+b*x)))/b^3-4*I*d*(c+d*x)^3*polylog(2,exp(I*(a+b*x)))/b^2-12*d^2*(c+d*x)^2*polylog(3,-exp(I*(a+b*x)))/b^3+24*d^3*(c+d*x)*polylog(3,-I*exp(I*(a+b*x)))/b^4-24*d^3*(c+d*x)*polylog(3,I*exp(I*(a+b*x)))/b^4+12*d^2*(c+d*x)^2*polylog(3,exp(I*(a+b*x)))/b^3-24*I*d^3*(c+d*x)*polylog(4,-exp(I*(a+b*x)))/b^4+24*I*d^4*polylog(4,-I*exp(I*(a+b*x)))/b^5-24*I*d^4*polylog(4,I*exp(I*(a+b*x)))/b^5+24*I*d^3*(c+d*x)*polylog(4,exp(I*(a+b*x)))/b^4+24*d^4*polylog(5,-exp(I*(a+b*x)))/b^5-24*d^4*polylog(5,exp(I*(a+b*x)))/b^5+(c+d*x)^4*sec(a+b*x)/b],
[(c+d*x)^3*csc(a+b*x)*sec(a+b*x)^2,x,23,6*I*d*(c+d*x)^2*arctan(exp(I*(a+b*x)))/b^2-2*(c+d*x)^3*arctanh(exp(I*(a+b*x)))/b+3*I*d*(c+d*x)^2*polylog(2,-exp(I*(a+b*x)))/b^2-6*I*d^2*(c+d*x)*polylog(2,-I*exp(I*(a+b*x)))/b^3+6*I*d^2*(c+d*x)*polylog(2,I*exp(I*(a+b*x)))/b^3-3*I*d*(c+d*x)^2*polylog(2,exp(I*(a+b*x)))/b^2-6*d^2*(c+d*x)*polylog(3,-exp(I*(a+b*x)))/b^3+6*d^3*polylog(3,-I*exp(I*(a+b*x)))/b^4-6*d^3*polylog(3,I*exp(I*(a+b*x)))/b^4+6*d^2*(c+d*x)*polylog(3,exp(I*(a+b*x)))/b^3-6*I*d^3*polylog(4,-exp(I*(a+b*x)))/b^4+6*I*d^3*polylog(4,exp(I*(a+b*x)))/b^4+(c+d*x)^3*sec(a+b*x)/b],
[(c+d*x)^2*csc(a+b*x)*sec(a+b*x)^2,x,19,4*I*d*(c+d*x)*arctan(exp(I*(a+b*x)))/b^2-2*(c+d*x)^2*arctanh(exp(I*(a+b*x)))/b+2*I*d*(c+d*x)*polylog(2,-exp(I*(a+b*x)))/b^2-2*I*d^2*polylog(2,-I*exp(I*(a+b*x)))/b^3+2*I*d^2*polylog(2,I*exp(I*(a+b*x)))/b^3-2*I*d*(c+d*x)*polylog(2,exp(I*(a+b*x)))/b^2-2*d^2*polylog(3,-exp(I*(a+b*x)))/b^3+2*d^2*polylog(3,exp(I*(a+b*x)))/b^3+(c+d*x)^2*sec(a+b*x)/b],
[(c+d*x)*csc(a+b*x)*sec(a+b*x)^2,x,10,-2*d*x*arctanh(exp(I*(a+b*x)))/b-c*arctanh(cos(a+b*x))/b-d*arctanh(sin(a+b*x))/b^2+I*d*polylog(2,-exp(I*(a+b*x)))/b^2-I*d*polylog(2,exp(I*(a+b*x)))/b^2+c*sec(a+b*x)/b+d*x*sec(a+b*x)/b,-2*d*x*arctanh(exp(I*(a+b*x)))/b+d*x*arctanh(cos(a+b*x))/b-(c+d*x)*arctanh(cos(a+b*x))/b-d*arctanh(sin(a+b*x))/b^2+I*d*polylog(2,-exp(I*(a+b*x)))/b^2-I*d*polylog(2,exp(I*(a+b*x)))/b^2+(c+d*x)*sec(a+b*x)/b],
[csc(a+b*x)*sec(a+b*x)^2/(c+d*x),x,0,CannotIntegrate(csc(a+b*x)*sec(a+b*x)^2/(c+d*x),x)],
[csc(a+b*x)*sec(a+b*x)^2/(c+d*x)^2,x,0,CannotIntegrate(csc(a+b*x)*sec(a+b*x)^2/(c+d*x)^2,x)],
[(c+d*x)^m*csc(a+b*x)^2*sec(a+b*x)^2,x,0,CannotIntegrate((c+d*x)^m*csc(a+b*x)^2*sec(a+b*x)^2,x)],
[(c+d*x)^3*csc(a+b*x)^2*sec(a+b*x)^2,x,7,-2*I*(c+d*x)^3/b-2*(c+d*x)^3*cot(2*a+2*b*x)/b+3*d*(c+d*x)^2*log(1-exp(4*I*(a+b*x)))/b^2-3/2*I*d^2*(c+d*x)*polylog(2,exp(4*I*(a+b*x)))/b^3+3/8*d^3*polylog(3,exp(4*I*(a+b*x)))/b^4],
[(c+d*x)^2*csc(a+b*x)^2*sec(a+b*x)^2,x,6,-2*I*(c+d*x)^2/b-2*(c+d*x)^2*cot(2*a+2*b*x)/b+2*d*(c+d*x)*log(1-exp(4*I*(a+b*x)))/b^2-1/2*I*d^2*polylog(2,exp(4*I*(a+b*x)))/b^3],
[(c+d*x)*csc(a+b*x)^2*sec(a+b*x)^2,x,3,-2*(c+d*x)*cot(2*a+2*b*x)/b+d*log(sin(2*a+2*b*x))/b^2],
[csc(a+b*x)^2*sec(a+b*x)^2/(c+d*x),x,1,4*Unintegrable(csc(2*a+2*b*x)^2/(c+d*x),x)],
[csc(a+b*x)^2*sec(a+b*x)^2/(c+d*x)^2,x,1,4*Unintegrable(csc(2*a+2*b*x)^2/(c+d*x)^2,x)],
[(c+d*x)^m*csc(a+b*x)^3*sec(a+b*x)^2,x,0,CannotIntegrate((c+d*x)^m*csc(a+b*x)^3*sec(a+b*x)^2,x)],
[(c+d*x)^3*csc(a+b*x)^3*sec(a+b*x)^2,x,64,12*I*c*d^2*x*arctan(exp(I*(a+b*x)))/b^2+6*I*d^3*x^2*arctan(exp(I*(a+b*x)))/b^2-6*d^3*x*arctanh(exp(I*(a+b*x)))/b^3-3*(c+d*x)^3*arctanh(exp(I*(a+b*x)))/b-3*c*d^2*arctanh(cos(a+b*x))/b^3-3*c^2*d*arctanh(sin(a+b*x))/b^2-3/2*c^2*d*csc(a+b*x)/b^2-3*c*d^2*x*csc(a+b*x)/b^2-3/2*d^3*x^2*csc(a+b*x)/b^2+3*I*d^3*polylog(2,-exp(I*(a+b*x)))/b^4+9/2*I*d*(c+d*x)^2*polylog(2,-exp(I*(a+b*x)))/b^2-6*I*c*d^2*polylog(2,-I*exp(I*(a+b*x)))/b^3-6*I*d^3*x*polylog(2,-I*exp(I*(a+b*x)))/b^3+6*I*c*d^2*polylog(2,I*exp(I*(a+b*x)))/b^3+6*I*d^3*x*polylog(2,I*exp(I*(a+b*x)))/b^3-3*I*d^3*polylog(2,exp(I*(a+b*x)))/b^4-9/2*I*d*(c+d*x)^2*polylog(2,exp(I*(a+b*x)))/b^2-9*d^2*(c+d*x)*polylog(3,-exp(I*(a+b*x)))/b^3+6*d^3*polylog(3,-I*exp(I*(a+b*x)))/b^4-6*d^3*polylog(3,I*exp(I*(a+b*x)))/b^4+9*d^2*(c+d*x)*polylog(3,exp(I*(a+b*x)))/b^3-9*I*d^3*polylog(4,-exp(I*(a+b*x)))/b^4+9*I*d^3*polylog(4,exp(I*(a+b*x)))/b^4+3/2*(c+d*x)^3*sec(a+b*x)/b-1/2*(c+d*x)^3*csc(a+b*x)^2*sec(a+b*x)/b],
[(c+d*x)^2*csc(a+b*x)^3*sec(a+b*x)^2,x,36,4*I*d^2*x*arctan(exp(I*(a+b*x)))/b^2-3*(c+d*x)^2*arctanh(exp(I*(a+b*x)))/b-d^2*arctanh(cos(a+b*x))/b^3-2*c*d*arctanh(sin(a+b*x))/b^2-c*d*csc(a+b*x)/b^2-d^2*x*csc(a+b*x)/b^2+3*I*d*(c+d*x)*polylog(2,-exp(I*(a+b*x)))/b^2-2*I*d^2*polylog(2,-I*exp(I*(a+b*x)))/b^3+2*I*d^2*polylog(2,I*exp(I*(a+b*x)))/b^3-3*I*d*(c+d*x)*polylog(2,exp(I*(a+b*x)))/b^2-3*d^2*polylog(3,-exp(I*(a+b*x)))/b^3+3*d^2*polylog(3,exp(I*(a+b*x)))/b^3+3/2*(c+d*x)^2*sec(a+b*x)/b-1/2*(c+d*x)^2*csc(a+b*x)^2*sec(a+b*x)/b],
[(c+d*x)*csc(a+b*x)^3*sec(a+b*x)^2,x,13,-3*d*x*arctanh(exp(I*(a+b*x)))/b-3/2*c*arctanh(cos(a+b*x))/b-d*arctanh(sin(a+b*x))/b^2-1/2*d*csc(a+b*x)/b^2+3/2*I*d*polylog(2,-exp(I*(a+b*x)))/b^2-3/2*I*d*polylog(2,exp(I*(a+b*x)))/b^2+3/2*(c+d*x)*sec(a+b*x)/b-1/2*(c+d*x)*csc(a+b*x)^2*sec(a+b*x)/b,-3*d*x*arctanh(exp(I*(a+b*x)))/b+3/2*d*x*arctanh(cos(a+b*x))/b-3/2*(c+d*x)*arctanh(cos(a+b*x))/b-d*arctanh(sin(a+b*x))/b^2-1/2*d*csc(a+b*x)/b^2+3/2*I*d*polylog(2,-exp(I*(a+b*x)))/b^2-3/2*I*d*polylog(2,exp(I*(a+b*x)))/b^2+3/2*(c+d*x)*sec(a+b*x)/b-1/2*(c+d*x)*csc(a+b*x)^2*sec(a+b*x)/b],
[csc(a+b*x)^3*sec(a+b*x)^2/(c+d*x),x,0,CannotIntegrate(csc(a+b*x)^3*sec(a+b*x)^2/(c+d*x),x)],
[csc(a+b*x)^3*sec(a+b*x)^2/(c+d*x)^2,x,0,CannotIntegrate(csc(a+b*x)^3*sec(a+b*x)^2/(c+d*x)^2,x)],
[x^m*csc(a+b*x)^3*sec(a+b*x)^2,x,0,CannotIntegrate(x^m*csc(a+b*x)^3*sec(a+b*x)^2,x)],
[x^3*csc(a+b*x)^3*sec(a+b*x)^2,x,40,6*I*x^2*arctan(exp(I*(a+b*x)))/b^2-6*x*arctanh(exp(I*(a+b*x)))/b^3-3*x^3*arctanh(exp(I*(a+b*x)))/b-3/2*x^2*csc(a+b*x)/b^2+3*I*polylog(2,-exp(I*(a+b*x)))/b^4+9/2*I*x^2*polylog(2,-exp(I*(a+b*x)))/b^2-6*I*x*polylog(2,-I*exp(I*(a+b*x)))/b^3+6*I*x*polylog(2,I*exp(I*(a+b*x)))/b^3-3*I*polylog(2,exp(I*(a+b*x)))/b^4-9/2*I*x^2*polylog(2,exp(I*(a+b*x)))/b^2-9*x*polylog(3,-exp(I*(a+b*x)))/b^3+6*polylog(3,-I*exp(I*(a+b*x)))/b^4-6*polylog(3,I*exp(I*(a+b*x)))/b^4+9*x*polylog(3,exp(I*(a+b*x)))/b^3-9*I*polylog(4,-exp(I*(a+b*x)))/b^4+9*I*polylog(4,exp(I*(a+b*x)))/b^4+3/2*x^3*sec(a+b*x)/b-1/2*x^3*csc(a+b*x)^2*sec(a+b*x)/b],
[x^2*csc(a+b*x)^3*sec(a+b*x)^2,x,29,4*I*x*arctan(exp(I*(a+b*x)))/b^2-3*x^2*arctanh(exp(I*(a+b*x)))/b-arctanh(cos(a+b*x))/b^3-x*csc(a+b*x)/b^2+3*I*x*polylog(2,-exp(I*(a+b*x)))/b^2-2*I*polylog(2,-I*exp(I*(a+b*x)))/b^3+2*I*polylog(2,I*exp(I*(a+b*x)))/b^3-3*I*x*polylog(2,exp(I*(a+b*x)))/b^2-3*polylog(3,-exp(I*(a+b*x)))/b^3+3*polylog(3,exp(I*(a+b*x)))/b^3+3/2*x^2*sec(a+b*x)/b-1/2*x^2*csc(a+b*x)^2*sec(a+b*x)/b],
[x*csc(a+b*x)^3*sec(a+b*x)^2,x,13,-3*x*arctanh(exp(I*(a+b*x)))/b-arctanh(sin(a+b*x))/b^2-1/2*csc(a+b*x)/b^2+3/2*I*polylog(2,-exp(I*(a+b*x)))/b^2-3/2*I*polylog(2,exp(I*(a+b*x)))/b^2+3/2*x*sec(a+b*x)/b-1/2*x*csc(a+b*x)^2*sec(a+b*x)/b],
[csc(a+b*x)^3*sec(a+b*x)^2/x,x,0,CannotIntegrate(csc(a+b*x)^3*sec(a+b*x)^2/x,x)],
[csc(a+b*x)^3*sec(a+b*x)^2/x^2,x,0,CannotIntegrate(csc(a+b*x)^3*sec(a+b*x)^2/x^2,x)],

# Integrands of the form (c+d x)^(m/2) Sec[a+b x]^2 Sin[a+b x]^p

# Integrands of the form (c+d x)^m Sec[a+b x]^3 Sin[a+b x]^p

# Integrands of the form (c+d x)^m Sec[a+b x]^3 Sin[a+b x]^p

# p>0
[(c+d*x)^m*sec(a+b*x)^2*tan(a+b*x),x,0,CannotIntegrate((c+d*x)^m*sec(a+b*x)^2*tan(a+b*x),x)],
[(c+d*x)^4*sec(a+b*x)^2*tan(a+b*x),x,7,2*I*d*(c+d*x)^3/b^2-6*d^2*(c+d*x)^2*log(1+exp(2*I*(a+b*x)))/b^3+6*I*d^3*(c+d*x)*polylog(2,-exp(2*I*(a+b*x)))/b^4-3*d^4*polylog(3,-exp(2*I*(a+b*x)))/b^5+1/2*(c+d*x)^4*sec(a+b*x)^2/b-2*d*(c+d*x)^3*tan(a+b*x)/b^2],
[(c+d*x)^3*sec(a+b*x)^2*tan(a+b*x),x,6,3/2*I*d*(c+d*x)^2/b^2-3*d^2*(c+d*x)*log(1+exp(2*I*(a+b*x)))/b^3+3/2*I*d^3*polylog(2,-exp(2*I*(a+b*x)))/b^4+1/2*(c+d*x)^3*sec(a+b*x)^2/b-3/2*d*(c+d*x)^2*tan(a+b*x)/b^2],
[(c+d*x)^2*sec(a+b*x)^2*tan(a+b*x),x,3,-d^2*log(cos(a+b*x))/b^3+1/2*(c+d*x)^2*sec(a+b*x)^2/b-d*(c+d*x)*tan(a+b*x)/b^2],
[(c+d*x)*sec(a+b*x)^2*tan(a+b*x),x,3,1/2*(c+d*x)*sec(a+b*x)^2/b-1/2*d*tan(a+b*x)/b^2],
[sec(a+b*x)^2*tan(a+b*x)/(c+d*x),x,0,CannotIntegrate(sec(a+b*x)^2*tan(a+b*x)/(c+d*x),x)],
[sec(a+b*x)^2*tan(a+b*x)/(c+d*x)^2,x,0,CannotIntegrate(sec(a+b*x)^2*tan(a+b*x)/(c+d*x)^2,x)],
[(c+d*x)^m*sec(a+b*x)*tan(a+b*x)^2,x,1,-Unintegrable((c+d*x)^m*sec(a+b*x),x)+Unintegrable((c+d*x)^m*sec(a+b*x)^3,x)],
[(c+d*x)^3*sec(a+b*x)*tan(a+b*x)^2,x,25,-6*I*d^2*(c+d*x)*arctan(exp(I*(a+b*x)))/b^3+I*(c+d*x)^3*arctan(exp(I*(a+b*x)))/b+3*I*d^3*polylog(2,-I*exp(I*(a+b*x)))/b^4-3/2*I*d*(c+d*x)^2*polylog(2,-I*exp(I*(a+b*x)))/b^2-3*I*d^3*polylog(2,I*exp(I*(a+b*x)))/b^4+3/2*I*d*(c+d*x)^2*polylog(2,I*exp(I*(a+b*x)))/b^2+3*d^2*(c+d*x)*polylog(3,-I*exp(I*(a+b*x)))/b^3-3*d^2*(c+d*x)*polylog(3,I*exp(I*(a+b*x)))/b^3+3*I*d^3*polylog(4,-I*exp(I*(a+b*x)))/b^4-3*I*d^3*polylog(4,I*exp(I*(a+b*x)))/b^4-3/2*d*(c+d*x)^2*sec(a+b*x)/b^2+1/2*(c+d*x)^3*sec(a+b*x)*tan(a+b*x)/b],
[(c+d*x)^2*sec(a+b*x)*tan(a+b*x)^2,x,17,I*(c+d*x)^2*arctan(exp(I*(a+b*x)))/b+d^2*arctanh(sin(a+b*x))/b^3-I*d*(c+d*x)*polylog(2,-I*exp(I*(a+b*x)))/b^2+I*d*(c+d*x)*polylog(2,I*exp(I*(a+b*x)))/b^2+d^2*polylog(3,-I*exp(I*(a+b*x)))/b^3-d^2*polylog(3,I*exp(I*(a+b*x)))/b^3-d*(c+d*x)*sec(a+b*x)/b^2+1/2*(c+d*x)^2*sec(a+b*x)*tan(a+b*x)/b],
[(c+d*x)*sec(a+b*x)*tan(a+b*x)^2,x,12,I*(c+d*x)*arctan(exp(I*(a+b*x)))/b-1/2*I*d*polylog(2,-I*exp(I*(a+b*x)))/b^2+1/2*I*d*polylog(2,I*exp(I*(a+b*x)))/b^2-1/2*d*sec(a+b*x)/b^2+1/2*(c+d*x)*sec(a+b*x)*tan(a+b*x)/b],
[sec(a+b*x)*tan(a+b*x)^2/(c+d*x),x,1,-Unintegrable(sec(a+b*x)/(c+d*x),x)+Unintegrable(sec(a+b*x)^3/(c+d*x),x)],
[sec(a+b*x)*tan(a+b*x)^2/(c+d*x)^2,x,1,-Unintegrable(sec(a+b*x)/(c+d*x)^2,x)+Unintegrable(sec(a+b*x)^3/(c+d*x)^2,x)],
[(c+d*x)^m*tan(a+b*x)^3,x,0,Unintegrable((c+d*x)^m*tan(a+b*x)^3,x)],
[(c+d*x)^3*tan(a+b*x)^3,x,13,3/2*I*d*(c+d*x)^2/b^2+1/2*(c+d*x)^3/b-1/4*I*(c+d*x)^4/d-3*d^2*(c+d*x)*log(1+exp(2*I*(a+b*x)))/b^3+(c+d*x)^3*log(1+exp(2*I*(a+b*x)))/b+3/2*I*d^3*polylog(2,-exp(2*I*(a+b*x)))/b^4-3/2*I*d*(c+d*x)^2*polylog(2,-exp(2*I*(a+b*x)))/b^2+3/2*d^2*(c+d*x)*polylog(3,-exp(2*I*(a+b*x)))/b^3+3/4*I*d^3*polylog(4,-exp(2*I*(a+b*x)))/b^4-3/2*d*(c+d*x)^2*tan(a+b*x)/b^2+1/2*(c+d*x)^3*tan(a+b*x)^2/b],
[(c+d*x)^2*tan(a+b*x)^3,x,9,c*d*x/b+1/2*d^2*x^2/b-1/3*I*(c+d*x)^3/d+(c+d*x)^2*log(1+exp(2*I*(a+b*x)))/b-d^2*log(cos(a+b*x))/b^3-I*d*(c+d*x)*polylog(2,-exp(2*I*(a+b*x)))/b^2+1/2*d^2*polylog(3,-exp(2*I*(a+b*x)))/b^3-d*(c+d*x)*tan(a+b*x)/b^2+1/2*(c+d*x)^2*tan(a+b*x)^2/b],
[(c+d*x)*tan(a+b*x)^3,x,7,1/2*d*x/b-1/2*I*(c+d*x)^2/d+(c+d*x)*log(1+exp(2*I*(a+b*x)))/b-1/2*I*d*polylog(2,-exp(2*I*(a+b*x)))/b^2-1/2*d*tan(a+b*x)/b^2+1/2*(c+d*x)*tan(a+b*x)^2/b],
[tan(a+b*x)^3/(c+d*x),x,0,Unintegrable(tan(a+b*x)^3/(c+d*x),x)],
[tan(a+b*x)^3/(c+d*x)^2,x,0,Unintegrable(tan(a+b*x)^3/(c+d*x)^2,x)],

# p<0
[(c+d*x)^m*csc(a+b*x)*sec(a+b*x)^3,x,0,CannotIntegrate((c+d*x)^m*csc(a+b*x)*sec(a+b*x)^3,x)],
[(c+d*x)^4*csc(a+b*x)*sec(a+b*x)^3,x,25,2*I*d*(c+d*x)^3/b^2+1/2*(c+d*x)^4/b-2*(c+d*x)^4*arctanh(exp(2*I*(a+b*x)))/b-6*d^2*(c+d*x)^2*log(1+exp(2*I*(a+b*x)))/b^3+6*I*d^3*(c+d*x)*polylog(2,-exp(2*I*(a+b*x)))/b^4+2*I*d*(c+d*x)^3*polylog(2,-exp(2*I*(a+b*x)))/b^2-2*I*d*(c+d*x)^3*polylog(2,exp(2*I*(a+b*x)))/b^2-3*d^4*polylog(3,-exp(2*I*(a+b*x)))/b^5-3*d^2*(c+d*x)^2*polylog(3,-exp(2*I*(a+b*x)))/b^3+3*d^2*(c+d*x)^2*polylog(3,exp(2*I*(a+b*x)))/b^3-3*I*d^3*(c+d*x)*polylog(4,-exp(2*I*(a+b*x)))/b^4+3*I*d^3*(c+d*x)*polylog(4,exp(2*I*(a+b*x)))/b^4+3/2*d^4*polylog(5,-exp(2*I*(a+b*x)))/b^5-3/2*d^4*polylog(5,exp(2*I*(a+b*x)))/b^5-2*d*(c+d*x)^3*tan(a+b*x)/b^2+1/2*(c+d*x)^4*tan(a+b*x)^2/b],
[(c+d*x)^3*csc(a+b*x)*sec(a+b*x)^3,x,22,3/2*I*d*(c+d*x)^2/b^2+1/2*(c+d*x)^3/b-2*(c+d*x)^3*arctanh(exp(2*I*(a+b*x)))/b-3*d^2*(c+d*x)*log(1+exp(2*I*(a+b*x)))/b^3+3/2*I*d^3*polylog(2,-exp(2*I*(a+b*x)))/b^4+3/2*I*d*(c+d*x)^2*polylog(2,-exp(2*I*(a+b*x)))/b^2-3/2*I*d*(c+d*x)^2*polylog(2,exp(2*I*(a+b*x)))/b^2-3/2*d^2*(c+d*x)*polylog(3,-exp(2*I*(a+b*x)))/b^3+3/2*d^2*(c+d*x)*polylog(3,exp(2*I*(a+b*x)))/b^3-3/4*I*d^3*polylog(4,-exp(2*I*(a+b*x)))/b^4+3/4*I*d^3*polylog(4,exp(2*I*(a+b*x)))/b^4-3/2*d*(c+d*x)^2*tan(a+b*x)/b^2+1/2*(c+d*x)^3*tan(a+b*x)^2/b],
[(c+d*x)^2*csc(a+b*x)*sec(a+b*x)^3,x,17,c*d*x/b+1/2*d^2*x^2/b-2*(c+d*x)^2*arctanh(exp(2*I*(a+b*x)))/b-d^2*log(cos(a+b*x))/b^3+I*d*(c+d*x)*polylog(2,-exp(2*I*(a+b*x)))/b^2-I*d*(c+d*x)*polylog(2,exp(2*I*(a+b*x)))/b^2-1/2*d^2*polylog(3,-exp(2*I*(a+b*x)))/b^3+1/2*d^2*polylog(3,exp(2*I*(a+b*x)))/b^3-d*(c+d*x)*tan(a+b*x)/b^2+1/2*(c+d*x)^2*tan(a+b*x)^2/b],
[(c+d*x)*csc(a+b*x)*sec(a+b*x)^3,x,11,1/2*d*x/b-2*d*x*arctanh(exp(2*I*a+2*I*b*x))/b+c*log(tan(a+b*x))/b+1/2*I*d*polylog(2,-exp(2*I*(a+b*x)))/b^2-1/2*I*d*polylog(2,exp(2*I*(a+b*x)))/b^2-1/2*d*tan(a+b*x)/b^2+1/2*c*tan(a+b*x)^2/b+1/2*d*x*tan(a+b*x)^2/b,1/2*d*x/b-2*d*x*arctanh(exp(2*I*(a+b*x)))/b-d*x*log(tan(a+b*x))/b+(c+d*x)*log(tan(a+b*x))/b+1/2*I*d*polylog(2,-exp(2*I*(a+b*x)))/b^2-1/2*I*d*polylog(2,exp(2*I*(a+b*x)))/b^2-1/2*d*tan(a+b*x)/b^2+1/2*(c+d*x)*tan(a+b*x)^2/b],
[csc(a+b*x)*sec(a+b*x)^3/(c+d*x),x,0,CannotIntegrate(csc(a+b*x)*sec(a+b*x)^3/(c+d*x),x)],
[csc(a+b*x)*sec(a+b*x)^3/(c+d*x)^2,x,0,CannotIntegrate(csc(a+b*x)*sec(a+b*x)^3/(c+d*x)^2,x)],
[(c+d*x)^m*csc(a+b*x)^2*sec(a+b*x)^3,x,0,CannotIntegrate((c+d*x)^m*csc(a+b*x)^2*sec(a+b*x)^3,x)],
[(c+d*x)^3*csc(a+b*x)^2*sec(a+b*x)^3,x,44,-6*I*d^2*(c+d*x)*arctan(exp(I*(a+b*x)))/b^3-3*I*(c+d*x)^3*arctan(exp(I*(a+b*x)))/b-6*d*(c+d*x)^2*arctanh(exp(I*(a+b*x)))/b^2-3/2*(c+d*x)^3*csc(a+b*x)/b+6*I*d^2*(c+d*x)*polylog(2,-exp(I*(a+b*x)))/b^3+3*I*d^3*polylog(2,-I*exp(I*(a+b*x)))/b^4+9/2*I*d*(c+d*x)^2*polylog(2,-I*exp(I*(a+b*x)))/b^2-3*I*d^3*polylog(2,I*exp(I*(a+b*x)))/b^4-9/2*I*d*(c+d*x)^2*polylog(2,I*exp(I*(a+b*x)))/b^2-6*I*d^2*(c+d*x)*polylog(2,exp(I*(a+b*x)))/b^3-6*d^3*polylog(3,-exp(I*(a+b*x)))/b^4-9*d^2*(c+d*x)*polylog(3,-I*exp(I*(a+b*x)))/b^3+9*d^2*(c+d*x)*polylog(3,I*exp(I*(a+b*x)))/b^3+6*d^3*polylog(3,exp(I*(a+b*x)))/b^4-9*I*d^3*polylog(4,-I*exp(I*(a+b*x)))/b^4+9*I*d^3*polylog(4,I*exp(I*(a+b*x)))/b^4-3/2*d*(c+d*x)^2*sec(a+b*x)/b^2+1/2*(c+d*x)^3*csc(a+b*x)*sec(a+b*x)^2/b],
[(c+d*x)^2*csc(a+b*x)^2*sec(a+b*x)^3,x,31,-3*I*(c+d*x)^2*arctan(exp(I*(a+b*x)))/b+2*d^2*x*arctanh(exp(I*(a+b*x)))/b^2-6*d*(c+d*x)*arctanh(exp(I*(a+b*x)))/b^2-d^2*x*arctanh(cos(a+b*x))/b^2+d*(c+d*x)*arctanh(cos(a+b*x))/b^2+d^2*arctanh(sin(a+b*x))/b^3-3/2*(c+d*x)^2*csc(a+b*x)/b+2*I*d^2*polylog(2,-exp(I*(a+b*x)))/b^3+3*I*d*(c+d*x)*polylog(2,-I*exp(I*(a+b*x)))/b^2-3*I*d*(c+d*x)*polylog(2,I*exp(I*(a+b*x)))/b^2-2*I*d^2*polylog(2,exp(I*(a+b*x)))/b^3-3*d^2*polylog(3,-I*exp(I*(a+b*x)))/b^3+3*d^2*polylog(3,I*exp(I*(a+b*x)))/b^3-d*(c+d*x)*sec(a+b*x)/b^2+1/2*(c+d*x)^2*csc(a+b*x)*sec(a+b*x)^2/b],
[(c+d*x)*csc(a+b*x)^2*sec(a+b*x)^3,x,13,-3*I*d*x*arctan(exp(I*(a+b*x)))/b-d*arctanh(cos(a+b*x))/b^2+3/2*c*arctanh(sin(a+b*x))/b-3/2*(c+d*x)*csc(a+b*x)/b+3/2*I*d*polylog(2,-I*exp(I*(a+b*x)))/b^2-3/2*I*d*polylog(2,I*exp(I*(a+b*x)))/b^2-1/2*d*sec(a+b*x)/b^2+1/2*(c+d*x)*csc(a+b*x)*sec(a+b*x)^2/b,-3*I*d*x*arctan(exp(I*(a+b*x)))/b-d*arctanh(cos(a+b*x))/b^2-3/2*d*x*arctanh(sin(a+b*x))/b+3/2*(c+d*x)*arctanh(sin(a+b*x))/b-3/2*(c+d*x)*csc(a+b*x)/b+3/2*I*d*polylog(2,-I*exp(I*(a+b*x)))/b^2-3/2*I*d*polylog(2,I*exp(I*(a+b*x)))/b^2-1/2*d*sec(a+b*x)/b^2+1/2*(c+d*x)*csc(a+b*x)*sec(a+b*x)^2/b],
[csc(a+b*x)^2*sec(a+b*x)^3/(c+d*x),x,0,CannotIntegrate(csc(a+b*x)^2*sec(a+b*x)^3/(c+d*x),x)],
[csc(a+b*x)^2*sec(a+b*x)^3/(c+d*x)^2,x,0,CannotIntegrate(csc(a+b*x)^2*sec(a+b*x)^3/(c+d*x)^2,x)],
[(c+d*x)^m*csc(a+b*x)^3*sec(a+b*x)^3,x,0,CannotIntegrate((c+d*x)^m*csc(a+b*x)^3*sec(a+b*x)^3,x)],
[(c+d*x)^3*csc(a+b*x)^3*sec(a+b*x)^3,x,16,-6*d^2*(c+d*x)*arctanh(exp(2*I*(a+b*x)))/b^3-4*(c+d*x)^3*arctanh(exp(2*I*(a+b*x)))/b-3*d*(c+d*x)^2*csc(2*a+2*b*x)/b^2-2*(c+d*x)^3*cot(2*a+2*b*x)*csc(2*a+2*b*x)/b+3/2*I*d^3*polylog(2,-exp(2*I*(a+b*x)))/b^4+3*I*d*(c+d*x)^2*polylog(2,-exp(2*I*(a+b*x)))/b^2-3/2*I*d^3*polylog(2,exp(2*I*(a+b*x)))/b^4-3*I*d*(c+d*x)^2*polylog(2,exp(2*I*(a+b*x)))/b^2-3*d^2*(c+d*x)*polylog(3,-exp(2*I*(a+b*x)))/b^3+3*d^2*(c+d*x)*polylog(3,exp(2*I*(a+b*x)))/b^3-3/2*I*d^3*polylog(4,-exp(2*I*(a+b*x)))/b^4+3/2*I*d^3*polylog(4,exp(2*I*(a+b*x)))/b^4],
[(c+d*x)^2*csc(a+b*x)^3*sec(a+b*x)^3,x,10,-4*(c+d*x)^2*arctanh(exp(2*I*(a+b*x)))/b-d^2*arctanh(cos(2*a+2*b*x))/b^3-2*d*(c+d*x)*csc(2*a+2*b*x)/b^2-2*(c+d*x)^2*cot(2*a+2*b*x)*csc(2*a+2*b*x)/b+2*I*d*(c+d*x)*polylog(2,-exp(2*I*(a+b*x)))/b^2-2*I*d*(c+d*x)*polylog(2,exp(2*I*(a+b*x)))/b^2-d^2*polylog(3,-exp(2*I*(a+b*x)))/b^3+d^2*polylog(3,exp(2*I*(a+b*x)))/b^3],
[(c+d*x)*csc(a+b*x)^3*sec(a+b*x)^3,x,7,-4*(c+d*x)*arctanh(exp(2*I*(a+b*x)))/b-d*csc(2*a+2*b*x)/b^2-2*(c+d*x)*cot(2*a+2*b*x)*csc(2*a+2*b*x)/b+I*d*polylog(2,-exp(2*I*(a+b*x)))/b^2-I*d*polylog(2,exp(2*I*(a+b*x)))/b^2],
[csc(a+b*x)^3*sec(a+b*x)^3/(c+d*x),x,1,8*Unintegrable(csc(2*a+2*b*x)^3/(c+d*x),x)],
[csc(a+b*x)^3*sec(a+b*x)^3/(c+d*x)^2,x,1,8*Unintegrable(csc(2*a+2*b*x)^3/(c+d*x)^2,x)],

# Integrands of the form (c+d x)^(m/2) Sec[a+b x]^3 Sin[a+b x]^p

# Integrands of the form (c+d x)^m Cos[a+b x]^(n/2) Sin[a+b x]^p

# Integrands of the form (c+d x)^m Cos[a+b x]^(n/2) Sin[a+b x]^1
[x*cos(a+b*x)^(5/2)*sin(a+b*x),x,4,-2/7*x*cos(a+b*x)^(7/2)/b+20/147*sqrt(cos(1/2*(a+b*x))^2)/cos(1/2*(a+b*x))*EllipticF(sin(1/2*(a+b*x)),sqrt(2))/b^2+4/49*cos(a+b*x)^(5/2)*sin(a+b*x)/b^2+20/147*sin(a+b*x)*sqrt(cos(a+b*x))/b^2],
[x*cos(a+b*x)^(3/2)*sin(a+b*x),x,3,-2/5*x*cos(a+b*x)^(5/2)/b+12/25*sqrt(cos(1/2*(a+b*x))^2)/cos(1/2*(a+b*x))*EllipticE(sin(1/2*(a+b*x)),sqrt(2))/b^2+4/25*cos(a+b*x)^(3/2)*sin(a+b*x)/b^2],
[x*sin(a+b*x)*sqrt(cos(a+b*x)),x,3,-2/3*x*cos(a+b*x)^(3/2)/b+4/9*sqrt(cos(1/2*(a+b*x))^2)/cos(1/2*(a+b*x))*EllipticF(sin(1/2*(a+b*x)),sqrt(2))/b^2+4/9*sin(a+b*x)*sqrt(cos(a+b*x))/b^2],
[x*sin(a+b*x)/sqrt(cos(a+b*x)),x,2,4*sqrt(cos(1/2*(a+b*x))^2)/cos(1/2*(a+b*x))*EllipticE(sin(1/2*(a+b*x)),sqrt(2))/b^2-2*x*sqrt(cos(a+b*x))/b],
[x*sin(a+b*x)/cos(a+b*x)^(3/2),x,2,-4*sqrt(cos(1/2*(a+b*x))^2)/cos(1/2*(a+b*x))*EllipticF(sin(1/2*(a+b*x)),sqrt(2))/b^2+2*x/(b*sqrt(cos(a+b*x)))],
[x*sin(a+b*x)/cos(a+b*x)^(5/2),x,3,2/3*x/(b*cos(a+b*x)^(3/2))+4/3*sqrt(cos(1/2*(a+b*x))^2)/cos(1/2*(a+b*x))*EllipticE(sin(1/2*(a+b*x)),sqrt(2))/b^2-4/3*sin(a+b*x)/(b^2*sqrt(cos(a+b*x)))],
[x*sin(a+b*x)/cos(a+b*x)^(7/2),x,3,2/5*x/(b*cos(a+b*x)^(5/2))-4/15*sqrt(cos(1/2*(a+b*x))^2)/cos(1/2*(a+b*x))*EllipticF(sin(1/2*(a+b*x)),sqrt(2))/b^2-4/15*sin(a+b*x)/(b^2*cos(a+b*x)^(3/2))],
[x*sin(a+b*x)/cos(a+b*x)^(9/2),x,4,2/7*x/(b*cos(a+b*x)^(7/2))+12/35*sqrt(cos(1/2*(a+b*x))^2)/cos(1/2*(a+b*x))*EllipticE(sin(1/2*(a+b*x)),sqrt(2))/b^2-4/35*sin(a+b*x)/(b^2*cos(a+b*x)^(5/2))-12/35*sin(a+b*x)/(b^2*sqrt(cos(a+b*x)))],

# Integrands of the form (c+d x)^m Sec[a+b x]^(n/2) Sin[a+b x]^1
[x*sec(a+b*x)^(9/2)*sin(a+b*x),x,5,2/7*x*sec(a+b*x)^(7/2)/b-4/35*sec(a+b*x)^(5/2)*sin(a+b*x)/b^2-12/35*sin(a+b*x)*sqrt(sec(a+b*x))/b^2+12/35*sqrt(cos(1/2*(a+b*x))^2)/cos(1/2*(a+b*x))*EllipticE(sin(1/2*(a+b*x)),sqrt(2))*sqrt(cos(a+b*x))*sqrt(sec(a+b*x))/b^2],
[x*sec(a+b*x)^(7/2)*sin(a+b*x),x,4,2/5*x*sec(a+b*x)^(5/2)/b-4/15*sec(a+b*x)^(3/2)*sin(a+b*x)/b^2-4/15*sqrt(cos(1/2*(a+b*x))^2)/cos(1/2*(a+b*x))*EllipticF(sin(1/2*(a+b*x)),sqrt(2))*sqrt(cos(a+b*x))*sqrt(sec(a+b*x))/b^2],
[x*sec(a+b*x)^(5/2)*sin(a+b*x),x,4,2/3*x*sec(a+b*x)^(3/2)/b-4/3*sin(a+b*x)*sqrt(sec(a+b*x))/b^2+4/3*sqrt(cos(1/2*(a+b*x))^2)/cos(1/2*(a+b*x))*EllipticE(sin(1/2*(a+b*x)),sqrt(2))*sqrt(cos(a+b*x))*sqrt(sec(a+b*x))/b^2],
[x*sec(a+b*x)^(3/2)*sin(a+b*x),x,3,2*x*sqrt(sec(a+b*x))/b-4*sqrt(cos(1/2*(a+b*x))^2)/cos(1/2*(a+b*x))*EllipticF(sin(1/2*(a+b*x)),sqrt(2))*sqrt(cos(a+b*x))*sqrt(sec(a+b*x))/b^2],
[x*sin(a+b*x)*sqrt(sec(a+b*x)),x,3,-2*x/(b*sqrt(sec(a+b*x)))+4*sqrt(cos(1/2*(a+b*x))^2)/cos(1/2*(a+b*x))*EllipticE(sin(1/2*(a+b*x)),sqrt(2))*sqrt(cos(a+b*x))*sqrt(sec(a+b*x))/b^2],
[x*sin(a+b*x)/sqrt(sec(a+b*x)),x,4,-2/3*x/(b*sec(a+b*x)^(3/2))+4/9*sin(a+b*x)/(b^2*sqrt(sec(a+b*x)))+4/9*sqrt(cos(1/2*(a+b*x))^2)/cos(1/2*(a+b*x))*EllipticF(sin(1/2*(a+b*x)),sqrt(2))*sqrt(cos(a+b*x))*sqrt(sec(a+b*x))/b^2],
[x*sin(a+b*x)/sec(a+b*x)^(3/2),x,4,-2/5*x/(b*sec(a+b*x)^(5/2))+4/25*sin(a+b*x)/(b^2*sec(a+b*x)^(3/2))+12/25*sqrt(cos(1/2*(a+b*x))^2)/cos(1/2*(a+b*x))*EllipticE(sin(1/2*(a+b*x)),sqrt(2))*sqrt(cos(a+b*x))*sqrt(sec(a+b*x))/b^2],
[x*sin(a+b*x)/sec(a+b*x)^(5/2),x,5,-2/7*x/(b*sec(a+b*x)^(7/2))+4/49*sin(a+b*x)/(b^2*sec(a+b*x)^(5/2))+20/147*sin(a+b*x)/(b^2*sqrt(sec(a+b*x)))+20/147*sqrt(cos(1/2*(a+b*x))^2)/cos(1/2*(a+b*x))*EllipticF(sin(1/2*(a+b*x)),sqrt(2))*sqrt(cos(a+b*x))*sqrt(sec(a+b*x))/b^2],

# Integrands of the form (c+d x)^m Cos[a+b x]^n Sin[a+b x]^(p/2)

# Integrands of the form (c+d x)^m Cos[a+b x]^1 Sin[a+b x]^(p/2)
[x*cos(a+b*x)*sin(a+b*x)^(5/2),x,4,-20/147*sqrt(cos(1/2*(a-1/2*Pi+b*x))^2)/cos(1/2*(a-1/2*Pi+b*x))*EllipticF(sin(1/2*(a-1/2*Pi+b*x)),sqrt(2))/b^2+4/49*cos(a+b*x)*sin(a+b*x)^(5/2)/b^2+2/7*x*sin(a+b*x)^(7/2)/b+20/147*cos(a+b*x)*sqrt(sin(a+b*x))/b^2],
[x*cos(a+b*x)*sin(a+b*x)^(3/2),x,3,-12/25*sqrt(cos(1/2*(a-1/2*Pi+b*x))^2)/cos(1/2*(a-1/2*Pi+b*x))*EllipticE(sin(1/2*(a-1/2*Pi+b*x)),sqrt(2))/b^2+4/25*cos(a+b*x)*sin(a+b*x)^(3/2)/b^2+2/5*x*sin(a+b*x)^(5/2)/b],
[x*cos(a+b*x)*sqrt(sin(a+b*x)),x,3,-4/9*sqrt(cos(1/2*(a-1/2*Pi+b*x))^2)/cos(1/2*(a-1/2*Pi+b*x))*EllipticF(sin(1/2*(a-1/2*Pi+b*x)),sqrt(2))/b^2+2/3*x*sin(a+b*x)^(3/2)/b+4/9*cos(a+b*x)*sqrt(sin(a+b*x))/b^2],
[x*cos(a+b*x)/sqrt(sin(a+b*x)),x,2,-4*sqrt(cos(1/2*(a-1/2*Pi+b*x))^2)/cos(1/2*(a-1/2*Pi+b*x))*EllipticE(sin(1/2*(a-1/2*Pi+b*x)),sqrt(2))/b^2+2*x*sqrt(sin(a+b*x))/b],
[x*cos(a+b*x)/sin(a+b*x)^(3/2),x,2,4*sqrt(cos(1/2*(a-1/2*Pi+b*x))^2)/cos(1/2*(a-1/2*Pi+b*x))*EllipticF(sin(1/2*(a-1/2*Pi+b*x)),sqrt(2))/b^2-2*x/(b*sqrt(sin(a+b*x)))],
[x*cos(a+b*x)/sin(a+b*x)^(5/2),x,3,-4/3*sqrt(cos(1/2*(a-1/2*Pi+b*x))^2)/cos(1/2*(a-1/2*Pi+b*x))*EllipticE(sin(1/2*(a-1/2*Pi+b*x)),sqrt(2))/b^2-2/3*x/(b*sin(a+b*x)^(3/2))-4/3*cos(a+b*x)/(b^2*sqrt(sin(a+b*x)))],
[x*cos(a+b*x)/sin(a+b*x)^(7/2),x,3,4/15*sqrt(cos(1/2*(a-1/2*Pi+b*x))^2)/cos(1/2*(a-1/2*Pi+b*x))*EllipticF(sin(1/2*(a-1/2*Pi+b*x)),sqrt(2))/b^2-2/5*x/(b*sin(a+b*x)^(5/2))-4/15*cos(a+b*x)/(b^2*sin(a+b*x)^(3/2))],
[x*cos(a+b*x)/sin(a+b*x)^(9/2),x,4,-12/35*sqrt(cos(1/2*(a-1/2*Pi+b*x))^2)/cos(1/2*(a-1/2*Pi+b*x))*EllipticE(sin(1/2*(a-1/2*Pi+b*x)),sqrt(2))/b^2-2/7*x/(b*sin(a+b*x)^(7/2))-4/35*cos(a+b*x)/(b^2*sin(a+b*x)^(5/2))-12/35*cos(a+b*x)/(b^2*sqrt(sin(a+b*x)))],

# Integrands of the form (c+d x)^m Cos[a+b x]^1 Csc[a+b x]^(p/2)
[x*cos(a+b*x)*csc(a+b*x)^(9/2),x,5,-4/35*cos(a+b*x)*csc(a+b*x)^(5/2)/b^2-2/7*x*csc(a+b*x)^(7/2)/b-12/35*cos(a+b*x)*sqrt(csc(a+b*x))/b^2-12/35*sqrt(cos(1/2*(a-1/2*Pi+b*x))^2)/cos(1/2*(a-1/2*Pi+b*x))*EllipticE(sin(1/2*(a-1/2*Pi+b*x)),sqrt(2))*sqrt(csc(a+b*x))*sqrt(sin(a+b*x))/b^2],
[x*cos(a+b*x)*csc(a+b*x)^(7/2),x,4,-4/15*cos(a+b*x)*csc(a+b*x)^(3/2)/b^2-2/5*x*csc(a+b*x)^(5/2)/b+4/15*sqrt(cos(1/2*(a-1/2*Pi+b*x))^2)/cos(1/2*(a-1/2*Pi+b*x))*EllipticF(sin(1/2*(a-1/2*Pi+b*x)),sqrt(2))*sqrt(csc(a+b*x))*sqrt(sin(a+b*x))/b^2],
[x*cos(a+b*x)*csc(a+b*x)^(5/2),x,4,-2/3*x*csc(a+b*x)^(3/2)/b-4/3*cos(a+b*x)*sqrt(csc(a+b*x))/b^2-4/3*sqrt(cos(1/2*(a-1/2*Pi+b*x))^2)/cos(1/2*(a-1/2*Pi+b*x))*EllipticE(sin(1/2*(a-1/2*Pi+b*x)),sqrt(2))*sqrt(csc(a+b*x))*sqrt(sin(a+b*x))/b^2],
[x*cos(a+b*x)*csc(a+b*x)^(3/2),x,3,-2*x*sqrt(csc(a+b*x))/b+4*sqrt(cos(1/2*(a-1/2*Pi+b*x))^2)/cos(1/2*(a-1/2*Pi+b*x))*EllipticF(sin(1/2*(a-1/2*Pi+b*x)),sqrt(2))*sqrt(csc(a+b*x))*sqrt(sin(a+b*x))/b^2],
[x*cos(a+b*x)*sqrt(csc(a+b*x)),x,3,2*x/(b*sqrt(csc(a+b*x)))-4*sqrt(cos(1/2*(a-1/2*Pi+b*x))^2)/cos(1/2*(a-1/2*Pi+b*x))*EllipticE(sin(1/2*(a-1/2*Pi+b*x)),sqrt(2))*sqrt(csc(a+b*x))*sqrt(sin(a+b*x))/b^2],
[x*cos(a+b*x)/sqrt(csc(a+b*x)),x,4,2/3*x/(b*csc(a+b*x)^(3/2))+4/9*cos(a+b*x)/(b^2*sqrt(csc(a+b*x)))-4/9*sqrt(cos(1/2*(a-1/2*Pi+b*x))^2)/cos(1/2*(a-1/2*Pi+b*x))*EllipticF(sin(1/2*(a-1/2*Pi+b*x)),sqrt(2))*sqrt(csc(a+b*x))*sqrt(sin(a+b*x))/b^2],
[x*cos(a+b*x)/csc(a+b*x)^(3/2),x,4,2/5*x/(b*csc(a+b*x)^(5/2))+4/25*cos(a+b*x)/(b^2*csc(a+b*x)^(3/2))-12/25*sqrt(cos(1/2*(a-1/2*Pi+b*x))^2)/cos(1/2*(a-1/2*Pi+b*x))*EllipticE(sin(1/2*(a-1/2*Pi+b*x)),sqrt(2))*sqrt(csc(a+b*x))*sqrt(sin(a+b*x))/b^2],
[x*cos(a+b*x)/csc(a+b*x)^(5/2),x,5,2/7*x/(b*csc(a+b*x)^(7/2))+4/49*cos(a+b*x)/(b^2*csc(a+b*x)^(5/2))+20/147*cos(a+b*x)/(b^2*sqrt(csc(a+b*x)))-20/147*sqrt(cos(1/2*(a-1/2*Pi+b*x))^2)/cos(1/2*(a-1/2*Pi+b*x))*EllipticF(sin(1/2*(a-1/2*Pi+b*x)),sqrt(2))*sqrt(csc(a+b*x))*sqrt(sin(a+b*x))/b^2],

# Integrands of the form (c+d x)^m Trig[a+b x]^n Trig[n (a+b x)]^p

# Integrands of the form (c+d x)^m Csc[a+b x]^n Sin[n (a+b x)]^p
[x*csc(x)*sin(3*x),x,6,1/2*x^2+3/4*cos(x)^2+2*x*cos(x)*sin(x)-1/4*sin(x)^2],
[(c+d*x)^4*csc(x)*sin(3*x),x,14,3/2*d^4*x-d*(c+d*x)^3+1/5*(c+d*x)^5/d-9/2*d^3*(c+d*x)*cos(x)^2+3*d*(c+d*x)^3*cos(x)^2+3*d^4*cos(x)*sin(x)-6*d^2*(c+d*x)^2*cos(x)*sin(x)+2*(c+d*x)^4*cos(x)*sin(x)+3/2*d^3*(c+d*x)*sin(x)^2-d*(c+d*x)^3*sin(x)^2],
[(c+d*x)^3*csc(x)*sin(3*x),x,10,-3/2*c*d^2*x-3/4*d^3*x^2+1/4*(c+d*x)^4/d-9/8*d^3*cos(x)^2+9/4*d*(c+d*x)^2*cos(x)^2-3*d^2*(c+d*x)*cos(x)*sin(x)+2*(c+d*x)^3*cos(x)*sin(x)+3/8*d^3*sin(x)^2-3/4*d*(c+d*x)^2*sin(x)^2],
[(c+d*x)^2*csc(x)*sin(3*x),x,10,-1/2*d^2*x+1/3*(c+d*x)^3/d+3/2*d*(c+d*x)*cos(x)^2-d^2*cos(x)*sin(x)+2*(c+d*x)^2*cos(x)*sin(x)-1/2*d*(c+d*x)*sin(x)^2],
[(c+d*x)*csc(x)*sin(3*x),x,6,c*x+1/2*d*x^2+3/4*d*cos(x)^2+2*(c+d*x)*cos(x)*sin(x)-1/4*d*sin(x)^2],
[csc(x)*sin(3*x)/(c+d*x),x,12,2*Ci(2*c/d+2*x)*cos(2*c/d)/d+log(c+d*x)/d+2*Si(2*c/d+2*x)*sin(2*c/d)/d],
[csc(x)*sin(3*x)/(c+d*x)^2,x,12,-3*cos(x)^2/(d*(c+d*x))-4*cos(2*c/d)*Si(2*c/d+2*x)/d^2+4*Ci(2*c/d+2*x)*sin(2*c/d)/d^2+sin(x)^2/(d*(c+d*x))],
[csc(x)*sin(3*x)/(c+d*x)^3,x,16,-4*Ci(2*c/d+2*x)*cos(2*c/d)/d^3-3/2*cos(x)^2/(d*(c+d*x)^2)-4*Si(2*c/d+2*x)*sin(2*c/d)/d^3+4*cos(x)*sin(x)/(d^2*(c+d*x))+1/2*sin(x)^2/(d*(c+d*x)^2)],
[(c+d*x)^4*csc(a+b*x)*sin(3*a+3*b*x),x,14,3/2*d^4*x/b^4-d*(c+d*x)^3/b^2+1/5*(c+d*x)^5/d-9/2*d^3*(c+d*x)*cos(a+b*x)^2/b^4+3*d*(c+d*x)^3*cos(a+b*x)^2/b^2+3*d^4*cos(a+b*x)*sin(a+b*x)/b^5-6*d^2*(c+d*x)^2*cos(a+b*x)*sin(a+b*x)/b^3+2*(c+d*x)^4*cos(a+b*x)*sin(a+b*x)/b+3/2*d^3*(c+d*x)*sin(a+b*x)^2/b^4-d*(c+d*x)^3*sin(a+b*x)^2/b^2],
[(c+d*x)^3*csc(a+b*x)*sin(3*a+3*b*x),x,10,-3/2*c*d^2*x/b^2-3/4*d^3*x^2/b^2+1/4*(c+d*x)^4/d-9/8*d^3*cos(a+b*x)^2/b^4+9/4*d*(c+d*x)^2*cos(a+b*x)^2/b^2-3*d^2*(c+d*x)*cos(a+b*x)*sin(a+b*x)/b^3+2*(c+d*x)^3*cos(a+b*x)*sin(a+b*x)/b+3/8*d^3*sin(a+b*x)^2/b^4-3/4*d*(c+d*x)^2*sin(a+b*x)^2/b^2],
[(c+d*x)^2*csc(a+b*x)*sin(3*a+3*b*x),x,10,-1/2*d^2*x/b^2+1/3*(c+d*x)^3/d+3/2*d*(c+d*x)*cos(a+b*x)^2/b^2-d^2*cos(a+b*x)*sin(a+b*x)/b^3+2*(c+d*x)^2*cos(a+b*x)*sin(a+b*x)/b-1/2*d*(c+d*x)*sin(a+b*x)^2/b^2],
[(c+d*x)*csc(a+b*x)*sin(3*a+3*b*x),x,6,c*x+1/2*d*x^2+3/4*d*cos(a+b*x)^2/b^2+2*(c+d*x)*cos(a+b*x)*sin(a+b*x)/b-1/4*d*sin(a+b*x)^2/b^2],
[csc(a+b*x)*sin(3*a+3*b*x)/(c+d*x),x,12,2*Ci(2*b*c/d+2*b*x)*cos(2*a-2*b*c/d)/d+log(c+d*x)/d-2*Si(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d],
[csc(a+b*x)*sin(3*a+3*b*x)/(c+d*x)^2,x,12,-3*cos(a+b*x)^2/(d*(c+d*x))-4*b*cos(2*a-2*b*c/d)*Si(2*b*c/d+2*b*x)/d^2-4*b*Ci(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^2+sin(a+b*x)^2/(d*(c+d*x))],
[csc(a+b*x)*sin(3*a+3*b*x)/(c+d*x)^3,x,16,-4*b^2*Ci(2*b*c/d+2*b*x)*cos(2*a-2*b*c/d)/d^3-3/2*cos(a+b*x)^2/(d*(c+d*x)^2)+4*b^2*Si(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^3+4*b*cos(a+b*x)*sin(a+b*x)/(d^2*(c+d*x))+1/2*sin(a+b*x)^2/(d*(c+d*x)^2)],
[csc(a+b*x)*sin(3*a+3*b*x)/(c+d*x)^4,x,16,-2/3*b^2/(d^3*(c+d*x))-cos(a+b*x)^2/(d*(c+d*x)^3)+2*b^2*cos(a+b*x)^2/(d^3*(c+d*x))+8/3*b^3*cos(2*a-2*b*c/d)*Si(2*b*c/d+2*b*x)/d^4+8/3*b^3*Ci(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^4+4/3*b*cos(a+b*x)*sin(a+b*x)/(d^2*(c+d*x)^2)+1/3*sin(a+b*x)^2/(d*(c+d*x)^3)-2/3*b^2*sin(a+b*x)^2/(d^3*(c+d*x))],
[(c+d*x)^3*csc(a+b*x)^2*sin(3*a+3*b*x),x,20,-6*(c+d*x)^3*arctanh(exp(I*(a+b*x)))/b-24*d^2*(c+d*x)*cos(a+b*x)/b^3+4*(c+d*x)^3*cos(a+b*x)/b+9*I*d*(c+d*x)^2*polylog(2,-exp(I*(a+b*x)))/b^2-9*I*d*(c+d*x)^2*polylog(2,exp(I*(a+b*x)))/b^2-18*d^2*(c+d*x)*polylog(3,-exp(I*(a+b*x)))/b^3+18*d^2*(c+d*x)*polylog(3,exp(I*(a+b*x)))/b^3-18*I*d^3*polylog(4,-exp(I*(a+b*x)))/b^4+18*I*d^3*polylog(4,exp(I*(a+b*x)))/b^4+24*d^3*sin(a+b*x)/b^4-12*d*(c+d*x)^2*sin(a+b*x)/b^2],
[(c+d*x)^2*csc(a+b*x)^2*sin(3*a+3*b*x),x,16,-6*(c+d*x)^2*arctanh(exp(I*(a+b*x)))/b-8*d^2*cos(a+b*x)/b^3+4*(c+d*x)^2*cos(a+b*x)/b+6*I*d*(c+d*x)*polylog(2,-exp(I*(a+b*x)))/b^2-6*I*d*(c+d*x)*polylog(2,exp(I*(a+b*x)))/b^2-6*d^2*polylog(3,-exp(I*(a+b*x)))/b^3+6*d^2*polylog(3,exp(I*(a+b*x)))/b^3-8*d*(c+d*x)*sin(a+b*x)/b^2],
[(c+d*x)*csc(a+b*x)^2*sin(3*a+3*b*x),x,12,-6*(c+d*x)*arctanh(exp(I*(a+b*x)))/b+4*(c+d*x)*cos(a+b*x)/b+3*I*d*polylog(2,-exp(I*(a+b*x)))/b^2-3*I*d*polylog(2,exp(I*(a+b*x)))/b^2-4*d*sin(a+b*x)/b^2],
[csc(a+b*x)^2*sin(3*a+3*b*x)/(c+d*x),x,9,-4*cos(a-b*c/d)*Si(b*c/d+b*x)/d-4*Ci(b*c/d+b*x)*sin(a-b*c/d)/d+3*Unintegrable(csc(a+b*x)/(c+d*x),x)],
[csc(a+b*x)^2*sin(3*a+3*b*x)/(c+d*x)^2,x,11,-4*b*Ci(b*c/d+b*x)*cos(a-b*c/d)/d^2+4*b*Si(b*c/d+b*x)*sin(a-b*c/d)/d^2+4*sin(a+b*x)/(d*(c+d*x))+3*Unintegrable(csc(a+b*x)/(c+d*x)^2,x)],
[csc(a+b*x)^2*sin(3*a+3*b*x)/(c+d*x)^3,x,13,2*b*cos(a+b*x)/(d^2*(c+d*x))+2*b^2*cos(a-b*c/d)*Si(b*c/d+b*x)/d^3+2*b^2*Ci(b*c/d+b*x)*sin(a-b*c/d)/d^3+2*sin(a+b*x)/(d*(c+d*x)^2)+3*Unintegrable(csc(a+b*x)/(c+d*x)^3,x)],

# Integrands of the form (c+d x)^m Sec[a+b x]^n Sin[n (a+b x)]^p
[(c+d*x)^4*sec(a+b*x)*sin(3*a+3*b*x),x,20,6*c*d^3*x/b^3+3*d^4*x^2/b^3-(c+d*x)^4/b-1/5*I*(c+d*x)^5/d+(c+d*x)^4*log(1+exp(2*I*(a+b*x)))/b-2*I*d*(c+d*x)^3*polylog(2,-exp(2*I*(a+b*x)))/b^2+3*d^2*(c+d*x)^2*polylog(3,-exp(2*I*(a+b*x)))/b^3+3*I*d^3*(c+d*x)*polylog(4,-exp(2*I*(a+b*x)))/b^4-3/2*d^4*polylog(5,-exp(2*I*(a+b*x)))/b^5-6*d^3*(c+d*x)*cos(a+b*x)*sin(a+b*x)/b^4+4*d*(c+d*x)^3*cos(a+b*x)*sin(a+b*x)/b^2+3*d^4*sin(a+b*x)^2/b^5-6*d^2*(c+d*x)^2*sin(a+b*x)^2/b^3+2*(c+d*x)^4*sin(a+b*x)^2/b],
[(c+d*x)^3*sec(a+b*x)*sin(3*a+3*b*x),x,19,3/2*d^3*x/b^3-(c+d*x)^3/b-1/4*I*(c+d*x)^4/d+(c+d*x)^3*log(1+exp(2*I*(a+b*x)))/b-3/2*I*d*(c+d*x)^2*polylog(2,-exp(2*I*(a+b*x)))/b^2+3/2*d^2*(c+d*x)*polylog(3,-exp(2*I*(a+b*x)))/b^3+3/4*I*d^3*polylog(4,-exp(2*I*(a+b*x)))/b^4-3/2*d^3*cos(a+b*x)*sin(a+b*x)/b^4+3*d*(c+d*x)^2*cos(a+b*x)*sin(a+b*x)/b^2-3*d^2*(c+d*x)*sin(a+b*x)^2/b^3+2*(c+d*x)^3*sin(a+b*x)^2/b],
[(c+d*x)^2*sec(a+b*x)*sin(3*a+3*b*x),x,14,-2*c*d*x/b-d^2*x^2/b-1/3*I*(c+d*x)^3/d+(c+d*x)^2*log(1+exp(2*I*(a+b*x)))/b-I*d*(c+d*x)*polylog(2,-exp(2*I*(a+b*x)))/b^2+1/2*d^2*polylog(3,-exp(2*I*(a+b*x)))/b^3+2*d*(c+d*x)*cos(a+b*x)*sin(a+b*x)/b^2-d^2*sin(a+b*x)^2/b^3+2*(c+d*x)^2*sin(a+b*x)^2/b],
[(c+d*x)*sec(a+b*x)*sin(3*a+3*b*x),x,13,-d*x/b-1/2*I*(c+d*x)^2/d+(c+d*x)*log(1+exp(2*I*(a+b*x)))/b-1/2*I*d*polylog(2,-exp(2*I*(a+b*x)))/b^2+d*cos(a+b*x)*sin(a+b*x)/b^2+2*(c+d*x)*sin(a+b*x)^2/b],
[sec(a+b*x)*sin(3*a+3*b*x)/(c+d*x),x,13,2*cos(2*a-2*b*c/d)*Si(2*b*c/d+2*b*x)/d+2*Ci(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d-Unintegrable(tan(a+b*x)/(c+d*x),x)],
[sec(a+b*x)*sin(3*a+3*b*x)/(c+d*x)^2,x,15,4*b*Ci(2*b*c/d+2*b*x)*cos(2*a-2*b*c/d)/d^2-4*b*Si(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^2-2*sin(2*a+2*b*x)/(d*(c+d*x))-Unintegrable(tan(a+b*x)/(c+d*x)^2,x)],
[sec(a+b*x)*sin(3*a+3*b*x)/(c+d*x)^3,x,17,-2*b*cos(2*a+2*b*x)/(d^2*(c+d*x))-4*b^2*cos(2*a-2*b*c/d)*Si(2*b*c/d+2*b*x)/d^3-4*b^2*Ci(2*b*c/d+2*b*x)*sin(2*a-2*b*c/d)/d^3-sin(2*a+2*b*x)/(d*(c+d*x)^2)-Unintegrable(tan(a+b*x)/(c+d*x)^3,x)],
[(c+d*x)^3*sec(a+b*x)^2*sin(3*a+3*b*x),x,19,-6*I*d*(c+d*x)^2*arctan(exp(I*(a+b*x)))/b^2+24*d^2*(c+d*x)*cos(a+b*x)/b^3-4*(c+d*x)^3*cos(a+b*x)/b+6*I*d^2*(c+d*x)*polylog(2,-I*exp(I*(a+b*x)))/b^3-6*I*d^2*(c+d*x)*polylog(2,I*exp(I*(a+b*x)))/b^3-6*d^3*polylog(3,-I*exp(I*(a+b*x)))/b^4+6*d^3*polylog(3,I*exp(I*(a+b*x)))/b^4-(c+d*x)^3*sec(a+b*x)/b-24*d^3*sin(a+b*x)/b^4+12*d*(c+d*x)^2*sin(a+b*x)/b^2],
[(c+d*x)^2*sec(a+b*x)^2*sin(3*a+3*b*x),x,15,-4*I*d*(c+d*x)*arctan(exp(I*(a+b*x)))/b^2+8*d^2*cos(a+b*x)/b^3-4*(c+d*x)^2*cos(a+b*x)/b+2*I*d^2*polylog(2,-I*exp(I*(a+b*x)))/b^3-2*I*d^2*polylog(2,I*exp(I*(a+b*x)))/b^3-(c+d*x)^2*sec(a+b*x)/b+8*d*(c+d*x)*sin(a+b*x)/b^2],
[(c+d*x)*sec(a+b*x)^2*sin(3*a+3*b*x),x,9,d*arctanh(sin(a+b*x))/b^2-4*(c+d*x)*cos(a+b*x)/b-(c+d*x)*sec(a+b*x)/b+4*d*sin(a+b*x)/b^2],
[sec(a+b*x)^2*sin(3*a+3*b*x)/(c+d*x),x,9,-CannotIntegrate(sec(a+b*x)*tan(a+b*x)/(c+d*x),x)+4*cos(a-b*c/d)*Si(b*c/d+b*x)/d+4*Ci(b*c/d+b*x)*sin(a-b*c/d)/d],
[sec(a+b*x)^2*sin(3*a+3*b*x)/(c+d*x)^2,x,11,-CannotIntegrate(sec(a+b*x)*tan(a+b*x)/(c+d*x)^2,x)+4*b*Ci(b*c/d+b*x)*cos(a-b*c/d)/d^2-4*b*Si(b*c/d+b*x)*sin(a-b*c/d)/d^2-4*sin(a+b*x)/(d*(c+d*x))],
[sec(a+b*x)^2*sin(3*a+3*b*x)/(c+d*x)^3,x,13,-CannotIntegrate(sec(a+b*x)*tan(a+b*x)/(c+d*x)^3,x)-2*b*cos(a+b*x)/(d^2*(c+d*x))-2*b^2*cos(a-b*c/d)*Si(b*c/d+b*x)/d^3-2*b^2*Ci(b*c/d+b*x)*sin(a-b*c/d)/d^3-2*sin(a+b*x)/(d*(c+d*x)^2)],

# Integrands of the form (c+d x)^m Sec[a+b x]^n Cos[n (a+b x)]^p
[x*cos(2*x)*sec(x),x,12,2*I*x*arctan(exp(I*x))+2*cos(x)-I*polylog(2,-I*exp(I*x))+I*polylog(2,I*exp(I*x))+2*x*sin(x)],
[x*cos(2*x)*sec(x)^2,x,5,x^2-log(cos(x))-x*tan(x)],
[x*cos(2*x)*sec(x)^3,x,19,-3*I*x*arctan(exp(I*x))+3/2*I*polylog(2,-I*exp(I*x))-3/2*I*polylog(2,I*exp(I*x))+1/2*sec(x)-1/2*x*sec(x)*tan(x)]]:

# Integrands of the form (c+d x)^m Csc[a+b x]^n Cos[n (a+b x)]^p
