# Maple integration test file: "4 Trig functions\4.5 Secant\4.5.10 (c+d x)^m (a+b sec)^n.txt"

lst:=[

# Integrands of the form (c+d x)^m (a+b Sec[e+f x])^n

# Integrands of the form (c+d x)^m (a+b Sec[e+f x])^n with a^2-b^2=0

# Integrands of the form (c+d x)^m (a+a Sec[e+f x])^n

# n>0
[(c+d*x)^3*(a+a*sec(e+f*x)),x,11,1/4*a*(c+d*x)^4/d-2*I*a*(c+d*x)^3*arctan(exp(I*(e+f*x)))/f+3*I*a*d*(c+d*x)^2*polylog(2,-I*exp(I*(e+f*x)))/f^2-3*I*a*d*(c+d*x)^2*polylog(2,I*exp(I*(e+f*x)))/f^2-6*a*d^2*(c+d*x)*polylog(3,-I*exp(I*(e+f*x)))/f^3+6*a*d^2*(c+d*x)*polylog(3,I*exp(I*(e+f*x)))/f^3-6*I*a*d^3*polylog(4,-I*exp(I*(e+f*x)))/f^4+6*I*a*d^3*polylog(4,I*exp(I*(e+f*x)))/f^4],
[(c+d*x)^2*(a+a*sec(e+f*x)),x,9,1/3*a*(c+d*x)^3/d-2*I*a*(c+d*x)^2*arctan(exp(I*(e+f*x)))/f+2*I*a*d*(c+d*x)*polylog(2,-I*exp(I*(e+f*x)))/f^2-2*I*a*d*(c+d*x)*polylog(2,I*exp(I*(e+f*x)))/f^2-2*a*d^2*polylog(3,-I*exp(I*(e+f*x)))/f^3+2*a*d^2*polylog(3,I*exp(I*(e+f*x)))/f^3],
[(c+d*x)*(a+a*sec(e+f*x)),x,7,1/2*a*(c+d*x)^2/d-2*I*a*(c+d*x)*arctan(exp(I*(e+f*x)))/f+I*a*d*polylog(2,-I*exp(I*(e+f*x)))/f^2-I*a*d*polylog(2,I*exp(I*(e+f*x)))/f^2],
[(a+a*sec(e+f*x))/(c+d*x),x,0,Unintegrable((a+a*sec(e+f*x))/(c+d*x),x)],
[(a+a*sec(e+f*x))/(c+d*x)^2,x,0,Unintegrable((a+a*sec(e+f*x))/(c+d*x)^2,x)],
[(c+d*x)^3*(a+a*sec(e+f*x))^2,x,17,-I*a^2*(c+d*x)^3/f+1/4*a^2*(c+d*x)^4/d-4*I*a^2*(c+d*x)^3*arctan(exp(I*(e+f*x)))/f+3*a^2*d*(c+d*x)^2*log(1+exp(2*I*(e+f*x)))/f^2+6*I*a^2*d*(c+d*x)^2*polylog(2,-I*exp(I*(e+f*x)))/f^2-6*I*a^2*d*(c+d*x)^2*polylog(2,I*exp(I*(e+f*x)))/f^2-3*I*a^2*d^2*(c+d*x)*polylog(2,-exp(2*I*(e+f*x)))/f^3-12*a^2*d^2*(c+d*x)*polylog(3,-I*exp(I*(e+f*x)))/f^3+12*a^2*d^2*(c+d*x)*polylog(3,I*exp(I*(e+f*x)))/f^3+3/2*a^2*d^3*polylog(3,-exp(2*I*(e+f*x)))/f^4-12*I*a^2*d^3*polylog(4,-I*exp(I*(e+f*x)))/f^4+12*I*a^2*d^3*polylog(4,I*exp(I*(e+f*x)))/f^4+a^2*(c+d*x)^3*tan(e+f*x)/f],
[(c+d*x)^2*(a+a*sec(e+f*x))^2,x,14,-I*a^2*(c+d*x)^2/f+1/3*a^2*(c+d*x)^3/d-4*I*a^2*(c+d*x)^2*arctan(exp(I*(e+f*x)))/f+2*a^2*d*(c+d*x)*log(1+exp(2*I*(e+f*x)))/f^2+4*I*a^2*d*(c+d*x)*polylog(2,-I*exp(I*(e+f*x)))/f^2-4*I*a^2*d*(c+d*x)*polylog(2,I*exp(I*(e+f*x)))/f^2-I*a^2*d^2*polylog(2,-exp(2*I*(e+f*x)))/f^3-4*a^2*d^2*polylog(3,-I*exp(I*(e+f*x)))/f^3+4*a^2*d^2*polylog(3,I*exp(I*(e+f*x)))/f^3+a^2*(c+d*x)^2*tan(e+f*x)/f],
[(c+d*x)*(a+a*sec(e+f*x))^2,x,9,1/2*a^2*(c+d*x)^2/d-4*I*a^2*(c+d*x)*arctan(exp(I*(e+f*x)))/f+a^2*d*log(cos(e+f*x))/f^2+2*I*a^2*d*polylog(2,-I*exp(I*(e+f*x)))/f^2-2*I*a^2*d*polylog(2,I*exp(I*(e+f*x)))/f^2+a^2*(c+d*x)*tan(e+f*x)/f],
[(a+a*sec(e+f*x))^2/(c+d*x),x,0,Unintegrable((a+a*sec(e+f*x))^2/(c+d*x),x)],
[(a+a*sec(e+f*x))^2/(c+d*x)^2,x,0,Unintegrable((a+a*sec(e+f*x))^2/(c+d*x)^2,x)],

# n<0
[(c+d*x)^3/(a+a*sec(e+f*x)),x,9,I*(c+d*x)^3/(a*f)+1/4*(c+d*x)^4/(a*d)-6*d*(c+d*x)^2*log(1+exp(I*(e+f*x)))/(a*f^2)+12*I*d^2*(c+d*x)*polylog(2,-exp(I*(e+f*x)))/(a*f^3)-12*d^3*polylog(3,-exp(I*(e+f*x)))/(a*f^4)-(c+d*x)^3*tan(1/2*e+1/2*f*x)/(a*f)],
[(c+d*x)^2/(a+a*sec(e+f*x)),x,8,I*(c+d*x)^2/(a*f)+1/3*(c+d*x)^3/(a*d)-4*d*(c+d*x)*log(1+exp(I*(e+f*x)))/(a*f^2)+4*I*d^2*polylog(2,-exp(I*(e+f*x)))/(a*f^3)-(c+d*x)^2*tan(1/2*e+1/2*f*x)/(a*f)],
[(c+d*x)/(a+a*sec(e+f*x)),x,5,1/2*(c+d*x)^2/(a*d)-2*d*log(cos(1/2*e+1/2*f*x))/(a*f^2)-(c+d*x)*tan(1/2*e+1/2*f*x)/(a*f)],
[1/((c+d*x)*(a+a*sec(e+f*x))),x,0,Unintegrable(1/((c+d*x)*(a+a*sec(e+f*x))),x)],
[1/((c+d*x)^2*(a+a*sec(e+f*x))),x,0,Unintegrable(1/((c+d*x)^2*(a+a*sec(e+f*x))),x)],
[(c+d*x)^3/(a+a*sec(e+f*x))^2,x,19,5/3*I*(c+d*x)^3/(a^2*f)+1/4*(c+d*x)^4/(a^2*d)-10*d*(c+d*x)^2*log(1+exp(I*(e+f*x)))/(a^2*f^2)+4*d^3*log(cos(1/2*e+1/2*f*x))/(a^2*f^4)+20*I*d^2*(c+d*x)*polylog(2,-exp(I*(e+f*x)))/(a^2*f^3)-20*d^3*polylog(3,-exp(I*(e+f*x)))/(a^2*f^4)-1/2*d*(c+d*x)^2*sec(1/2*e+1/2*f*x)^2/(a^2*f^2)+2*d^2*(c+d*x)*tan(1/2*e+1/2*f*x)/(a^2*f^3)-5/3*(c+d*x)^3*tan(1/2*e+1/2*f*x)/(a^2*f)+1/6*(c+d*x)^3*sec(1/2*e+1/2*f*x)^2*tan(1/2*e+1/2*f*x)/(a^2*f)],
[(c+d*x)^2/(a+a*sec(e+f*x))^2,x,17,5/3*I*(c+d*x)^2/(a^2*f)+1/3*(c+d*x)^3/(a^2*d)-20/3*d*(c+d*x)*log(1+exp(I*(e+f*x)))/(a^2*f^2)+20/3*I*d^2*polylog(2,-exp(I*(e+f*x)))/(a^2*f^3)-1/3*d*(c+d*x)*sec(1/2*e+1/2*f*x)^2/(a^2*f^2)+2/3*d^2*tan(1/2*e+1/2*f*x)/(a^2*f^3)-5/3*(c+d*x)^2*tan(1/2*e+1/2*f*x)/(a^2*f)+1/6*(c+d*x)^2*sec(1/2*e+1/2*f*x)^2*tan(1/2*e+1/2*f*x)/(a^2*f)],
[(c+d*x)/(a+a*sec(e+f*x))^2,x,9,1/2*(c+d*x)^2/(a^2*d)-10/3*d*log(cos(1/2*e+1/2*f*x))/(a^2*f^2)-1/6*d*sec(1/2*e+1/2*f*x)^2/(a^2*f^2)-5/3*(c+d*x)*tan(1/2*e+1/2*f*x)/(a^2*f)+1/6*(c+d*x)*sec(1/2*e+1/2*f*x)^2*tan(1/2*e+1/2*f*x)/(a^2*f)],
[1/((c+d*x)*(a+a*sec(e+f*x))^2),x,0,Unintegrable(1/((c+d*x)*(a+a*sec(e+f*x))^2),x)],
[1/((c+d*x)^2*(a+a*sec(e+f*x))^2),x,0,Unintegrable(1/((c+d*x)^2*(a+a*sec(e+f*x))^2),x)],

# Integrands of the form (c+d x)^m (a+a Sec[e+f x])^n with m symbolic
[(c+d*x)^m*(a+a*sec(e+f*x))^n,x,0,Unintegrable((c+d*x)^m*(a+a*sec(e+f*x))^n,x)],
[(c+d*x)^m*(a+a*sec(e+f*x)),x,0,Unintegrable((c+d*x)^m*(a+a*sec(e+f*x)),x)],
[(c+d*x)^m/(a+a*sec(e+f*x)),x,0,Unintegrable((c+d*x)^m/(a+a*sec(e+f*x)),x)],

# Integrands of the form (c+d x)^m (a+b Sec[e+f x])^n

# Integrands of the form (c+d x)^m (a+b Sec[e+f x])^n

# n>0
[(c+d*x)^3*(a+b*sec(e+f*x)),x,11,1/4*a*(c+d*x)^4/d-2*I*b*(c+d*x)^3*arctan(exp(I*(e+f*x)))/f+3*I*b*d*(c+d*x)^2*polylog(2,-I*exp(I*(e+f*x)))/f^2-3*I*b*d*(c+d*x)^2*polylog(2,I*exp(I*(e+f*x)))/f^2-6*b*d^2*(c+d*x)*polylog(3,-I*exp(I*(e+f*x)))/f^3+6*b*d^2*(c+d*x)*polylog(3,I*exp(I*(e+f*x)))/f^3-6*I*b*d^3*polylog(4,-I*exp(I*(e+f*x)))/f^4+6*I*b*d^3*polylog(4,I*exp(I*(e+f*x)))/f^4],
[(c+d*x)^2*(a+b*sec(e+f*x)),x,9,1/3*a*(c+d*x)^3/d-2*I*b*(c+d*x)^2*arctan(exp(I*(e+f*x)))/f+2*I*b*d*(c+d*x)*polylog(2,-I*exp(I*(e+f*x)))/f^2-2*I*b*d*(c+d*x)*polylog(2,I*exp(I*(e+f*x)))/f^2-2*b*d^2*polylog(3,-I*exp(I*(e+f*x)))/f^3+2*b*d^2*polylog(3,I*exp(I*(e+f*x)))/f^3],
[(c+d*x)*(a+b*sec(e+f*x)),x,7,1/2*a*(c+d*x)^2/d-2*I*b*(c+d*x)*arctan(exp(I*(e+f*x)))/f+I*b*d*polylog(2,-I*exp(I*(e+f*x)))/f^2-I*b*d*polylog(2,I*exp(I*(e+f*x)))/f^2],
[(a+b*sec(e+f*x))/(c+d*x),x,0,Unintegrable((a+b*sec(e+f*x))/(c+d*x),x)],
[(a+b*sec(e+f*x))/(c+d*x)^2,x,0,Unintegrable((a+b*sec(e+f*x))/(c+d*x)^2,x)],
[(c+d*x)^3*(a+b*sec(e+f*x))^2,x,17,-I*b^2*(c+d*x)^3/f+1/4*a^2*(c+d*x)^4/d-4*I*a*b*(c+d*x)^3*arctan(exp(I*(e+f*x)))/f+3*b^2*d*(c+d*x)^2*log(1+exp(2*I*(e+f*x)))/f^2+6*I*a*b*d*(c+d*x)^2*polylog(2,-I*exp(I*(e+f*x)))/f^2-6*I*a*b*d*(c+d*x)^2*polylog(2,I*exp(I*(e+f*x)))/f^2-3*I*b^2*d^2*(c+d*x)*polylog(2,-exp(2*I*(e+f*x)))/f^3-12*a*b*d^2*(c+d*x)*polylog(3,-I*exp(I*(e+f*x)))/f^3+12*a*b*d^2*(c+d*x)*polylog(3,I*exp(I*(e+f*x)))/f^3+3/2*b^2*d^3*polylog(3,-exp(2*I*(e+f*x)))/f^4-12*I*a*b*d^3*polylog(4,-I*exp(I*(e+f*x)))/f^4+12*I*a*b*d^3*polylog(4,I*exp(I*(e+f*x)))/f^4+b^2*(c+d*x)^3*tan(e+f*x)/f],
[(c+d*x)^2*(a+b*sec(e+f*x))^2,x,14,-I*b^2*(c+d*x)^2/f+1/3*a^2*(c+d*x)^3/d-4*I*a*b*(c+d*x)^2*arctan(exp(I*(e+f*x)))/f+2*b^2*d*(c+d*x)*log(1+exp(2*I*(e+f*x)))/f^2+4*I*a*b*d*(c+d*x)*polylog(2,-I*exp(I*(e+f*x)))/f^2-4*I*a*b*d*(c+d*x)*polylog(2,I*exp(I*(e+f*x)))/f^2-I*b^2*d^2*polylog(2,-exp(2*I*(e+f*x)))/f^3-4*a*b*d^2*polylog(3,-I*exp(I*(e+f*x)))/f^3+4*a*b*d^2*polylog(3,I*exp(I*(e+f*x)))/f^3+b^2*(c+d*x)^2*tan(e+f*x)/f],
[(c+d*x)*(a+b*sec(e+f*x))^2,x,9,1/2*a^2*(c+d*x)^2/d-4*I*a*b*(c+d*x)*arctan(exp(I*(e+f*x)))/f+b^2*d*log(cos(e+f*x))/f^2+2*I*a*b*d*polylog(2,-I*exp(I*(e+f*x)))/f^2-2*I*a*b*d*polylog(2,I*exp(I*(e+f*x)))/f^2+b^2*(c+d*x)*tan(e+f*x)/f],
[(a+b*sec(e+f*x))^2/(c+d*x),x,0,Unintegrable((a+b*sec(e+f*x))^2/(c+d*x),x)],
[(a+b*sec(e+f*x))^2/(c+d*x)^2,x,0,Unintegrable((a+b*sec(e+f*x))^2/(c+d*x)^2,x)],

# n<0
[(c+d*x)^3/(a+b*sec(e+f*x)),x,14,1/4*(c+d*x)^4/(a*d)+I*b*(c+d*x)^3*log(1+a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a*f*sqrt(-a^2+b^2))-I*b*(c+d*x)^3*log(1+a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a*f*sqrt(-a^2+b^2))+3*b*d*(c+d*x)^2*polylog(2,-a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a*f^2*sqrt(-a^2+b^2))-3*b*d*(c+d*x)^2*polylog(2,-a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a*f^2*sqrt(-a^2+b^2))+6*I*b*d^2*(c+d*x)*polylog(3,-a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a*f^3*sqrt(-a^2+b^2))-6*I*b*d^2*(c+d*x)*polylog(3,-a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a*f^3*sqrt(-a^2+b^2))-6*b*d^3*polylog(4,-a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a*f^4*sqrt(-a^2+b^2))+6*b*d^3*polylog(4,-a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a*f^4*sqrt(-a^2+b^2))],
[(c+d*x)^2/(a+b*sec(e+f*x)),x,12,1/3*(c+d*x)^3/(a*d)+I*b*(c+d*x)^2*log(1+a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a*f*sqrt(-a^2+b^2))-I*b*(c+d*x)^2*log(1+a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a*f*sqrt(-a^2+b^2))+2*b*d*(c+d*x)*polylog(2,-a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a*f^2*sqrt(-a^2+b^2))-2*b*d*(c+d*x)*polylog(2,-a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a*f^2*sqrt(-a^2+b^2))+2*I*b*d^2*polylog(3,-a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a*f^3*sqrt(-a^2+b^2))-2*I*b*d^2*polylog(3,-a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a*f^3*sqrt(-a^2+b^2))],
[(c+d*x)/(a+b*sec(e+f*x)),x,10,1/2*(c+d*x)^2/(a*d)+I*b*(c+d*x)*log(1+a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a*f*sqrt(-a^2+b^2))-I*b*(c+d*x)*log(1+a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a*f*sqrt(-a^2+b^2))+b*d*polylog(2,-a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a*f^2*sqrt(-a^2+b^2))-b*d*polylog(2,-a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a*f^2*sqrt(-a^2+b^2))],
[1/((c+d*x)*(a+b*sec(e+f*x))),x,0,Unintegrable(1/((c+d*x)*(a+b*sec(e+f*x))),x)],
[1/((c+d*x)^2*(a+b*sec(e+f*x))),x,0,Unintegrable(1/((c+d*x)^2*(a+b*sec(e+f*x))),x)],
[(c+d*x)^3/(a+b*sec(e+f*x))^2,x,36,-I*b^2*(c+d*x)^3/(a^2*(a^2-b^2)*f)+1/4*(c+d*x)^4/(a^2*d)+3*b^2*d*(c+d*x)^2*log(1+a*exp(I*(e+f*x))/(b-I*sqrt(a^2-b^2)))/(a^2*(a^2-b^2)*f^2)+3*b^2*d*(c+d*x)^2*log(1+a*exp(I*(e+f*x))/(b+I*sqrt(a^2-b^2)))/(a^2*(a^2-b^2)*f^2)-I*b^3*(c+d*x)^3*log(1+a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*f)+I*b^3*(c+d*x)^3*log(1+a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*f)-6*I*b^2*d^2*(c+d*x)*polylog(2,-a*exp(I*(e+f*x))/(b-I*sqrt(a^2-b^2)))/(a^2*(a^2-b^2)*f^3)-6*I*b^2*d^2*(c+d*x)*polylog(2,-a*exp(I*(e+f*x))/(b+I*sqrt(a^2-b^2)))/(a^2*(a^2-b^2)*f^3)-3*b^3*d*(c+d*x)^2*polylog(2,-a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*f^2)+3*b^3*d*(c+d*x)^2*polylog(2,-a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*f^2)+6*b^2*d^3*polylog(3,-a*exp(I*(e+f*x))/(b-I*sqrt(a^2-b^2)))/(a^2*(a^2-b^2)*f^4)+6*b^2*d^3*polylog(3,-a*exp(I*(e+f*x))/(b+I*sqrt(a^2-b^2)))/(a^2*(a^2-b^2)*f^4)-6*I*b^3*d^2*(c+d*x)*polylog(3,-a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*f^3)+6*I*b^3*d^2*(c+d*x)*polylog(3,-a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*f^3)+6*b^3*d^3*polylog(4,-a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*f^4)-6*b^3*d^3*polylog(4,-a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*f^4)+b^2*(c+d*x)^3*sin(e+f*x)/(a*(a^2-b^2)*f*(b+a*cos(e+f*x)))+2*I*b*(c+d*x)^3*log(1+a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a^2*f*sqrt(-a^2+b^2))-2*I*b*(c+d*x)^3*log(1+a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a^2*f*sqrt(-a^2+b^2))+6*b*d*(c+d*x)^2*polylog(2,-a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a^2*f^2*sqrt(-a^2+b^2))-6*b*d*(c+d*x)^2*polylog(2,-a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a^2*f^2*sqrt(-a^2+b^2))+12*I*b*d^2*(c+d*x)*polylog(3,-a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a^2*f^3*sqrt(-a^2+b^2))-12*I*b*d^2*(c+d*x)*polylog(3,-a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a^2*f^3*sqrt(-a^2+b^2))-12*b*d^3*polylog(4,-a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a^2*f^4*sqrt(-a^2+b^2))+12*b*d^3*polylog(4,-a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a^2*f^4*sqrt(-a^2+b^2))],
[(c+d*x)^2/(a+b*sec(e+f*x))^2,x,30,-I*b^2*(c+d*x)^2/(a^2*(a^2-b^2)*f)+1/3*(c+d*x)^3/(a^2*d)+2*b^2*d*(c+d*x)*log(1+a*exp(I*(e+f*x))/(b-I*sqrt(a^2-b^2)))/(a^2*(a^2-b^2)*f^2)+2*b^2*d*(c+d*x)*log(1+a*exp(I*(e+f*x))/(b+I*sqrt(a^2-b^2)))/(a^2*(a^2-b^2)*f^2)-I*b^3*(c+d*x)^2*log(1+a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*f)+I*b^3*(c+d*x)^2*log(1+a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*f)-2*I*b^2*d^2*polylog(2,-a*exp(I*(e+f*x))/(b-I*sqrt(a^2-b^2)))/(a^2*(a^2-b^2)*f^3)-2*I*b^2*d^2*polylog(2,-a*exp(I*(e+f*x))/(b+I*sqrt(a^2-b^2)))/(a^2*(a^2-b^2)*f^3)-2*b^3*d*(c+d*x)*polylog(2,-a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*f^2)+2*b^3*d*(c+d*x)*polylog(2,-a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*f^2)-2*I*b^3*d^2*polylog(3,-a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*f^3)+2*I*b^3*d^2*polylog(3,-a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*f^3)+b^2*(c+d*x)^2*sin(e+f*x)/(a*(a^2-b^2)*f*(b+a*cos(e+f*x)))+2*I*b*(c+d*x)^2*log(1+a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a^2*f*sqrt(-a^2+b^2))-2*I*b*(c+d*x)^2*log(1+a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a^2*f*sqrt(-a^2+b^2))+4*b*d*(c+d*x)*polylog(2,-a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a^2*f^2*sqrt(-a^2+b^2))-4*b*d*(c+d*x)*polylog(2,-a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a^2*f^2*sqrt(-a^2+b^2))+4*I*b*d^2*polylog(3,-a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a^2*f^3*sqrt(-a^2+b^2))-4*I*b*d^2*polylog(3,-a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a^2*f^3*sqrt(-a^2+b^2))],
[(c+d*x)/(a+b*sec(e+f*x))^2,x,21,1/2*(c+d*x)^2/(a^2*d)+b^2*d*log(b+a*cos(e+f*x))/(a^2*(a^2-b^2)*f^2)-I*b^3*(c+d*x)*log(1+a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*f)+I*b^3*(c+d*x)*log(1+a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*f)-b^3*d*polylog(2,-a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*f^2)+b^3*d*polylog(2,-a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a^2*(-a^2+b^2)^(3/2)*f^2)+b^2*(c+d*x)*sin(e+f*x)/(a*(a^2-b^2)*f*(b+a*cos(e+f*x)))+2*I*b*(c+d*x)*log(1+a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a^2*f*sqrt(-a^2+b^2))-2*I*b*(c+d*x)*log(1+a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a^2*f*sqrt(-a^2+b^2))+2*b*d*polylog(2,-a*exp(I*(e+f*x))/(b-sqrt(-a^2+b^2)))/(a^2*f^2*sqrt(-a^2+b^2))-2*b*d*polylog(2,-a*exp(I*(e+f*x))/(b+sqrt(-a^2+b^2)))/(a^2*f^2*sqrt(-a^2+b^2))],
[1/((c+d*x)*(a+b*sec(e+f*x))^2),x,0,Unintegrable(1/((c+d*x)*(a+b*sec(e+f*x))^2),x)],
[1/((c+d*x)^2*(a+b*sec(e+f*x))^2),x,0,Unintegrable(1/((c+d*x)^2*(a+b*sec(e+f*x))^2),x)],

# Integrands of the form (c+d x)^m (a+b Sec[e+f x])^n with m symbolic
[(c+d*x)^m*(a+b*sec(e+f*x))^n,x,0,Unintegrable((c+d*x)^m*(a+b*sec(e+f*x))^n,x)],
[(c+d*x)^m*(a+b*sec(e+f*x)),x,0,Unintegrable((c+d*x)^m*(a+b*sec(e+f*x)),x)],
[(c+d*x)^m/(a+b*sec(e+f*x)),x,0,Unintegrable((c+d*x)^m/(a+b*sec(e+f*x)),x)]]:
