# Maple integration test file: "4 Trig functions\4.7 Miscellaneous\4.7.4 x^m (a+b trig^n)^p.txt"

lst:=[

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

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

# Integrands of the form x^m (a+b Sin[c+d x]^2)^p
[x/(a+b*sin(x)^2),x,9,-1/2*I*x*log(1-b*exp(2*I*x)/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))+1/2*I*x*log(1-b*exp(2*I*x)/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))-1/4*polylog(2,b*exp(2*I*x)/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))+1/4*polylog(2,b*exp(2*I*x)/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))],
[x^2/(a+b*sin(x)^2),x,11,-1/2*I*x^2*log(1-b*exp(2*I*x)/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))+1/2*I*x^2*log(1-b*exp(2*I*x)/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))-1/2*x*polylog(2,b*exp(2*I*x)/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))+1/2*x*polylog(2,b*exp(2*I*x)/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))-1/4*I*polylog(3,b*exp(2*I*x)/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))+1/4*I*polylog(3,b*exp(2*I*x)/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))],
[x^3/(a+b*sin(x)^2),x,13,-1/2*I*x^3*log(1-b*exp(2*I*x)/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))+1/2*I*x^3*log(1-b*exp(2*I*x)/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))-3/4*x^2*polylog(2,b*exp(2*I*x)/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))+3/4*x^2*polylog(2,b*exp(2*I*x)/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))-3/4*I*x*polylog(3,b*exp(2*I*x)/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))+3/4*I*x*polylog(3,b*exp(2*I*x)/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))+3/8*polylog(4,b*exp(2*I*x)/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))-3/8*polylog(4,b*exp(2*I*x)/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))],
[x/(a+b*sin(c+d*x)^2)^2,x,12,-1/4*log(2*a+b-b*cos(2*c+2*d*x))/(a*(a+b)*d^2)-1/4*I*(2*a+b)*x*log(1-b*exp(2*I*(c+d*x))/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(a^(3/2)*(a+b)^(3/2)*d)+1/4*I*(2*a+b)*x*log(1-b*exp(2*I*(c+d*x))/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(a^(3/2)*(a+b)^(3/2)*d)-1/8*(2*a+b)*polylog(2,b*exp(2*I*(c+d*x))/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(a^(3/2)*(a+b)^(3/2)*d^2)+1/8*(2*a+b)*polylog(2,b*exp(2*I*(c+d*x))/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(a^(3/2)*(a+b)^(3/2)*d^2)+1/2*b*x*sin(2*c+2*d*x)/(a*(a+b)*d*(2*a+b-b*cos(2*c+2*d*x)))],
[x*sqrt(sin(x)^2),x,3,sqrt(sin(x)^2)-x*cot(x)*sqrt(sin(x)^2)],

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

# Integrands of the form x^m (a+b Cos[c+d x]^2)^p
[x/(a+b*cos(x)^2),x,9,-1/2*I*x*log(1+b*exp(2*I*x)/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))+1/2*I*x*log(1+b*exp(2*I*x)/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))-1/4*polylog(2,-b*exp(2*I*x)/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))+1/4*polylog(2,-b*exp(2*I*x)/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))],
[x^2/(a+b*cos(x)^2),x,11,-1/2*I*x^2*log(1+b*exp(2*I*x)/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))+1/2*I*x^2*log(1+b*exp(2*I*x)/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))-1/2*x*polylog(2,-b*exp(2*I*x)/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))+1/2*x*polylog(2,-b*exp(2*I*x)/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))-1/4*I*polylog(3,-b*exp(2*I*x)/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))+1/4*I*polylog(3,-b*exp(2*I*x)/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))],
[x^3/(a+b*cos(x)^2),x,13,-1/2*I*x^3*log(1+b*exp(2*I*x)/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))+1/2*I*x^3*log(1+b*exp(2*I*x)/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))-3/4*x^2*polylog(2,-b*exp(2*I*x)/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))+3/4*x^2*polylog(2,-b*exp(2*I*x)/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))-3/4*I*x*polylog(3,-b*exp(2*I*x)/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))+3/4*I*x*polylog(3,-b*exp(2*I*x)/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))+3/8*polylog(4,-b*exp(2*I*x)/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))-3/8*polylog(4,-b*exp(2*I*x)/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(sqrt(a)*sqrt(a+b))],
[x/(a+b*cos(c+d*x)^2)^2,x,12,-1/4*log(2*a+b+b*cos(2*c+2*d*x))/(a*(a+b)*d^2)-1/4*I*(2*a+b)*x*log(1+b*exp(2*I*(c+d*x))/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(a^(3/2)*(a+b)^(3/2)*d)+1/4*I*(2*a+b)*x*log(1+b*exp(2*I*(c+d*x))/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(a^(3/2)*(a+b)^(3/2)*d)-1/8*(2*a+b)*polylog(2,-b*exp(2*I*(c+d*x))/(2*a+b-2*sqrt(a)*sqrt(a+b)))/(a^(3/2)*(a+b)^(3/2)*d^2)+1/8*(2*a+b)*polylog(2,-b*exp(2*I*(c+d*x))/(2*a+b+2*sqrt(a)*sqrt(a+b)))/(a^(3/2)*(a+b)^(3/2)*d^2)-1/2*b*x*sin(2*c+2*d*x)/(a*(a+b)*d*(2*a+b+b*cos(2*c+2*d*x)))]]:
