\[ \int \cos ^3(e+f x) (b \csc (e+f x))^n \, dx \]
Optimal antiderivative \[ -\frac {b^{3} \left (b \csc \left (f x +e \right )\right )^{-3+n}}{f \left (3-n \right )}+\frac {b \left (b \csc \left (f x +e \right )\right )^{-1+n}}{f \left (1-n \right )} \]
command
int(cos(f*x+e)^3*(b*csc(f*x+e))^n,x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| risch | \(\text {Expression too large to display}\) | \(2446\) |
Maple 2021.1 output
\[ \int \left (\cos ^{3}\left (f x +e \right )\right ) \left (b \csc \left (f x +e \right )\right )^{n}\, dx \]________________________________________________________________________________________