\[ \int \csc ^2(e+f x) (a+b \sin (e+f x))^3 \, dx \]
Optimal antiderivative \[ 3 a \,b^{2} x -\frac {3 a^{2} b \arctanh \left (\cos \left (f x +e \right )\right )}{f}+\frac {b \left (a^{2}-b^{2}\right ) \cos \left (f x +e \right )}{f}-\frac {a^{2} \cot \left (f x +e \right ) \left (a +b \sin \left (f x +e \right )\right )}{f} \]
command
integrate(csc(f*x+e)^2*(a+b*sin(f*x+e))^3,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {6 \, {\left (f x + e\right )} a b^{2} + 6 \, a^{2} b \log \left ({\left | \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right ) \right |}\right ) + a^{3} \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right ) - \frac {2 \, a^{2} b \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right )^{3} + a^{3} \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right )^{2} + 2 \, a^{2} b \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right ) + 4 \, b^{3} \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right ) + a^{3}}{\tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right )^{3} + \tan \left (\frac {1}{2} \, f x + \frac {1}{2} \, e\right )}}{2 \, f} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________