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