\[ \int \sin ^5(e+f x) \left (a+b \tan ^2(e+f x)\right ) \, dx \]
Optimal antiderivative \[ -\frac {\left (a -3 b \right ) \cos \left (f x +e \right )}{f}+\frac {\left (2 a -3 b \right ) \left (\cos ^{3}\left (f x +e \right )\right )}{3 f}-\frac {\left (a -b \right ) \left (\cos ^{5}\left (f x +e \right )\right )}{5 f}+\frac {b \sec \left (f x +e \right )}{f} \]
command
integrate(sin(f*x+e)^5*(a+b*tan(f*x+e)^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {output too large to display} \]
Giac 1.7.0 via sagemath 9.3 output \[ \text {Timed out} \]_______________________________________________________