\[ \int \sin ^6(e+f x) \left (a+b \tan ^2(e+f x)\right ) \, dx \]
Optimal antiderivative \[ \frac {5 \left (a -7 b \right ) x}{16}-\frac {\left (11 a -29 b \right ) \cos \left (f x +e \right ) \sin \left (f x +e \right )}{16 f}+\frac {\left (13 a -19 b \right ) \left (\cos ^{3}\left (f x +e \right )\right ) \sin \left (f x +e \right )}{24 f}-\frac {\left (a -b \right ) \left (\cos ^{5}\left (f x +e \right )\right ) \sin \left (f x +e \right )}{6 f}+\frac {b \tan \left (f x +e \right )}{f} \]
command
integrate(sin(f*x+e)^6*(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 \[ \text {Exception raised: NotImplementedError} \]_______________________________________________________