\[ \int (a+i a \tan (e+f x))^m (c-i c \tan (e+f x)) \, dx \]
Optimal antiderivative \[ -\frac {i c \left (a +i a \tan \left (f x +e \right )\right )^{m}}{f m} \]
command
integrate((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e)),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {i \, {\left (i \, a \tan \left (f x + e\right ) + a\right )}^{m} c}{f m} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________