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