\[ \int (a+i a \tan (e+f x)) \sqrt {c-i c \tan (e+f x)} \, dx \]
Optimal antiderivative \[ \frac {2 i a \sqrt {c -i c \tan \left (f x +e \right )}}{f} \]
command
integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e)),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {2 i \, \sqrt {-i \, c \tan \left (f x + e\right ) + c} a}{f} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________