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