\[ \int \frac {\sqrt {c+d \tan (e+f x)}}{\sqrt {a+b \tan (e+f x)}} \, dx \]
Optimal antiderivative \[ -\frac {i \arctanh \left (\frac {\sqrt {-i d +c}\, \sqrt {a +b \tan \left (f x +e \right )}}{\sqrt {-i b +a}\, \sqrt {c +d \tan \left (f x +e \right )}}\right ) \sqrt {-i d +c}}{f \sqrt {-i b +a}}+\frac {i \arctanh \left (\frac {\sqrt {i d +c}\, \sqrt {a +b \tan \left (f x +e \right )}}{\sqrt {i b +a}\, \sqrt {c +d \tan \left (f x +e \right )}}\right ) \sqrt {i d +c}}{f \sqrt {i b +a}} \]
command
int((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(1/2),x)
Maple 2022.1 output
\[\text {output too large to display}\]
Maple 2021.1 output
\[ \int \frac {\sqrt {c +d \tan \left (f x +e \right )}}{\sqrt {a +b \tan \left (f x +e \right )}}\, dx \]________________________________________________________________________________________