\[ \int (a+b \tan (e+f x))^2 \sqrt {c+d \tan (e+f x)} \, dx \]
Optimal antiderivative \[ -\frac {i \left (-i b +a \right )^{2} \arctanh \left (\frac {\sqrt {c +d \tan \left (f x +e \right )}}{\sqrt {-i d +c}}\right ) \sqrt {-i d +c}}{f}+\frac {i \left (i b +a \right )^{2} \arctanh \left (\frac {\sqrt {c +d \tan \left (f x +e \right )}}{\sqrt {i d +c}}\right ) \sqrt {i d +c}}{f}+\frac {4 a b \sqrt {c +d \tan \left (f x +e \right )}}{f}+\frac {2 b^{2} \left (c +d \tan \left (f x +e \right )\right )^{\frac {3}{2}}}{3 d f} \]
command
integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^2,x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \text {output too large to display} \]
Fricas 1.3.7 via sagemath 9.3 output \[ \text {Timed out} \]