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