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