\[ \int (b \sec (e+f x))^{5/2} \sin (e+f x) \, dx \]
Optimal antiderivative \[ \frac {2 b \left (b \sec \left (f x +e \right )\right )^{\frac {3}{2}}}{3 f} \]
command
integrate((b*sec(f*x+e))^(5/2)*sin(f*x+e),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {2 \, b^{3} \mathrm {sgn}\left (\cos \left (f x + e\right )\right )}{3 \, \sqrt {b \cos \left (f x + e\right )} f \cos \left (f x + e\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________