\[ \int \frac {\sinh (e+f x)}{\left (a+b \sinh ^2(e+f x)\right )^{3/2}} \, dx \]
Optimal antiderivative \[ \frac {\cosh \left (f x +e \right )}{\left (a -b \right ) f \sqrt {a -b +b \left (\cosh ^{2}\left (f x +e \right )\right )}} \]
command
integrate(sinh(f*x+e)/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {\frac {a e^{\left (2 \, f x + 4 \, e\right )}}{a^{2} e^{\left (2 \, e\right )} - a b e^{\left (2 \, e\right )}} + \frac {a e^{\left (2 \, e\right )}}{a^{2} e^{\left (2 \, e\right )} - a b e^{\left (2 \, e\right )}}}{\sqrt {b e^{\left (4 \, f x + 4 \, e\right )} + 4 \, a e^{\left (2 \, f x + 2 \, e\right )} - 2 \, b e^{\left (2 \, f x + 2 \, e\right )} + b} f} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________