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