\[ \int \frac {\text {sech}^3(e+f x)}{\left (a+b \sinh ^2(e+f x)\right )^{3/2}} \, dx \]
Optimal antiderivative \[ \frac {\left (a -4 b \right ) \arctan \left (\frac {\sinh \left (f x +e \right ) \sqrt {a -b}}{\sqrt {a +b \left (\sinh ^{2}\left (f x +e \right )\right )}}\right )}{2 \left (a -b \right )^{\frac {5}{2}} f}+\frac {b \left (a +2 b \right ) \sinh \left (f x +e \right )}{2 a \left (a -b \right )^{2} f \sqrt {a +b \left (\sinh ^{2}\left (f x +e \right )\right )}}+\frac {\mathrm {sech}\left (f x +e \right ) \tanh \left (f x +e \right )}{2 \left (a -b \right ) f \sqrt {a +b \left (\sinh ^{2}\left (f x +e \right )\right )}} \]
command
integrate(sech(f*x+e)^3/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {output too large to display} \]
Giac 1.7.0 via sagemath 9.3 output \[ \text {Exception raised: TypeError} \]_______________________________________________________