\[ \int \frac {\tanh ^5(e+f x)}{\sqrt {a+b \sinh ^2(e+f x)}} \, dx \]
Optimal antiderivative \[ -\frac {\left (8 a^{2}-8 a b +3 b^{2}\right ) \arctanh \left (\frac {\sqrt {a +b \left (\sinh ^{2}\left (f x +e \right )\right )}}{\sqrt {a -b}}\right )}{8 \left (a -b \right )^{\frac {5}{2}} f}+\frac {\left (8 a -5 b \right ) \mathrm {sech}\left (f x +e \right )^{2} \sqrt {a +b \left (\sinh ^{2}\left (f x +e \right )\right )}}{8 \left (a -b \right )^{2} f}-\frac {\mathrm {sech}\left (f x +e \right )^{4} \sqrt {a +b \left (\sinh ^{2}\left (f x +e \right )\right )}}{4 \left (a -b \right ) f} \]
command
integrate(tanh(f*x+e)^5/(a+b*sinh(f*x+e)^2)^(1/2),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 \[ \text {Exception raised: TypeError} \]_______________________________________________________