\[ \int \frac {\coth ^2(x)}{\left (a+b \tanh ^2(x)\right )^{5/2}} \, dx \]
Optimal antiderivative \[ \frac {\arctanh \left (\frac {\sqrt {a +b}\, \tanh \left (x \right )}{\sqrt {a +b \left (\tanh ^{2}\left (x \right )\right )}}\right )}{\left (a +b \right )^{\frac {5}{2}}}+\frac {b \left (7 a +4 b \right ) \coth \left (x \right )}{3 a^{2} \left (a +b \right )^{2} \sqrt {a +b \left (\tanh ^{2}\left (x \right )\right )}}-\frac {\left (3 a +2 b \right ) \left (a +4 b \right ) \coth \left (x \right ) \sqrt {a +b \left (\tanh ^{2}\left (x \right )\right )}}{3 a^{3} \left (a +b \right )^{2}}+\frac {b \coth \left (x \right )}{3 a \left (a +b \right ) \left (a +b \left (\tanh ^{2}\left (x \right )\right )\right )^{\frac {3}{2}}} \]
command
integrate(coth(x)^2/(a+b*tanh(x)^2)^(5/2),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 \[ \text {Exception raised: TypeError} \]_______________________________________________________