\[ \int \frac {\coth (x)}{\left (a+b \text {sech}^2(x)\right )^{5/2}} \, dx \]
Optimal antiderivative \[ \frac {\arctanh \left (\frac {\sqrt {a +b \mathrm {sech}\left (x \right )^{2}}}{\sqrt {a}}\right )}{a^{\frac {5}{2}}}-\frac {\arctanh \left (\frac {\sqrt {a +b \mathrm {sech}\left (x \right )^{2}}}{\sqrt {a +b}}\right )}{\left (a +b \right )^{\frac {5}{2}}}-\frac {b}{3 a \left (a +b \right ) \left (a +b \mathrm {sech}\left (x \right )^{2}\right )^{\frac {3}{2}}}-\frac {b \left (2 a +b \right )}{a^{2} \left (a +b \right )^{2} \sqrt {a +b \mathrm {sech}\left (x \right )^{2}}} \]
command
integrate(coth(x)/(a+b*sech(x)^2)^(5/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \text {output too large to display} \]
Fricas 1.3.7 via sagemath 9.3 output \[ \text {Timed out} \]