\[ \int \frac {\tanh ^6(x)}{\left (a+b \tanh ^2(x)\right )^{5/2}} \, dx \]
Optimal antiderivative \[ -\frac {\arctanh \left (\frac {\sqrt {b}\, \tanh \left (x \right )}{\sqrt {a +b \left (\tanh ^{2}\left (x \right )\right )}}\right )}{b^{\frac {5}{2}}}+\frac {\arctanh \left (\frac {\sqrt {a +b}\, \tanh \left (x \right )}{\sqrt {a +b \left (\tanh ^{2}\left (x \right )\right )}}\right )}{\left (a +b \right )^{\frac {5}{2}}}+\frac {a \left (a +2 b \right ) \tanh \left (x \right )}{b^{2} \left (a +b \right )^{2} \sqrt {a +b \left (\tanh ^{2}\left (x \right )\right )}}+\frac {a \left (\tanh ^{3}\left (x \right )\right )}{3 b \left (a +b \right ) \left (a +b \left (\tanh ^{2}\left (x \right )\right )\right )^{\frac {3}{2}}} \]
command
integrate(tanh(x)^6/(a+b*tanh(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 \[ \text {Timed out} \]