\[ \int \frac {x^5}{\sqrt {\text {csch}(2 \log (c x))}} \, dx \]
Optimal antiderivative \[ -\frac {2 x^{2}}{21 c^{4} \sqrt {\mathrm {csch}\left (2 \ln \left (c x \right )\right )}}+\frac {x^{6}}{7 \sqrt {\mathrm {csch}\left (2 \ln \left (c x \right )\right )}}+\frac {2 \EllipticF \left (\frac {1}{c x}, i\right )}{21 c^{7} x \sqrt {1-\frac {1}{c^{4} x^{4}}}\, \sqrt {\mathrm {csch}\left (2 \ln \left (c x \right )\right )}} \]
command
integrate(x^5/csch(2*log(c*x))^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {\sqrt {2} {\left (3 \, c^{10} x^{8} - 5 \, c^{6} x^{4} + 2 \, c^{2}\right )} \sqrt {\frac {c^{2} x^{2}}{c^{4} x^{4} - 1}} + 2 \, \sqrt {2} \sqrt {c^{4}} {\rm ellipticF}\left (\frac {1}{c x}, -1\right )}{42 \, c^{8}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {x^{5}}{\sqrt {\operatorname {csch}\left (2 \, \log \left (c x\right )\right )}}, x\right ) \]