\[ \int \frac {\text {csch}^{\frac {3}{2}}(2 \log (c x))}{x} \, dx \]
Optimal antiderivative \[ -\cosh \left (2 \ln \left (c x \right )\right ) \sqrt {\mathrm {csch}\left (2 \ln \left (c x \right )\right )}+\frac {i \sqrt {\frac {1}{2}+\frac {i \sinh \left (2 \ln \left (c x \right )\right )}{2}}\, \EllipticE \left (\cos \left (\frac {\pi }{4}+i \ln \left (c x \right )\right ), \sqrt {2}\right )}{\sin \left (\frac {\pi }{4}+i \ln \left (c x \right )\right ) \sqrt {\mathrm {csch}\left (2 \ln \left (c x \right )\right )}\, \sqrt {i \sinh \left (2 \ln \left (c x \right )\right )}} \]
command
integrate(csch(2*log(c*x))^(3/2)/x,x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ -\sqrt {2} \sqrt {\frac {c^{2} x^{2}}{c^{4} x^{4} - 1}} c^{2} x^{2} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\operatorname {csch}\left (2 \, \log \left (c x\right )\right )^{\frac {3}{2}}}{x}, x\right ) \]