\[ \int \frac {1}{\text {csch}^{\frac {5}{2}}(a+b x)} \, dx \]
Optimal antiderivative \[ \frac {2 \cosh \left (b x +a \right )}{5 b \mathrm {csch}\left (b x +a \right )^{\frac {3}{2}}}-\frac {6 i \sqrt {\frac {1}{2}+\frac {\sin \left (i b x +i a \right )}{2}}\, \EllipticE \left (\cos \left (\frac {1}{2} i a +\frac {1}{4} \pi +\frac {1}{2} i b x \right ), \sqrt {2}\right )}{5 \sin \left (\frac {1}{2} i a +\frac {1}{4} \pi +\frac {1}{2} i b x \right ) b \sqrt {\mathrm {csch}\left (b x +a \right )}\, \sqrt {i \sinh \left (b x +a \right )}} \]
command
integrate(1/csch(b*x+a)^(5/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {\sqrt {2} {\left (\cosh \left (b x + a\right )^{6} + 6 \, \cosh \left (b x + a\right ) \sinh \left (b x + a\right )^{5} + \sinh \left (b x + a\right )^{6} + {\left (15 \, \cosh \left (b x + a\right )^{2} + 11\right )} \sinh \left (b x + a\right )^{4} + 11 \, \cosh \left (b x + a\right )^{4} + 4 \, {\left (5 \, \cosh \left (b x + a\right )^{3} + 11 \, \cosh \left (b x + a\right )\right )} \sinh \left (b x + a\right )^{3} + {\left (15 \, \cosh \left (b x + a\right )^{4} + 66 \, \cosh \left (b x + a\right )^{2} - 13\right )} \sinh \left (b x + a\right )^{2} - 13 \, \cosh \left (b x + a\right )^{2} + 2 \, {\left (3 \, \cosh \left (b x + a\right )^{5} + 22 \, \cosh \left (b x + a\right )^{3} - 13 \, \cosh \left (b x + a\right )\right )} \sinh \left (b x + a\right ) + 1\right )} \sqrt {\frac {\cosh \left (b x + a\right ) + \sinh \left (b x + a\right )}{\cosh \left (b x + a\right )^{2} + 2 \, \cosh \left (b x + a\right ) \sinh \left (b x + a\right ) + \sinh \left (b x + a\right )^{2} - 1}} + 24 \, {\left (\sqrt {2} \cosh \left (b x + a\right )^{3} + 3 \, \sqrt {2} \cosh \left (b x + a\right )^{2} \sinh \left (b x + a\right ) + 3 \, \sqrt {2} \cosh \left (b x + a\right ) \sinh \left (b x + a\right )^{2} + \sqrt {2} \sinh \left (b x + a\right )^{3}\right )} {\rm weierstrassZeta}\left (4, 0, {\rm weierstrassPInverse}\left (4, 0, \cosh \left (b x + a\right ) + \sinh \left (b x + a\right )\right )\right )}{20 \, {\left (b \cosh \left (b x + a\right )^{3} + 3 \, b \cosh \left (b x + a\right )^{2} \sinh \left (b x + a\right ) + 3 \, b \cosh \left (b x + a\right ) \sinh \left (b x + a\right )^{2} + b \sinh \left (b x + a\right )^{3}\right )}} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {1}{\operatorname {csch}\left (b x + a\right )^{\frac {5}{2}}}, x\right ) \]