\[ \int \frac {\text {sech}^4(x)}{i+\text {csch}(x)} \, dx \]
Optimal antiderivative \[ -\frac {\mathrm {sech}\! \left (x \right )^{5}}{5}-\frac {\mathrm {I} \left (\tanh ^{3}\left (x \right )\right )}{3}+\frac {\mathrm {I} \left (\tanh ^{5}\left (x \right )\right )}{5} \]
command
integrate(sech(x)^4/(I+csch(x)),x, algorithm="maxima")
Maxima 5.46 SBCL 2.0.1.debian via sagemath 9.6 output
\[ \text {Exception raised: RuntimeError} \]
Maxima 5.44 via sagemath 9.3 output
\[ \frac {32 \, e^{\left (-x\right )}}{120 i \, e^{\left (-x\right )} - 120 \, e^{\left (-2 \, x\right )} + 360 i \, e^{\left (-3 \, x\right )} + 360 i \, e^{\left (-5 \, x\right )} + 120 \, e^{\left (-6 \, x\right )} + 120 i \, e^{\left (-7 \, x\right )} + 60 \, e^{\left (-8 \, x\right )} - 60} + \frac {32 i \, e^{\left (-2 \, x\right )}}{120 i \, e^{\left (-x\right )} - 120 \, e^{\left (-2 \, x\right )} + 360 i \, e^{\left (-3 \, x\right )} + 360 i \, e^{\left (-5 \, x\right )} + 120 \, e^{\left (-6 \, x\right )} + 120 i \, e^{\left (-7 \, x\right )} + 60 \, e^{\left (-8 \, x\right )} - 60} + \frac {96 \, e^{\left (-3 \, x\right )}}{120 i \, e^{\left (-x\right )} - 120 \, e^{\left (-2 \, x\right )} + 360 i \, e^{\left (-3 \, x\right )} + 360 i \, e^{\left (-5 \, x\right )} + 120 \, e^{\left (-6 \, x\right )} + 120 i \, e^{\left (-7 \, x\right )} + 60 \, e^{\left (-8 \, x\right )} - 60} - \frac {240 i \, e^{\left (-4 \, x\right )}}{120 i \, e^{\left (-x\right )} - 120 \, e^{\left (-2 \, x\right )} + 360 i \, e^{\left (-3 \, x\right )} + 360 i \, e^{\left (-5 \, x\right )} + 120 \, e^{\left (-6 \, x\right )} + 120 i \, e^{\left (-7 \, x\right )} + 60 \, e^{\left (-8 \, x\right )} - 60} + \frac {16 i}{120 i \, e^{\left (-x\right )} - 120 \, e^{\left (-2 \, x\right )} + 360 i \, e^{\left (-3 \, x\right )} + 360 i \, e^{\left (-5 \, x\right )} + 120 \, e^{\left (-6 \, x\right )} + 120 i \, e^{\left (-7 \, x\right )} + 60 \, e^{\left (-8 \, x\right )} - 60} \]