79.4 Problem number 183

\[ \int \frac {1}{1-\sinh ^3(x)} \, dx \]

Optimal antiderivative \[ -\frac {\left (-1\right )^{\frac {5}{6}} \ln \left (1+\left (-1\right )^{\frac {5}{6}}+\left (-1\right )^{\frac {2}{3}} \tanh \left (\frac {x}{2}\right )\right )}{3}+\frac {\left (-1\right )^{\frac {5}{6}} \ln \left (1+\left (-1\right )^{\frac {1}{6}}+\left (-1\right )^{\frac {5}{6}} \tanh \left (\frac {x}{2}\right )\right )}{3}+\frac {\arctanh \left (\frac {\left (1+\tanh \left (\frac {x}{2}\right )\right ) \sqrt {2}}{2}\right ) \sqrt {2}}{3}+\frac {2 \left (-1\right )^{\frac {5}{6}} \arctan \left (\frac {i-\left (-1\right )^{\frac {5}{6}} \tanh \left (\frac {x}{2}\right )}{\sqrt {1+\left (-1\right )^{\frac {2}{3}}}}\right )}{3 \sqrt {1+\left (-1\right )^{\frac {2}{3}}}} \]

command

integrate(1/(1-sinh(x)**3),x)

Sympy 1.10.1 under Python 3.10.4 output

\[ \text {output too large to display} \]

Sympy 1.8 under Python 3.8.8 output \[ \text {Timed out} \]_____________________________________________________