79.3 Problem number 182

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

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

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 \[ \text {Timed out} \]_____________________________________________________