81.1 Problem number 63

\[ \int \frac {1}{(a+b \tanh (c+d x))^3} \, dx \]

Optimal antiderivative \[ \frac {a \left (a^{2}+3 b^{2}\right ) x}{\left (a^{2}-b^{2}\right )^{3}}-\frac {b \left (3 a^{2}+b^{2}\right ) \ln \left (a \cosh \left (d x +c \right )+b \sinh \left (d x +c \right )\right )}{\left (a^{2}-b^{2}\right )^{3} d}+\frac {b}{2 \left (a^{2}-b^{2}\right ) d \left (a +b \tanh \left (d x +c \right )\right )^{2}}+\frac {2 a b}{\left (a^{2}-b^{2}\right )^{2} d \left (a +b \tanh \left (d x +c \right )\right )} \]

command

integrate(1/(a+b*tanh(d*x+c))**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 \[ \text {Timed out} \]_____________________________________________________