\[ \int \frac {1}{(5+3 i \sinh (c+d x))^3} \, dx \]
Optimal antiderivative \[ \frac {59 x}{2048}-\frac {59 i \arctan \left (\frac {\cosh \left (d x +c \right )}{3+i \sinh \left (d x +c \right )}\right )}{1024 d}-\frac {3 i \cosh \left (d x +c \right )}{32 d \left (5+3 i \sinh \left (d x +c \right )\right )^{2}}-\frac {45 i \cosh \left (d x +c \right )}{512 d \left (5+3 i \sinh \left (d x +c \right )\right )} \]
command
integrate(1/(5+3*I*sinh(d*x+c))**3,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \frac {- 177 i e^{3 c} e^{3 d x} - 885 e^{2 c} e^{2 d x} + 723 i e^{c} e^{d x} + 135}{2304 d e^{4 c} e^{4 d x} - 15360 i d e^{3 c} e^{3 d x} - 30208 d e^{2 c} e^{2 d x} + 15360 i d e^{c} e^{d x} + 2304 d} + \frac {- \frac {59 \log {\left (e^{d x} - 3 i e^{- c} \right )}}{2048} + \frac {59 \log {\left (e^{d x} - \frac {i e^{- c}}{3} \right )}}{2048}}{d} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Exception raised: NotInvertible} \]________________________________________________________________________________________