\[ \int e^{c+d x} \cosh ^3(a+b x) \sinh ^2(a+b x) \, dx \]
Optimal antiderivative \[ \frac {d \,{\mathrm e}^{d x +c} \cosh \left (b x +a \right )}{8 b^{2}-8 d^{2}}-\frac {d \,{\mathrm e}^{d x +c} \cosh \left (3 b x +3 a \right )}{16 \left (9 b^{2}-d^{2}\right )}-\frac {d \,{\mathrm e}^{d x +c} \cosh \left (5 b x +5 a \right )}{16 \left (25 b^{2}-d^{2}\right )}-\frac {b \,{\mathrm e}^{d x +c} \sinh \left (b x +a \right )}{8 \left (b^{2}-d^{2}\right )}+\frac {3 b \,{\mathrm e}^{d x +c} \sinh \left (3 b x +3 a \right )}{16 \left (9 b^{2}-d^{2}\right )}+\frac {5 b \,{\mathrm e}^{d x +c} \sinh \left (5 b x +5 a \right )}{16 \left (25 b^{2}-d^{2}\right )} \]
command
integrate(exp(d*x+c)*cosh(b*x+a)**3*sinh(b*x+a)**2,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 \[ \text {Timed out} \]_____________________________________________________