\[ \int e^{a+b x} \cosh ^3(a+b x) \sinh ^3(a+b x) \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{-5 b x -5 a}}{320 b}-\frac {3 \,{\mathrm e}^{-b x -a}}{64 b}-\frac {{\mathrm e}^{3 b x +3 a}}{64 b}+\frac {{\mathrm e}^{7 b x +7 a}}{448 b} \]
command
integrate(exp(b*x+a)*cosh(b*x+a)**3*sinh(b*x+a)**3,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \begin {cases} - \frac {2 e^{a} e^{b x} \sinh ^{6}{\left (a + b x \right )}}{35 b} + \frac {2 e^{a} e^{b x} \sinh ^{5}{\left (a + b x \right )} \cosh {\left (a + b x \right )}}{35 b} + \frac {e^{a} e^{b x} \sinh ^{4}{\left (a + b x \right )} \cosh ^{2}{\left (a + b x \right )}}{7 b} - \frac {e^{a} e^{b x} \sinh ^{3}{\left (a + b x \right )} \cosh ^{3}{\left (a + b x \right )}}{7 b} + \frac {e^{a} e^{b x} \sinh ^{2}{\left (a + b x \right )} \cosh ^{4}{\left (a + b x \right )}}{7 b} + \frac {2 e^{a} e^{b x} \sinh {\left (a + b x \right )} \cosh ^{5}{\left (a + b x \right )}}{35 b} - \frac {2 e^{a} e^{b x} \cosh ^{6}{\left (a + b x \right )}}{35 b} & \text {for}\: b \neq 0 \\x e^{a} \sinh ^{3}{\left (a \right )} \cosh ^{3}{\left (a \right )} & \text {otherwise} \end {cases} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________