\[ \int e^{-b^2 x^2} x^5 \text {Erfi}(b x) \, dx \]
Optimal antiderivative \[ -\frac {\erfi \left (b x \right ) {\mathrm e}^{-b^{2} x^{2}}}{b^{6}}-\frac {x^{2} \erfi \left (b x \right ) {\mathrm e}^{-b^{2} x^{2}}}{b^{4}}-\frac {x^{4} \erfi \left (b x \right ) {\mathrm e}^{-b^{2} x^{2}}}{2 b^{2}}+\frac {2 x}{b^{5} \sqrt {\pi }}+\frac {2 x^{3}}{3 b^{3} \sqrt {\pi }}+\frac {x^{5}}{5 b \sqrt {\pi }} \]
command
integrate(x**5*erfi(b*x)/exp(b**2*x**2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \begin {cases} \frac {x^{5}}{5 \sqrt {\pi } b} - \frac {x^{4} e^{- b^{2} x^{2}} \operatorname {erfi}{\left (b x \right )}}{2 b^{2}} + \frac {2 x^{3}}{3 \sqrt {\pi } b^{3}} - \frac {x^{2} e^{- b^{2} x^{2}} \operatorname {erfi}{\left (b x \right )}}{b^{4}} + \frac {2 x}{\sqrt {\pi } b^{5}} - \frac {e^{- b^{2} x^{2}} \operatorname {erfi}{\left (b x \right )}}{b^{6}} & \text {for}\: b \neq 0 \\0 & \text {otherwise} \end {cases} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________