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