95.15 Problem number 176

\[ \int \frac {e^{c+b^2 x^2} \text {Erfc}(b x)}{x^2} \, dx \]

Optimal antiderivative \[ -\frac {{\mathrm e}^{b^{2} x^{2}+c} \mathrm {erfc}\left (b x \right )}{x}-\frac {2 b^{3} {\mathrm e}^{c} x^{2} \hypergeom \left (\left [1, 1\right ], \left [\frac {3}{2}, 2\right ], b^{2} x^{2}\right )}{\sqrt {\pi }}-\frac {2 b \,{\mathrm e}^{c} \ln \left (x \right )}{\sqrt {\pi }}+b \,{\mathrm e}^{c} \erfi \left (b x \right ) \sqrt {\pi } \]

command

integrate(exp(b**2*x**2+c)*erfc(b*x)/x**2,x)

Sympy 1.10.1 under Python 3.10.4 output

\[ - \frac {2 b^{3} x^{2} e^{c} {{}_{2}F_{2}\left (\begin {matrix} 1, 1 \\ 2, \frac {5}{2} \end {matrix}\middle | {b^{2} x^{2}} \right )}}{3 \sqrt {\pi }} - \frac {b e^{c} \log {\left (b^{2} x^{2} \right )}}{\sqrt {\pi }} - i \sqrt {\pi } b e^{c} \operatorname {erf}{\left (i b x \right )} - \frac {e^{c} e^{b^{2} x^{2}}}{x} \]

Sympy 1.8 under Python 3.8.8 output

\[ \text {Exception raised: AttributeError} \]________________________________________________________________________________________