\[ \int \frac {e^{c+b^2 x^2} \text {Erf}(b x)}{x^4} \, dx \]
Optimal antiderivative \[ -\frac {{\mathrm e}^{b^{2} x^{2}+c} \erf \left (b x \right )}{3 x^{3}}-\frac {2 b^{2} {\mathrm e}^{b^{2} x^{2}+c} \erf \left (b x \right )}{3 x}-\frac {b \,{\mathrm e}^{c}}{3 x^{2} \sqrt {\pi }}+\frac {4 b^{5} {\mathrm e}^{c} x^{2} \hypergeom \left (\left [1, 1\right ], \left [\frac {3}{2}, 2\right ], b^{2} x^{2}\right )}{3 \sqrt {\pi }}+\frac {4 b^{3} {\mathrm e}^{c} \ln \left (x \right )}{3 \sqrt {\pi }} \]
command
integrate(exp(b**2*x**2+c)*erf(b*x)/x**4,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \frac {b^{3} {G_{3, 2}^{1, 2}\left (\begin {matrix} 2, 1 & \frac {5}{2} \\2 & 0 \end {matrix} \middle | {\frac {e^{- i \pi }}{b^{2} x^{2}}} \right )} e^{c}}{2} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________