\int _1^{\infty }x^2e^{- \frac{x^2}{2}}dx=\frac{1}{\sqrt{e}}+\sqrt{2}\left(\frac{\sqrt{\pi }}{2}-\frac{\sqrt{\pi }}{2}\mathrm{Erf}\left(\frac{1}{\sqrt{2}}\right)\right)=\frac{1}{\sqrt{e}}+\sqrt{\frac{\pi }{2}}-\sqrt{\frac{\pi }{2}} \mathrm{Erf}\left(\frac{1}{\sqrt{2}}\right)\approx 1.004220405135985