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\end{equation}  Using inverse symbolic methods thanks to RIES and ISC, we find from accurate numerical integration \begin{equation}  s_1 = \frac{-2}{\sqrt{pi}}\int_{-\infty}^{\infty} x^2e^{-x^2}\mathrm{ln}(\frac{2}{\sqrt{pi}}x^2e^{-x^2})\;dx \frac{-2}{\sqrt{\pi}}\int_{-\infty}^{\infty} x^2e^{-x^2}\mathrm{ln}(\frac{2}{\sqrt{\pi}}x^2e^{-x^2})\;dx  = -\frac{1}{2} + \gamma + \mathrm{ln}(2) + \frac{1}{2}\mathrm{ln}(\pi) \end{equation}  where $\gamma$ is the Euler-Mascheroni constant.