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## Main Question or Discussion Point

I'm trying to solve numerically this multiple integral. But i don't know how to calculate it with Mathamtica or Sage software.

$$\int{e^{-(\vec{v}^2_1+\vec{v}^2_2)}e^{-E(\tau)}}d\vec{r}_1d\vec{r}_2d\vec{v}_1d\vec{v}_2$$

$$E(\tau)=\frac{k}{\tau^2}e^{-\tau/\tau_0}$$

$$\tau(\vec{r}_{12};\vec{v}_{12})=\frac{b-\sqrt{b^2-ac}}{a}$$

$$a=||\vec{v}_{12}||$$

$$b=\vec{r}_{12}\cdot\vec{v}_{12}$$

$$c=||\vec{r}_{12}|| - (2R)^2$$

Thank you!

$$\int{e^{-(\vec{v}^2_1+\vec{v}^2_2)}e^{-E(\tau)}}d\vec{r}_1d\vec{r}_2d\vec{v}_1d\vec{v}_2$$

$$E(\tau)=\frac{k}{\tau^2}e^{-\tau/\tau_0}$$

$$\tau(\vec{r}_{12};\vec{v}_{12})=\frac{b-\sqrt{b^2-ac}}{a}$$

$$a=||\vec{v}_{12}||$$

$$b=\vec{r}_{12}\cdot\vec{v}_{12}$$

$$c=||\vec{r}_{12}|| - (2R)^2$$

Thank you!