My Math Forum 6 dimensional integral

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 October 11th, 2012, 12:35 PM #1 Newbie   Joined: Oct 2012 Posts: 1 Thanks: 0 6 dimensional integral I need to solve the following integral: $I= \int_{-\infty}^{\infty} e^{-2\alpha (r_1 + r_2)} \frac{d\vec{r}_1 d\vec{r}_2}{|\vec{r}_1 - \vec{r}_2|$ Where $r_i= |\vec{r}_i|, \quad \vec{r}_i = x_i \hat{i} + y_i\hat{j} + z_i\hat{k}, \quad i = 1,2$ and the integral is evaluated over 6-dimensional space. I know that the answer is $I= \frac{5\pi^2}{16^2}$, however I can't seem to find a method for solving this type of integral in any of my books. I have tried using spherical coordinates, which seemed logical since the answer has a factor of $\pi^2$, but with no luck - and it has been a couple of years since I've done this, so a point in the right direction would be greatly appreciated. (I'm sorry if I've put this question in the wrong forum; if so, please move it to the right one)

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### 6 dimensional integral

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