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I was wondering whether there was an explicit formula for the following integral:

$$\int_{B_r}\int_{B_r}|x-y|^{-(d-1)} dx dy$$

Here $dx$ and $dy$ is lebesgue measure on $R^d$ and $B_r$ is some ball of radius $r$.

I was able to write down an expression for it using polar coordinates and areas of spherical caps but the thing is nasty.

It seems rather strange that I have never seen a solution to this.

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closed as too localized by Marc Palm, MTS, Anthony Quas, Yemon Choi, Zev Chonoles Apr 16 '12 at 6:03

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

Why is that strange? Why do you feel that you should have seen a computation of this integral? Where does it arise? Unless you provide some background and motivation for this problem, it will likely be closed for being too localized/not research level. – MTS Apr 16 '12 at 5:06

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