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## Homework Statement

Does the triple integral

[itex]\int^{1}_{0}\int^{1}_{0}\int^{1}_{0}\frac{1}{1+x^2 y^2 z^2}[/itex] = [itex]\sum^{∞}_{n=0}\frac{1}{(2n+1)^3}[/itex]

## Homework Equations

## The Attempt at a Solution

I've not a single clue on what to do with this problem. I figured maybe I could find a decent conversion of variables and find the Jacobian and switch variables to make this easier but tht didn't seem to work.

I don't know why but I think the series expansion of arcsin or arctan is needed here, but I'm not exactly sure how to incorporate it in. I don't even know how to evaluate this triple integral..