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$$\iiint'_{\mathbb{R}^3} \frac{du \; dv \; dw}{|u^3+v^3+w^3|^{\frac{2}{3}}}$$ where the $'$ integration constraint is that only $u,v,w$ for which $|(u^3+v^3)(u^3+w^3)(v^3+w^3)| \leq 1 $ are taken into account. Is it possible to determine whether this integral converges or not?

Do you think that under the transformation $x:=u^3+v^3,y:=u^3+w^3$ etc.. one could even compute a value for the integral ?

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    Did this integral come from somewhere...?2011-08-25

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