I am searching for some theorems and books about convergence of multiple integrals of the form: $$ \int_{\infty}^{\infty}\int_{\infty}^{\infty}\;f(x,y)\;\mathrm{d}x\,\mathrm{d}y. $$ In particular, maybe it is trivial, I want to know if this integral converges if $$ f(x,y)=\frac{1}{(x²y(xy))^{1/3}(c+(1x)^{1/3})(x^{1/3}+(xy)^{1/3})} $$ where $c$ is a real number. If it converges, does anybody have an idea how to calculate it?
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