convergence of multiple integral on infinite domain

Question

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 $$ f(x,y)=\frac{1}{(x²y(x-y))^{1/3}(c+(1-x)^{1/3})(x^{1/3}+(x-y)^{1/3})} $$ where $c$ is a real number. If it converges, does anybody have an idea how to calculate it?