# convergence of multiple integral on infinite domain

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?

-
 Did you mean $$\int_{-\infty}^{\infty}\int_{-\infty}^{\infty} f(x,y) dy\ dx ?$$ As it is written now, it evaluates to $\infty \cdot \infty \cdot f(x,y) = \infty$ for $f(x,y) \neq 0$. – nullUser Jul 16 '12 at 13:16