If we attempt to do the x integral first, we get an elliptic integral, so we reverse the order of integration:

Now, integrating with respect to y, we make the change of variables

(via a table of integrals)

Using the substitution

This is an improper integral, with the integrand undefined at both limits. The limit as does exist, but the limit as is infinite. A little work, however, could be used to do this integral (if it exists)

--Kevin C.