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)
The integral is finite: the antiderivative of the integrand is defined at v=1, and the limit as also exists and is finite.