Can polar coordinates solve overlapping divergences in integrals?

[zetafunction]

how can we treat overlapping divergences ? i mean integrals like

$$\int_{0}^{\infty} dx \int_{0}^{\infty}dy \frac{1+xy}{x+y+xy+1}$$

my idea is that in this case you can use polar coordinates $$x=rcos(u)$$ $$y=rsin(u)$$ , and then if you integrate over the angular variable 'u' then you have a normal divergence $$\int_{0}^{\infty} rf(r)dr$$ so there is no more overlapping.. but can this be done or you must perform a BHPZ taylor substraction ??

 

[shiekh]

One can't really just mix up variables, as one needs to show that the divergence can be reabsorbed by the original Lagrangian, and this will not be at all clear if one makes the wrong transformations (which anyhow may or may not be permitted in the original divergent integral)