I want to calculate the following integral (in polar coordinates): $$ \int_{\mathbb{R}^3}\delta(|\vec{s}|-R)\frac{\hat{e}_\phi(\vec{s})}{|\vec{r}-\vec{s}|}\mathrm d\vec{s} $$ but I don't know how to deal with the absolute value term. I don't know how to vary it so that a $|\vec{s}|$ stands alone. Hope you have some tips for me. Or tell me that it isnt integrable :S
PS: $\phi$ is the one that that goes from $0$ to $\pi$. So the one that isn't in the $xy$ plane.