I want to perform a double integration over a line segment in 2D and I am wondering if can it be done in Mathematica. An added difficulty is that the integral is singular.

$ $ I = \int_{[3,3]}^{[2,5]}\int_{[3,3]}^{[2,5]} \log|x-y|dydx.$ $

I am not that concerned with efficiency here, I would just like to have a nice way to integrate these types of integrals compared to how I have to do it in Python which involves analytically regularizing them first to deal with the singular integrands and then transformation to reference intervals before finally coding the actual integration.

So can this be done ‘nicely’ in Mathematica?