The goal is to prove, using Mathematica, that for $ \mathbb{D}$ the unit disk and $ u,v \in \mathbb{D}$ , $ u \neq v$ , $ $ \frac{1}{\pi} \int_{\mathbb{D}} \frac{\mathrm{d}^2z}{(z-u)\overline{(z-v)}} = \ln(1-u\bar{v}) – \ln|u-v|^2.$ $ It looks like the techniques suggested in previous posts do not work. For example, the expression : Integrate[ (r/((u –Read more