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How to calculate $\int_{|z|=r}\ln(1-z)\,dz$ in dependence of $r\neq1$?
With the integration I mean one counter-clockwise turn around the origin, i.e.
$$\int_{\phi=0}^{2\pi}\ln(1-re^{i\phi})ire^{i\phi}d\phi$$
For $r<1$, this is simply a contour integration on a ...
