$f$ has a double pole ... complex-analysis complex-integration residue-calculus asked days ago user silver badges bronze badges votes answers views proving $\int_ ^{\pi} rac{\log ( +r- \sqrt{r}\cos(t))}{ +r- \sqrt{r} \cos(t)}\,dt = rac{ \pi}{ -r}\log( -r)$, when $ $. we have to prove that if $\left|...