An exotic integral
Posted: Wed Nov 16, 2016 10:37 am
Let ${\rm Li}_2$ denote the dilogarithm function. Evaluate
$$\int_{0}^{\pi/2} \left ( \frac{\log \left ( \tan x +1 \right )}{\log \tan x} - \frac{{\rm Li}_2 \left ( -\cot x \right )}{\log^2 \cot x} - \frac{\zeta(2)}{2 \log^2 \tan x} \right ) \, {\rm d}x$$
(Corel Ioan Valean)
$$\int_{0}^{\pi/2} \left ( \frac{\log \left ( \tan x +1 \right )}{\log \tan x} - \frac{{\rm Li}_2 \left ( -\cot x \right )}{\log^2 \cot x} - \frac{\zeta(2)}{2 \log^2 \tan x} \right ) \, {\rm d}x$$
(Corel Ioan Valean)
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