An exotic integral

Calculus (Integrals, Series)
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Riemann
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Joined: Sat Nov 14, 2015 6:32 am
Location: Melbourne, Australia

An exotic integral

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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)
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I have no clue how to tackle it.
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$
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