How to prove ∫10tan−1[tanh−1x−tan−1xπ+tanh−1x−tan−1x]dxx=π8lnπ28?\int_0^1\tan^{-1}\left[\frac{\tanh^{-1}x-\tan^{-1}x}{\pi+\tanh^{-1}x-\tan^{-1}x}\right]\frac{dx}{x}=\frac{\pi}{8}\ln\frac{\pi^2}{8}?

How can one prove that
10tan1[tanh1xtan1xπ+tanh1xtan1x]dxx=π8lnπ28?

Answer

I re-posted larry’s question on MathOverflow, and the FINAL ANSWER posted by Prof. Juan Arias de Reyna(here and here) comes after a month!

Attribution
Source : Link , Question Author : larry , Answer Author : Community

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