prove that ∫_0 ^1 arctan(x) cot(((πx)/2)) dx = ((3 ln^2 (2))/(2π))+((lnπ ln2)/π)+∫


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Question Number 63852 by aliesam last updated on 10/Jul/19

$p r o v e t h a t$ $\int_{0}^{1} a r c t a n (x) c o t (\frac{π x}{2}) d x = \frac{3 {l n}^{2} (2)}{2 π} + \frac{l n π l n 2}{π} + \int_{0}^{\infty} \frac{l n (1 + x^{2})}{e^{2 π x} + 1} d x$
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