prove-that-0-1-arctan-x-cot-pix-2-dx-3-ln-2-2-2pi-lnpi-ln2-pi-0-ln-1-x-2-e-2pix-1-dx-

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