mathematics-prove-that-0-arctan-x-ln-1-x-2-1-x-2-dx-pi-2-ln-2-4-7-8-3-

Question Number 138940 by mnjuly1970 last updated on 20/Apr/21

\dots m a t h e m a t i c s . .

p r o v e t h a t :

ϕ = \int_{0}^{\infty} \frac{a r c t a n (x) . l n (1 + x^{2})}{1 + x^{2}} d x

= \frac{π^{2} l n (2)}{4} + \frac{7}{8} ζ (3)