... mathematics.. prove that: 𝛗=∫_0 ^( ∞) ((arctan(x).ln(1+x^2 ))/(1+x^2 ))dx =((π^2 ln(2))/4)+(7/8) ζ(3)


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

$. . . m a t h e m a t i c s . .$ $p r o v e t h a t :$ $ϕ = \int_{0}^{\infty} \frac{a r c t a n (x) . l n (1 + x^{2})}{1 + x^{2}} d x$ $= \frac{π^{2} l n (2)}{4} + \frac{7}{8} ζ (3)$
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