.......mathematical....analysis....... if : 𝛗=∫_0 ^( 1) ((arctan(x).ln(1+x^2 ))/x^2 )dx =(1/(48))(aπ^2 −bπln(2)+c ln^2 (2)) ......then .... a^2 +(b−c+1)^2 =???


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Question Number 138171 by mnjuly1970 last updated on 11/Apr/21

$. . . . . . . m a t h e m a t i c a l . . . . a n a l y s i s . . . . . . .$ $i f : ϕ = \int_{0}^{1} \frac{a r c t a n (x) . l n (1 + x^{2})}{x^{2}} d x$ $= \frac{1}{48} (a π^{2} - b π l n (2) + c {l n}^{2} (2))$ $. . . . . . t h e n . . . . a^{2} + {(b - c + 1)}^{2} = ? ? ?$
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