Menu Close

mathematical-analysis-if-0-1-arctan-x-ln-1-x-2-x-2-dx-1-48-api-2-bpiln-2-c-ln-2-2-then-a-2-b-c-1-2-




Question Number 138171 by mnjuly1970 last updated on 11/Apr/21
           .......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 =???
$$\:\:\:\:\:\:\:\:\:\:\:…….{mathematical}….{analysis}……. \\ $$$$\:\:\:\:\:{if}\::\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{arctan}\left({x}\right).{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{48}}\left({a}\pi^{\mathrm{2}} −{b}\pi{ln}\left(\mathrm{2}\right)+{c}\:{ln}^{\mathrm{2}} \left(\mathrm{2}\right)\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:……{then}\:\:….\:{a}^{\mathrm{2}} +\left({b}−{c}+\mathrm{1}\right)^{\mathrm{2}} =??? \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *