Question Number 138940 by mnjuly1970 last updated on 20/Apr/21
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{mathematics}.. \\ $$$${prove}\:{that}: \\ $$$$\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{arctan}\left({x}\right).{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$\:\:\:=\frac{\pi^{\mathrm{2}} {ln}\left(\mathrm{2}\right)}{\mathrm{4}}+\frac{\mathrm{7}}{\mathrm{8}}\:\zeta\left(\mathrm{3}\right) \\ $$