Question Number 152839 by mnjuly1970 last updated on 02/Sep/21
$$ \\ $$$$\:\:\:\mathrm{Prove}\:\:\mathrm{that}\:: \\ $$$$ \\ $$$$\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\mathrm{ln}^{\:\mathrm{3}} \:\left(\mathrm{1}\:+\:{x}\:\right)}{{x}^{\:\mathrm{2}} }{dx}\:=\:\frac{\mathrm{3}}{\mathrm{4}}\:\zeta\:\left(\mathrm{3}\:\right)−\:\mathrm{2ln}^{\:\mathrm{3}} \left(\:\mathrm{2}\:\right)\:\:\:\:\:\:\:\:\blacksquare \\ $$$$\:\:\:\:\:\:\:\mathrm{Prepared}\:\mathrm{by}:\:\:\:\:\:\:\mathrm{M}.\mathrm{N} \\ $$$$ \\ $$