Question Number 134613 by Ñï= last updated on 05/Mar/21
![Prove::∫_0 ^(π/2) ln(sin x)ln(cos x)dx=(π/2)(ln^2 2−(π^2 /(24)))](https://www.tinkutara.com/question/Q134613.png)
$${Prove}::\int_{\mathrm{0}} ^{\pi/\mathrm{2}} {ln}\left({sin}\:{x}\right){ln}\left({cos}\:{x}\right){dx}=\frac{\pi}{\mathrm{2}}\left({ln}^{\mathrm{2}} \mathrm{2}−\frac{\pi^{\mathrm{2}} }{\mathrm{24}}\right) \\ $$