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1-find-A-0-ln-x-ln-1-x-dx-with-0-lt-lt-1-2-calculate-0-1-ln-x-ln-1-x-dx-




Question Number 42770 by maxmathsup by imad last updated on 02/Sep/18
1)find A(ξ) = ∫_0 ^ξ ln(x)ln(1−x)dx  with  0<ξ<1  2) calculate ∫_0 ^1 ln(x)ln(1−x)dx
$$\left.\mathrm{1}\right){find}\:{A}\left(\xi\right)\:=\:\int_{\mathrm{0}} ^{\xi} {ln}\left({x}\right){ln}\left(\mathrm{1}−{x}\right){dx}\:\:{with}\:\:\mathrm{0}<\xi<\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left({x}\right){ln}\left(\mathrm{1}−{x}\right){dx} \\ $$

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