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Question Number 153829 by mathdanisur last updated on 10/Sep/21

L(x) = (6/Ο€^2 )(Li_2 (x) + (1/2) log(x)log(1-x)  Find:  𝛀 =∫_( 0) ^( 1)  L(x)βˆ™Li_2 (x) dx

$$\mathrm{L}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{6}}{\pi^{\mathrm{2}} }\left(\mathrm{Li}_{\mathrm{2}} \left(\mathrm{x}\right)\:+\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{log}\left(\mathrm{x}\right)\mathrm{log}\left(\mathrm{1}-\mathrm{x}\right)\right. \\ $$$$\mathrm{Find}:\:\:\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\mathrm{L}\left(\mathrm{x}\right)\centerdot\mathrm{Li}_{\mathrm{2}} \left(\mathrm{x}\right)\:\mathrm{dx} \\ $$

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