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pls-how-to-calculate-this-1-2-1-ln-x-1-x-dx-




Question Number 205264 by pticantor last updated on 13/Mar/24
pls how to calculate this?  ∫_(1/2) ^1 ((ln(x+1))/x)dx
plshowtocalculatethis?121ln(x+1)xdx
Answered by Berbere last updated on 13/Mar/24
=−(−∫_(1/2) ^1 ((ln(1−(−x)))/((−x)))d(−x))  =−[Li_2 (−x)]_(1/2) ^1 =−Li_2 (−1)+Li_2 (−(1/2))  =(π^2 /(12))+Li_2 (−(1/2))
=(121ln(1(x))(x)d(x))=[Li2(x)]121=Li2(1)+Li2(12)=π212+Li2(12)

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