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0-1-ln-x-1-ln-1-x-x-dx-0-1-ln-x-1-ln-1-x-x-dx-by-M-A-




Question Number 163785 by amin96 last updated on 10/Jan/22
∫_0 ^1 ((ln(x−1)ln(1−x))/x)dx=?  ∫_0 ^1 ((ln(x−1)ln(1+x))/x)dx=?  by M.A
$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}−\mathrm{1}\right)\boldsymbol{\mathrm{ln}}\left(\mathrm{1}−\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}}=? \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}−\mathrm{1}\right)\boldsymbol{\mathrm{ln}}\left(\mathrm{1}+\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}}=? \\ $$$$\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{M}}.\boldsymbol{\mathrm{A}} \\ $$

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