let-give-I-0-1-ln-x-1-x-dx-and-J-0-1-ln-1-x-x-dx-1-prove-the-existence-of-I-and-J-2-calculate-I-J-and-2I-J-3-find-I-and-J-

Tinku Tara June 4, 2023 Integration 0 Comments

Question Number 34216 by abdo imad last updated on 02/May/18

let give I =∫_0 ^1 ((ln(x+1))/x)dx and J = ∫_0 ^1 ((ln(1−x))/x)dx 1) prove the existence of I and J 2) calculate I +J and 2I +J 3) find I and J .

$${let}\:{give}\:{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left({x}+\mathrm{1}\right)}{{x}}{dx}\:{and}\:{J}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}−{x}\right)}{{x}}{dx} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{the}\:{existence}\:{of}\:{I}\:{and}\:{J} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{I}\:+{J}\:{and}\:\mathrm{2}{I}\:+{J} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{I}\:{and}\:{J}\:. \\ $$

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let-give-I-0-1-ln-x-1-x-dx-and-J-0-1-ln-1-x-x-dx-1-prove-the-existence-of-I-and-J-2-calculate-I-J-and-2I-J-3-find-I-and-J-

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