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

$l e t g i v e I = \int_{0}^{1} \frac{l n (x + 1)}{x} d x a n d J = \int_{0}^{1} \frac{l n (1 - x)}{x} d x$ $1) p r o v e t h e e x i s t e n c e o f I a n d J$ $2) c a l c u l a t e I + J a n d 2 I + J$ $3) f i n d I a n d J .$
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