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Evaluate: int(log(1+1/x))/(x(1+x))dx...

Evaluate: `int(log(1+1/x))/(x(1+x))dx`

Text Solution

Verified by Experts

The correct Answer is:
` -((log(1+(1)/(x)))^(2))/(2) + C`
Let `log(1+(1)/(x))=t`
` :. (0-(1)/(x^(2)))/(1+(1)/(x)) dx=dt `
` implies (-dx)/(x(x+1))=dt `
` implies int(log(1+(1)/(x)))/(x(1+x))dx=-int t dt `
`=- (t^(2))/(2) +c `
` = -((log(1+(1)/(x)))^(2))/(2) + c`
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