Evaluate: (i) `int(logx)/x\ dx` (ii) `int(log(1+1/x))/(x(1+x))\ dx`

Explanation

`(i)`Let `I =int ("log x ")/(x) dx`
`"Let" log x=t`
` rArr " " 1/x =(dt)/(dx) rArr " " (dx)/(x) =dt`
`:. " "i= int" t dt "= 1/2 t^(2) +c`
`=1/2 ("log x")^(2) +c.`






`(ii)`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`