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int{(1)/((logx))-(1)/((logx)^(2))}dx=?...

`int{(1)/((logx))-(1)/((logx)^(2))}dx=?`

A

x log x+C

B

`(x)/(logx)+C`

C

`x+(1)/(logx)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int{(1)/underset(I)((logx))*underset(II)(1)}dx-int(1)/((logx)^(2))dx`
`=(1)/((logx))*x-int(-1)*(1)/((logx)^(2))*(1)/(x)*xdx-int(1)/((logx)^(2))dx+C`
`=(x)/((logx))+C`
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