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If int(dx)/(xlogx)=f(x)+constant, then f...

If `int(dx)/(xlogx)=f(x)+`constant, then f(x) is equal to

A

`(1)/(logx)`

B

`logx`

C

`log(logx)`

D

`(x)/(logx)`

Text Solution

Verified by Experts

The correct Answer is:
C
Put `logx=timplies(1)/(x)dx=dt`
`thereforeint(dx)/(xlogx)=int(dt)/(t)`
`=logt`+constant
=log (log x)+constant
=f(x)+constant
`thereforef(x)=log(logx)`
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