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int1/[xlogx[log(logx)]].dx...

`int1/[xlogx[log(logx)]].dx`

Text Solution

Verified by Experts

Let `I = int 1/(xlogx[log(logx)])`
Let `log(logx) = t`
`=>1/logx(1/x)dx = dt`
`:. I = int dt/t`
`=>I = logt+c`
`=>I = log[log(logx)]+c`
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Knowledge Check

  • int(1)/(xlogx(2+logx))dx=

    A
    `(1)/(2)log|(2+logx)/(logx)|+c`
    B
    `(1)/(2)log|(logx)/(2+logx)|+c`
    C
    `(1)/(4)log|(2+logx)/(logx)|+c`
    D
    `(1)/(4)log|(logx)/(2+logx)|+c`

  • intdx/(x.logx. log(logx)) =

    A
    log [log (log x)]+C
    B
    log [x log x]
    C
    log (log x)
    D
    log[x log (log x)]

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