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Math Help - Advanced Ln Integration Problem

  1. #1
    MHF Contributor Jason76's Avatar
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    Advanced Ln Integration Problem

    \int \dfrac{\ln(\ln x)}{x\ln x}dx

    hint?
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  2. #2
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    Re: Advanced Ln Integration Problem

    Let u= ln(x) seems a pretty obvious first step!
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  3. #3
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    Re: Advanced Ln Integration Problem

    put ln(lnx)=t,
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  4. #4
    MHF Contributor Jason76's Avatar
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    Re: Advanced Ln Integration Problem

    \int \dfrac{\ln(\ln x)}{x\ln x}dx

    u = \ln x

    du = \dfrac{1}{x} dx

    \int \dfrac{\ln(u)}{du} ??? Correct? Next step?
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  5. #5
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    Re: Advanced Ln Integration Problem

    \int \frac{\ln u}{u}du = \frac{1}{2}(\ln u)^{2}+c=\frac{1}{2}(\ln (\ln x))^{2}+c

    With the last expression obtained by back substituting u=\ln x
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