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Math Help - Integral-how to solve?

  1. #1
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    Question Integral-how to solve?

    Hi guys,

    Can anyone help me solve this integral:

    Integral-how to solve?-int.jpg
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  2. #2
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    Re: Integral-how to solve?

    I think you might make some progress by substituting u=ln(x), so du=(dx/x).

    - Hollywood
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  3. #3
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    Re: Integral-how to solve?

    I know for that kind of progress. But what is the next step? Thnx anyway
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  4. #4
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    Re: Integral-how to solve?

    Well, this is interesting. After substituting:

    \int\frac{du}{u^3(\ln{u})^2}

    And then substituting again:

    v=lnu

    u=e^v
    dv=\frac{du}{u}

    we have:

    \int\frac{dv}{e^{2v}v^2}

    Now integrating by parts gives:

    \int{e^{-2v}}\frac{dv}{v^2}=\int{e^{-2v}}d\left(-\frac{1}{v}\right)
    =-\frac{e^{-2v}}{v}-\int\left(-\frac{1}{v}\right)d(e^{-2v})
    =-\frac{e^{-2v}}{v}-2\int\frac{e^{-2v}dv}{v}
    =-\frac{e^{-2v}}{v}-2\int\frac{e^wdw}{w}

    and we are stuck since \int\frac{e^wdw}{w} can not be integrated in terms of elementary functions. See Exponential integral - Wikipedia, the free encyclopedia

    Can anyone else help? Maybe I made a mistake somewhere.

    - Hollywood
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  5. #5
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    Re: Integral-how to solve?

    Yes, I got the same result. So I wanted to ask if anyone knows the solution...
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