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Math Help - integrate logarithm with base 10

  1. #1
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    integrate logarithm with base 10

    I don't know how to make the symbols yet so if you don't understand what the problem is feel free to say it, I can't seem to get a hold on integrating log quotients.
    The Problem: Indefinite integral of (log10(x))/x dx --> log (base 10)x divided by x --> seems really easy, i just don't know why I can't figure it out. I tried by parts but I got confused thinking that I can't use that method for quotients, I'm not even sure if that's true if not please tell me.
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  2. #2
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    Quote Originally Posted by bgonzal8 View Post
    I don't know how to make the symbols yet so if you don't understand what the problem is feel free to say it, I can't seem to get a hold on integrating log quotients.
    The Problem: Indefinite integral of (log10(x))/x dx --> log (base 10)x divided by x --> seems really easy, i just don't know why I can't figure it out. I tried by parts but I got confused thinking that I can't use that method for quotients, I'm not even sure if that's true if not please tell me.
    note ... \log_{10}x = \frac{\ln{x}}{\ln(10)}

    \frac{1}{\ln(10)} \int \frac{\ln{x}}{x} \, dx<br />

    method of substitution ...

    let u = \ln{x} ... du = \frac{1}{x} \, dx
    Last edited by Chris L T521; September 13th 2009 at 06:14 PM. Reason: fixed minor typo
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