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Math Help - Integration with natural l og

  1. #1
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    Integration with natural l og

    Please help me solve the integral I = ln(x)/(x^2) dx Thank you
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  2. #2
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    Re: Integration with natural l og

    Quote Originally Posted by jdesak View Post
    Please help me solve the integral I = ln(x)/(x^2) dx

    Use parts: u=\ln(x)~\&~dv=\frac{1}{x^2}.
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  3. #3
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    Re: Integration with natural l og

    \int ln(x)x^{-2}dx

    Integration by parts.
    \int f(x)g'(x)dx = f(x)g(x)-\int f'(x)g(x)dx

    Using the substitutions:
    f(x) = ln(x)

    f'(x) = \frac{1}{x}

    g(x) = -\frac{1}{x}

    g'(x) = x^{-2}

    Which ends up as:

    -\frac{ln(x)}{x}+\int \frac{1}{x^2}dx

    -\frac{ln(x)}{x}-\frac{1}{x} + C

    -\frac{ln(x)}{x}-\frac{1}{x} \right )+C
    Last edited by Bradyns; April 23rd 2013 at 07:26 AM.
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    Re: Integration with natural l og

    Bradyns,

    Should g(x) be -1/x?
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  5. #5
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    Re: Integration with natural l og

    Quote Originally Posted by jdesak View Post
    Bradyns,
    Should g(x) be -1/x?

    Post #3 is not correct. See the solution here.
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  6. #6
    Junior Member Bradyns's Avatar
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    Re: Integration with natural l og

    Sorry about that, I've fixed it up.
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