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Thread: Integration by parts

  1. #1
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    Integration by parts

    The question:
    Use integration by parts to evaluate the following integral

    $\displaystyle \int ln(x) dx$

    I'm not sure what to do, since this looks like a single part to me. I'm clearly missing something fundamental here. Thanks.
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  2. #2
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    The general form is

    $\displaystyle \int u \, dv = u v - \int v \, du$

    Let $\displaystyle u=\ln x$ and $\displaystyle dv=dx$. What does this give you?

    Notice that if you work this problem this way, you do not have to know what the integral of $\displaystyle \ln x$ is! Instead you only need to know the derivative of $\displaystyle \ln x$ to compute $\displaystyle du$. That is the reason for using the method.
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  3. #3
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    Thanks dude!
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