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Thread: Integration help

  1. #1
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    Integration help

    Integral of ln(x)/x^2
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Link88 View Post
    Integral of ln(x)/x^2
    Try parts with $\displaystyle u=\ln(x)$...to make this a tad clearer try the sub $\displaystyle z=\ln(x)$ first
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    I had to do it twice and my final result was lnx
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    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Link88 View Post
    I had to do it twice and my final result was lnx
    If we do as I said and let $\displaystyle \ln(x)\longmapsto z$ then

    $\displaystyle \begin{aligned}\int\frac{\ln(x)}{dx}&\overbrace{\l ongmapsto}^{\ln(x)=z}\int\frac{z}{e^{2z}}\cdot e^z dz\\
    &=\int z\cdot e^{-z}dz\\
    &=-z\cdot e^{-z}-e^{-z}\quad{\color{red}\star}\\
    &=\frac{-\ln(x)}{x}-\frac{1}{x}+C\end{aligned}$

    $\displaystyle \color{red}\star$ was gotten using integration by parts with $\displaystyle u=z$
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  5. #5
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    Quote Originally Posted by Link88 View Post
    I had to do it twice and my final result was lnx
    It always helps if you show your work ....
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