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Math Help - Integrating by parts

  1. #1
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    Integrating by parts

    Can someone help with this, please? I'm realy struggling...

    Thanks!

    <br />
\int u^4 e^{\frac{-1}{2}u^2}\ du<br />
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  2. #2
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    Quote Originally Posted by paolopiace View Post
    Can someone help with this, please? I'm realy struggling...

    Thanks!

    <br />
\int u^4 e^{\frac{-1}{2}u^2}\ du<br />
    \int x^4 e^{-x^2/2} ~ dx = -\int x^3 \left( e^{-x^2/2} \right)' dx

    But, \int x^3 \left( e^{-x^2/2} \right)' dx = x^3 e^{-x^2/2} - 3\int x^2 e^{-x^2/2} ~ dx

    But, -\int x^2 e^{-x^2/2} dx = \int x \left( e^{-x^2/2} \right)' dx = xe^{-x^2/2} - \int e^{-x^2/2} ~ dx

    The last one has no primitive.
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