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Math Help - [SOLVED] Integration by Parts

  1. #1
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    [SOLVED] Integration by Parts

    I've having trouble integrating this expression by parts:



    The first expression is the one I want to solve by using the second equation.

    I've tried solving it by parts but I can't seem to impliment the limits.

    Just so you know, the answer is:

    4[((llamda^3)/2*Pi)]^(1/4)
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  2. #2
    Moo
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    Hello,

    Write \int_0^\infty x \cdot \left(x e^{-2\lambda x^2}\right) ~dx

    You can see that x is (with some constant) the derivative of -2\lambda x^2

    So let u=x and dv=xe^{-2\lambda x^2}

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  3. #3
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    Ah cheers, that's nifty.

    What do I do if it's x^3 in front of the integral instead of x^2?

    [Edit: Nevermind just worked it out, seems obvious now ]
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    And here comes the next inevitable question.

    What happens if it's x^4 in front of the exponential expression? Is there a similar easy trick?
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  5. #5
    Moo
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    Quote Originally Posted by Gingerbread Man View Post
    And here comes the next inevitable question.

    What happens if it's x^4 in front of the exponential expression? Is there a similar easy trick?
    Yup, isolating a factor x to get xe^{-2\lambda x^2} and then integration by parts, successively



    If you want another method... : you can recognize the Gamma function (http://en.wikipedia.org/wiki/Gamma_function), by letting t=-2\lambda x^2.
    Last edited by Moo; May 3rd 2009 at 12:05 AM. Reason: remooving an incorrect part
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  6. #6
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    Thankyou!
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