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Rewriting an integral involving an exponential

  1. Aug 23, 2006 #1
    Can someone help me show the following:

    [tex]\int_0^{\infty}r^k e^{-a r} dr=\frac{k!}{a^{k+1}}[/tex]

    I tried to use the polynomial expansion of e^x:

    [tex]\sum_{n=0,1...} \frac{x^n}{n!}[/tex]

    ...but I get stuck pretty fast. Can someone give me a few hints?

  2. jcsd
  3. Aug 23, 2006 #2

    matt grime

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    Just do integration by parts and apply one more well known technique of proof (it might help if you let that integral be I(k), 'cos then what is I(k-1), and how does that link up with the hint to do things by parts?)
  4. Aug 23, 2006 #3
    I got it now!! I wasn't really as difficult as it first seemed. Thanks alot! :-)
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