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Math Help - Integration - shortcut using factorials?

  1. #1
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    Integration - shortcut using factorials?

    \int_0^{\infty} x^{10} e^{-\frac{90}{x}} dx


    \int_0^{\infty} x^{11}  e^{-\frac{90}{x}} dx

    Is there a shortcut to seeing that the top equation divided by the bottom equation is equal to 10?
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  2. #2
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    Re: Integration - shortcut using factorials?

    You may have to use the Gamma Function to help you with these...
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  3. #3
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    Re: Integration - shortcut using factorials?

    It's an inverse gamma, but I think that there's a shortcut around the integration if you don't realize the distribution. I'm not sure though.
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