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

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

Is there a shortcut to seeing that the top equation divided by the bottom equation is equal to 10?

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- Jun 10th 2013, 06:22 PMtedmetroIntegration - shortcut using factorials?
$\displaystyle \int_0^{\infty} x^{10} e^{-\frac{90}{x}} dx$

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

Is there a shortcut to seeing that the top equation divided by the bottom equation is equal to 10? - Jun 10th 2013, 06:57 PMProve ItRe: Integration - shortcut using factorials?
You may have to use the Gamma Function to help you with these...

- Jun 11th 2013, 07:27 PMtedmetroRe: 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.