# Integration - shortcut using factorials?

• June 10th 2013, 07:22 PM
tedmetro
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?
• June 10th 2013, 07:57 PM
Prove It
Re: Integration - shortcut using factorials?
You may have to use the Gamma Function to help you with these...
• June 11th 2013, 08:27 PM
tedmetro
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.