# Math Help - Integration - shortcut using factorials?

1. ## 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?

2. ## Re: Integration - shortcut using factorials?

You may have to use the Gamma Function to help you with these...

3. ## 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.