# Calculating exponential integral

• Dec 3rd 2012, 04:34 AM
magikeren
Calculating exponential integral
Hi,

I have problem calculating the integral of e^(-x)^(Beta) from 0 to infinity. Anyone who knows how?
Attachment 26033
• Dec 3rd 2012, 06:58 AM
Plato
Re: Calculating exponential integral
Quote:

Originally Posted by magikeren
calculating the integral of e^(-x)^(Beta) from 0 to infinity. Anyone who knows how?
Attachment 26033

There is no elementary solution. We need the gamma function.

$\beta > 0,\quad \int_0^\infty {e^{ - x^\beta } } = \Gamma \left( {\frac{1}{\beta } + 1} \right)$