Calculating exponential integral

**magikeren** · December 3rd 2012, 04:34 AM

Hi,

I have problem calculating the integral of e^(-x)^(Beta) from 0 to infinity. Anyone who knows how?

Calculating exponential integral-skaermbillede-2012-12-03-kl.-14.58.07.png

**Plato** · December 3rd 2012, 06:58 AM

Originally Posted by magikeren

calculating the integral of e^(-x)^(Beta) from 0 to infinity. Anyone who knows how?

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

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

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