integration of (e^x)/x ?

**raladin** · October 29th 2008, 10:08 AM

Hi all,
can anybody find a solution for the integration of (e^x)/x ?

Best regards.

**Mathstud28** · October 29th 2008, 12:31 PM

Originally Posted by raladin

Hi all,
can anybody find a solution for the integration of (e^x)/x ?

Best regards.

It has no closed form solution...by try converting to power series $\frac{e^x}{x}=\sum_{n=1}^{\infty}\frac{x^{n-1}}{n!}$

**galactus** · October 29th 2008, 12:45 PM

Just as an aside, this particular integral is known as the Exponential Integral

and is represented by Ei(x).

Actually, $\int_{x}^{\infty}\frac{e^{-t}}{t}dt$ is called the exponential integral and can be represented as an 'incomplete' Gamma function.

An incomplete Gamma function is $\int_{x}^{\infty}t^{n-1}e^{-t}dt$ for $x\neq 0$

By repeated integration by parts we can find several terms of the asymptotic series for the above integral.

Just some useless information for you

mathstuds series is easier.

**raladin** · October 29th 2008, 01:25 PM

thanks a lot guys for your help, I really appreciate it.

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