# Thread: integration of (e^x)/x ?

1. ## integration of (e^x)/x ?

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

Best regards.

2. 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 $\displaystyle \frac{e^x}{x}=\sum_{n=1}^{\infty}\frac{x^{n-1}}{n!}$

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

and is represented by Ei(x).

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

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

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.

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