Integrating e^x /x using Laurent series

1. Sep 27, 2006

pivoxa15

How does one integrate $$\int_{}^{} \frac{e^x}{x}dx$$

I could expand it using a Laurent series and than integrating term by term but are there more elementary methods?

Last edited: Sep 27, 2006
2. Sep 27, 2006

Stu091

This just keeps expanding. Using ILATE, the algebraic part should be u, but this just keeping increasing in the power on the bottom. I don't think it's a good candidate for parts.

Edit: I'm not sure what happened to that post. Disregard I guess.

3. Sep 29, 2006

dextercioby

Since

$$\int \frac{e^{x}}{x} \ dx =\mbox{Ei}\left(x)$$

you can search Abramowitz & Stegun's book on series expansion for this function.

Daniel.