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Integrating e^x /x using Laurent series

  1. Sep 27, 2006 #1
    How does one integrate [tex]\int_{}^{} \frac{e^x}{x}dx[/tex]

    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. jcsd
  3. Sep 27, 2006 #2
    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.
  4. Sep 29, 2006 #3


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    [tex]\int \frac{e^{x}}{x} \ dx =\mbox{Ei}\left(x)[/tex]

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

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