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Integral of e^(1/x)

  1. Mar 2, 2009 #1
    Here's my problem. [tex]\int e^{1/x} dx[/tex]

    This was my attempt:

    [tex]\int e^{1/x} dx , u = e^{1/x} , du = -\frac{ e^{1/x}}{x^{2}}[/tex]

    so, [tex]x^{2} du = - e^{1/x}[/tex]

    I = - [tex]\int x^{2} du , t = x , dt = (1) dx[/tex]

    I = [tex]\int x^{2} [\frac{ e^{1/x}}{x^{2}}] (1) dx = \int e^{1/x} dx[/tex]

    As you can see... I've only gone full circle with this approach. Any help would be greatly appreciated. Thanks.
  2. jcsd
  3. Mar 2, 2009 #2
    This integral can not be written in terms of elementary functions, only in terms of the http://en.wikipedia.org/wiki/Exponential_integral" [Broken]. To do this, you will need a substitution (different from the one you did, but simple) and partial integration.
    Last edited by a moderator: May 4, 2017
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