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How to do the indefinite integral

  1. Feb 22, 2010 #1
    1. The problem statement, all variables and given/known data
    I hope someone can help me with this integral. It is really an improper integral, but I cannot figure out how to do the indefinite integral on it:


    Any help would be appreciated, thanks.

    2. Relevant equations

    3. The attempt at a solution

    I tried integration by parts, substitution and using the table of integrals. I couldn't get any of them to work.
  2. jcsd
  3. Feb 22, 2010 #2


    Staff: Mentor

    Re: integral

    I would be included to split it up as (1/x) *[ (1/x^2)*e^(1/x)] and try integration by parts on that. IOW, u = 1/x, and dv = (1/x^2)*e^(1/x)dx.

    I don't know that this would work, but that's what I would start with.
  4. Feb 22, 2010 #3
    Re: integral

    This is definetly a U substitution problem, when things are kinda odd inside an exponential, its the best method to try.

    pick u=1/x,
    that means du= (-1/x^2) dx.

    [tex]\int \frac{e^{1/x}}{x^{3}} dx[/tex] = [tex]\int \frac{-1}{x} e^{1/x}(\frac{-1}{x^{2}}dx)[/tex]
  5. Feb 22, 2010 #4
    Re: integral

    Thank you so much! The substitution did the trick!
  6. Feb 22, 2010 #5
    Re: integral

    perfect. Now if only I could get help with my cray cray math.
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