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Any way to evaluate such an integral

  1. Nov 11, 2008 #1
    1. The problem statement, all variables and given/known data

    Is there any way to evaluate such an integral; [tex]\int e^{2x}x^{-1}dx[/tex]

    Any attempts will be appreciated.
  2. jcsd
  3. Nov 11, 2008 #2
    Re: Integration

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

    and then partial integration

    that's my first guess...

  4. Nov 11, 2008 #3


    Staff: Mentor

    Re: Integration

    I don't believe that this integral is amenable to the application of integration by parts. I tried a couple of the obvious substitutions for integration by parts, but didn't get anything that was simpler.
  5. Nov 11, 2008 #4
    Re: Integration

    I guess if we proceed it, we will get back into the starting integral and can obtain no solution.
  6. Nov 11, 2008 #5


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    Science Advisor
    Homework Helper

    Re: Integration

    There is a special function called the 'exponential integral' that's closely related to your integral. http://en.wikipedia.org/wiki/Exponential_integral That's a pretty good sign there is no simple way to reduce that to elementary functions.
  7. Nov 12, 2008 #6
    Re: Integration

    So this integral requires a complex solution? What does that mean in terms of the geometric interpretation of integrals?
  8. Nov 12, 2008 #7


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    Re: Integration

    It's not complex, Ei is real.
    What geometric interpretation (other than the usual of integral as area under a curve) would you expect?
  9. Nov 12, 2008 #8
    Re: Integration

    None, now that you said Ei is real. The equation on the wiki page threw me off where it has Ei is related to E1 as follows and then it has some odd symbol I haven't seen and an i. What does the funny + looking symbol mean?
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