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Evaluate the following integral

  1. Mar 1, 2013 #1
    Evaluate the following integral:

    [itex]\int_0^{∞}[/itex] [itex]\frac{e^{-(x+x^{-1})}}{x}dx[/itex]
    Last edited: Mar 1, 2013
  2. jcsd
  3. Mar 1, 2013 #2
    Re: Challenge


  4. Mar 1, 2013 #3
    Re: Challenge

    Evaluate the following integral (symbolically and not numerically), should've specified that.
  5. Mar 1, 2013 #4
    Re: Challenge

    My guess is that you express e = (1+1/x)^x then work with that.
  6. Mar 1, 2013 #5
    Re: Challenge

    Since x is already a variable in the problem, I assume you mean ##e=\lim\limits_{n\to0}\left(\left(1+\dfrac1n \right)^n\right)##?

    For some reason, I feel like some sort of substitution of ... wait a second ...

    How about the substitution ##u=\dfrac1x##?
  7. Mar 2, 2013 #6
    The integral given does not converge. Its antiderivative is [itex]\displaystyle e^{-1/x}\text{Ei}(-x)[/itex] where Ei is the exponential integral function. I think simply plugging in zero for x shows why it wouldn't converge.
  8. Mar 2, 2013 #7
    Hi !
    the integral can be expressed in terms of a Bessel function (attachment)

    Attached Files:

  9. Mar 2, 2013 #8
    Thank you again JJacquelin! I can always count on you! :)
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