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Integral of sqrt(x^2-a^2)exp(-x)

  1. May 19, 2009 #1
    New to the forum, thanks for having me.

    I've looked in tables and tried Mathmatica but have not came
    up with a formula for the integral over x of


    If anyone could point me in the right direction I'd be appreciative.
  2. jcsd
  3. May 20, 2009 #2

    Integration by parts?

    There is a standard formula for integrating [tex]\int\sqrt{x^2-a^2}dx[/tex] (that involves logs which might help later with the exponential).

    Haven't worked it out myself but that's where i'd start.
  4. May 20, 2009 #3


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    You won't be able to find a primitive.
  5. May 20, 2009 #4
    yeah. wolfram didn't like it when i plugged it in.
  6. May 23, 2009 #5
    Thanks for your help. Seems integration by parts will just require further integrals
    of the form (x^2-a^2)^n/2 exp(-x). Maybe I'll just have to integrate numberially for fixed values of a.
  7. May 23, 2009 #6
    The integral from a to infinity can be expressed in terms of a modified Bessel function of the first kind.
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