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

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  • #1
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Main Question or Discussion Point

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

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

If anyone could point me in the right direction I'd be appreciative.
Thanks
 

Answers and Replies

  • #2
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[tex]\int\sqrt{x^2-a^2}e^{-x}dx[/tex]

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.
 
  • #3
Cyosis
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You won't be able to find a primitive.
 
  • #4
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yeah. wolfram didn't like it when i plugged it in.
 
  • #5
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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.
 
  • #6
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The integral from a to infinity can be expressed in terms of a modified Bessel function of the first kind.
 

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