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How to compute the following integral

  1. Nov 20, 2006 #1
    I was wondering how to compute the following integral:
    [tex]\int xe^{\frac{-x^2+2x\cdot x_0-x_{0}^2}{2a^2}}dx[/tex]

    it would be quite simple if there was no term in the exponent x times x0 i think...any help on this thanks
     
  2. jcsd
  3. Nov 20, 2006 #2
    Factor the expression in the exponent and then make a substitution.
     
  4. Nov 20, 2006 #3
    i factored the exponent to be -(x-x0)^2 but what is the substitution to make? u = x-xo? this does not help because of the x...
     
  5. Nov 20, 2006 #4
    use integration by parts after making the substitution.
     
  6. Nov 20, 2006 #5
    so the substitution i proposed is the correct one to make?
     
  7. Nov 20, 2006 #6
    Try u=(x-x0)2, I think that should work, but it might be a bit messy, I'm pretty sure parts will not work though.
     
  8. Nov 20, 2006 #7
    but for what you propose then du=2(x-xo)dx, which cannot be put into the integral like this...
     
  9. Nov 21, 2006 #8

    dextercioby

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    It has to have some error function in it, so definitely it's not an elementary integral.

    Daniel.
     
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