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How to compute the following integral

  • #1
187
0
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
 

Answers and Replies

  • #2
1,074
1
Factor the expression in the exponent and then make a substitution.
 
  • #3
187
0
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...
 
  • #4
1,235
1
use integration by parts after making the substitution.
 
  • #5
187
0
so the substitution i proposed is the correct one to make?
 
  • #6
1,074
1
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.
 
  • #7
187
0
but for what you propose then du=2(x-xo)dx, which cannot be put into the integral like this...
 
  • #8
dextercioby
Science Advisor
Homework Helper
Insights Author
12,978
540
It has to have some error function in it, so definitely it's not an elementary integral.

Daniel.
 

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