(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Basically, i have to find the solution to:

Int( x^{2}* exp (-(x-w)^2) , x= -infinity.. infinity)

2. Relevant equations

I realise this is connected to Gaussian Integration. So that if i have Int (exp(-x^{2}), x=-infinity ... infinity) the answer is sqrt(Pi)

Also, i have read that there is a trick to solving such an integral.

you would consider F(a) = Int exp( - a * x^2) ( = sqrt(pi/a) ).

and then int dx x^2 exp(-x^2) = - F'(a) for a=1.

i understand this.

3. The attempt at a solution

Basically, the above is how i have attempted to work a way towards the solution, the trouble i am having is with a substitution i realise i must make at some point. at some point i must have x = x - w

But how do i implement this substitution??

This is my first post here, so hopefully that was somewhat clear and the relevant info is there. Thanks for any help.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Gaussian Integral Help

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