# Fourier Transform of x*f(x)

#### paxprobellum

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

I'm trying to do the Fourier Transform of "x*f(x)". According to some web sites (http://everything2.com/index.pl?node=fourier transform), it is simply a "property of integration", but I've having some issues.

2. Relevant equations

I'm using the form:
1/2pi int ( x f(x) e ^ (iwx) dx )

3. The attempt at a solution

I've tried doing it by parts, but I can't get it to work. My two attempts were:
1) u=f(x) and dV = x e^(iwx) dx
and
2) u=x*f(x) and dV = e^(iwx) dx

Using 1) I got -1/w^2 dF/dW
Using 2) I got (1/iw)[-int (e^(iwx) x f'(x) dx) - F(w)]

I know the answer is -i dF/dw (as it is in the Fourier transform table), but I can't seem to get there. =/

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