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Hi, I am taking a random process class and I came across a problem that has stumped me. I believe I know the end result but I would like to know how it is solved. I have been out of college for a while and I am a little rusty with integration.

What I need is to find out the inverse Fourier transform of

I know that

I tried to solve it using by parts, but it got very messy and I may be heading the wrong path. This is what I did:

I plugged it in to the by parts equation and I felt like going on wouldn't help. I would appreciate any help. Thanks.

## Homework Statement

What I need is to find out the inverse Fourier transform of

**S(ω)=1/((1+ω^2)^2)**## Homework Equations

I know that

**F^-1(S(ω)) = 1/(2∏) * ∫(S(ω)*e^(j*ω*t), ω,-∞,∞)**where j is an imaginary number.**→ F^-1(S(ω)) = ∫(1/((1+ω^2)^2)*e^(j*ω*t), ω,-∞,∞)**## The Attempt at a Solution

I tried to solve it using by parts, but it got very messy and I may be heading the wrong path. This is what I did:

**u = (1+ω^2)^-2 du = -4*ω*(1+ω^2)^-3**

dv = e^(j*ω*t) v = e^(j*ω*t)/(j*t)dv = e^(j*ω*t) v = e^(j*ω*t)/(j*t)

I plugged it in to the by parts equation and I felt like going on wouldn't help. I would appreciate any help. Thanks.

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