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**1. Homework Statement**

I need to take the inverse Fourier transform of

[tex]\frac{b}{\pi(x^2+b^2)}[/tex]

**2. Homework Equations**

f(t)=[tex]\int_{-\infty}^{\infty}e^{itx}\frac{b}{\pi(x^2+b^2)}dx[/tex]

*It might be useful that [tex]\frac{2b}{\pi(x^2+b^2)}=\frac{1}{b+ix}+\frac{1}{b-ix}[/tex]*

**3. The Attempt at a Solution**

I know the result is [tex]e^{(-b|t|)}[/tex], and I can get from [tex]e^{(-b|t|)}[/tex] to

[tex]\frac{b}{\pi(x^2+b^2)}[/tex], but how do I do it in reverse if I didn't already know the pair existed? This doesn't require complex integration does it?

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