Q:

I need to find the Fourier transform of the following function

I need to find the Fourier transform of $e^{-2 \pi |x|}$. Normally, I can do something like this, but the absolute value is kind of confusing me.

A:

Hint 
$$f(x)=\begin{align}e^{-2\pi x}\;\;\;\;\;\;x>0\\ e^{2\pi x}\;\;\;\;\;\;\;x<0 \end{align}$$
Thus the fourier transform is 
$$\hat{f}{(\psi)}=\int_{-\infty}^0e^{-2\pi i\psi x}e^{2\pi x}d\psi+\int_0^{\infty}e^{-2\pi i\psi x}e^{-2\pi x}d\psi$$

