I already can solve the Fourier Transform for $e^{-p|x|}$ but I dont know how to use it to find the Fourier transform of the function below:
$e^{-p|x+3|} + 2e^{-(p|x|-iqx)}$
The first part might be okay but I don't know how to to deal with the second part because there is something outside the absolute and have complex number in it.
The Fourier transform of $e^{-p|x|}$,$e^{-p|x+3|}$ and $2e^{-p(|x|)+iqx}$ are $\frac 1 {\pi} \frac p {p^{2}+x^{2}}$, $e^{3ix}\frac 1 {\pi} \frac p {p^{2}+x^{2}}$ and $\frac 2 {\pi} \frac p {p^{2}+(x-q)^{2}}$. You get the second and the third from the first of these by just writing down the definition of Fourier transform and making simple change of variable.