# Inverse Fourier Transform

## Homework Statement

Hi!

I tried to get the inverse fourier transform of the function:

$X(j\omega)=1/(jw+a)$​

for a>0, using the integral:

$x(t)=(1/2\pi)\int_{-\infty}^{+\infty} X(j\omega)e^{j\omega t}d\omega$​

I know that the inverse Fourier transform of $X(j\omega)$ is:

$x(t)=e^{-at}u(t), a>0$​

but when i tried to calculate the integral i got:

$x(t)=(1/2\pi)\int_{-\infty}^{+\infty} e^{j\omega t}/(jw+a)$​

,and i wasnt able to get that integral using any of the techniques i know. What am i doing wrong or isnt possible to get the inverse Fourier transform of that function this way?