I am having trouble getting Mathematica to evaluate a trivial Fourier transform.

I would like to be able to evaluate the Fourier transform of the right-sided exponential decay function as shown below. (The real proof is explored here: fourier.eng.hmc.edu)

$\mathscr{F}[e^{- t }u(t)] = \frac{1}{1 + j \omega} $

Once I have evaulated the Fourier transform I would like to plot it for $\omega = {1,5}$

I have tried the following:

FourierTransform[Exp[-t],t,w]
Table[%,{w,5}]
ListLinePlot[Abs[%]]

The output from the "FourierTransform" command is just exactly what I asked it with some formatting.

My attempt to create the table doesn't work...

Where am I going wrong?

(Thank you for your patience with a new Mathematica user!)

I am having trouble getting Mathematica to evaluate a trivial Fourier transform.

I would like to be able to evaluate the Fourier transform of the right-sided exponential decay function as shown below. (The real proof is explored here: fourier.eng.hmc.edu)

$\qquad \mathscr{F}[e^{- t }u(t)] = \frac{1}{1 + j \omega} $

Once I have evaulated the Fourier transform I would like to plot it for $\omega = {1,5}$

I have tried the following:

FourierTransform[Exp[-t], t, w]
Table[%, {w, 5}]
ListLinePlot[Abs[%]]

The output from FourierTransform is my input with some formatting.

My attempt to create the table doesn't work...

Where am I going wrong?