How can I compute the Fourier transform of the signal?

Question

I am trying to compute the Fourier transform of the signal below, but I could not compute it. How can I compute it? Thanks in advance for your help.

The signal is:

$$x(t) = e^{-3|t|}\sin(2)u(t)$$

Also, how can I plot the Fourier transform of this signal?

The Fourier transform that I computed is:

$$3j/(9(w+2)^{2})-3j/(9+(w-2)^{2})$$

Answer 1

Your signal is actually equal to $$ x(t)=e^{-3t}\sin 2tu(t) $$ since $x(t)=0\ \ \ ,\ \ \ t<0$. Also $$ x(t)=\frac{1}{2j}e^{(-3+2j)t}u(t)-\frac{1}{2j}e^{(-3-2j)t}u(t) $$ of which, the Fourier transform can be calculated easily.