Compute the Fourier Transform of x(t):
$ \,x(t)=2e^{-3t}u(t)+3[u(t+3)-u(t-3)] $
Using the Formula for Fourier Transforms:
$ \mathcal{F}(x(t))= \mathcal{X}(\omega)= \int_{-\infty}^{\infty}x(t)e^{-j\omega t} \,dt $
So the calculation follows as: $ \mathcal{X}(\omega)= \int_{-\infty}^{\infty}(2e^{-3t}u(t)+3[u(t+3)-u(t-3)])e^{-j\omega t} \,dt $
