Fourier Transform Question Help

Question

To find the fourier transform of $$f(x) = e^{-3|x|}cosx$$ By using Euler's formula $$cosx=\frac{e^{ix}+e^{-ix}}{2}$$By definition, $$\mathcal{F[f(x)] = \hat{f}(\omega)=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^\infty}f(x)e^{-i\omega x}dx$$ How should I continue to find the fourier transform?