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## Homework Statement

calculate the Fourier Transform of the following function:

## Homework Equations

x(t) = e

^{-|t|}cos(2t)

## The Attempt at a Solution

∫

^{0}

_{-∞}e

^{t}((e

^{2jt}+ e

^{-2jt}) / 2) e

^{-jωt}+ ∫

^{∞}

_{0}e

^{-t}((e

^{2jt}+ e

^{-2jt}) / 2) e

^{-jωt}

The first integral is easy to calculate and equals: (1/2) * (1/(1+(2-ω)j) + 1/(1+(-2-ω)j))

But how about the second integral?