$ x(t) = e^{-|t-1|} \, $
$ X(w) = \int_{-\infty}^{\infty}e^{-|t-1|}e^{-jwt}dt $
$ X(w) = \int_{-\infty}^{1}e^{(t-1)}e^{-jwt}dt+\int_{1}^{\infty}e^{-(t-1)}e^{-jwt}dt $
$ X(w) = \int_{-\infty}^{1}e^{-1}e^{(1-jw)t}dt+\int_{1}^{\infty}e^{1}e^{-(1+jw)t}dt $
$ X(w) = {\left.\frac{e^{-1}e^{(1-jw)t}}{1-jw}\right]^1_{-\infty} }+{\left.\frac{-e^{1}e^{-(1+jw)t}}{1+jw}\right]^{\infty}_1 }<br><br> $
