$ 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) = e^{-1}\frac{e^{(1-jw)t}}{1-jw}\right]^{\infty}_0 }+e^{1}\frac{e^{-(1+jw)t}}{1+jw}]^{\infty}_0 } $
