Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.7 The Second Shifting Theorem - Problems - Page 704: 19

$e^{-(t-2)}\sin (t-2)u_2(t)$

We are given that $F(s)=\frac{e^{-2s}}{s^2+2s+2}$ Now,$f(t)= L^{-1}[\frac{e^{-2s}}{s^2+2s+2}]\\ =L^{-1}[\frac{e^{-2s}}{(s+1)^2+1}]\\ =L^{-1}[e^{-2s}(L(e^{-t}\sin t))]\\ =e^{-(t-2)}\sin (t-2)u_2(t)$