Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.5 The First Shifting Theorem - Problems - Page 695: 32

$ e^{-2t} \cos (3t)$

Since, $F(s)=\dfrac{s+2}{(s+2)^2+ 9}$ The inverse Laplace transform of function can be expressed as: $F(t)=L[ \cos 3t] =\dfrac{s}{s^2+3^2} $ Now, apply the first shifting Theorem. $f(t)= e^{-2t} \cos (3t)$