Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.5 The First Shifting Theorem - Problems - Page 695: 29

$f(t)=2 t^2 e^{-2t}$

Since, $F(s)=\dfrac{1}{(s+2)^2}$ The inverse Laplace transform of function can be expressed as: $F(t)=t^2 $ This yields: $F(s)=\dfrac{2 !}{s^3}=\dfrac{2}{s^3}$ Now, apply the first shifting Theorem. $F(s)=\dfrac{4}{(s+2)^3}= 2 [\dfrac{2}{(s+2)^3}]$ So, $f(t)=2 t^2 e^{-2t}$