Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.5 The First Shifting Theorem - Problems - Page 695: 48

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Since, $y(s)=\dfrac{2}{s+1} +\dfrac{3}{(s+1)^2}+\dfrac{2}{(s+1)^3}$ The inverse Laplace transform of function can be expressed as: $y(t)=\dfrac{2}{s+1} +\dfrac{3}{(s+1)^2}+\dfrac{2}{(s+1)^3}$ Now, apply the first shifting Theorem. $f(t)= 2e^{-t} +3te^{-t} +t^2e^{-t} $