Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.5 The First Shifting Theorem - Problems - Page 695: 45

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