Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.7 The Second Shifting Theorem - Problems - Page 704: 8

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We are given that $f(t)= (t -1)^2u_{2} (t)\\=(t-2+1)^2 u_2(t)\\ = (t-2)^2u_2(t)+2(t-2)u_2(t)+u_2 (t) $ Now,$F(s)= L[(t-2)^2u_2(t)+2(t-2)u_2(t)+u_2 (t) ]\\= \dfrac{2e^{-2s}}{s^3}+ \dfrac{2 e^{-2 s}}{s^2}+\frac{e^{-2s}}{s}$