Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.7 The Second Shifting Theorem - Problems - Page 705: 26

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We are given that $F(s)=\frac{50e^{-3s}}{(s+1)^2(s^2+4)}$ Now,$f(t)= L^{-1}[\frac{50e^{-3s}}{(s+1)^2(s^2+4)}]\\ =L^{-1}[\frac{2se^{-3s}}{s+1}+\frac{10e^{-3s}}{(s+1)^2}-\frac{25se^{-3s}}{s^2+4}]\\ =5u_3(t)[se^{-(t-3)}+2e^{-(t-3)}(t-3)-5\cos 2(t-3)]$