Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.9 The Convolution Integral - Problems - Page 716: 22

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Using the Convolution Theorem $L^{-1}[F(s)* G(s)]=L^{-1}[\frac{s+1}{s^2+2s+2}.\frac{1}{(s+3)^2}]\\ =L^{-1}[\frac{s+1}{s^2+2s+2}].L^{-1}[\frac{1}{(s+3)^2}]\\ =e^{-t}\cos t*e^{-3t}t\\ =\int^t_0 e^{-(t-x)}\cos (t-x)xe^{-3x}dx\\ =\int^t_0 e^{-(x+2x)}x\cos (t-x)dx$