Answer
See below
Work Step by Step
Using the Convolution Theorem
$L^{-1}[F(s)* G(s)]=L^{-1}[\frac{4}{s^3}.\frac{s-1}{s^2-2s+5}]\\
=L^{-1}[\frac{4(s-1)}{s^3(s^2-2s+5)}]\\
=2\int^t_0 e^{\omega} (t-\omega)^2\cos (2 \omega)d\omega$
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.9 The Convolution Integral - Problems - Page 716: 21
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