Answer
$L[ t^3 e^{-4t}]=\dfrac{6}{(s+4)^4}$
Work Step by Step
The Laplace transform of function $t^3$ is given as:
$L(t^3)=\dfrac{3 !}{s^4}$
The first shifting Theorem for $a=-4$ can be expressed as:
$L[ t^3 e^{-4t}]=\dfrac{6}{(s+4)^4}$
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 - 10.5 The First Shifting Theorem - Problems - Page 694: 22
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