Answer
$=\frac{5}{s^3}$
Work Step by Step
Given: $f(t)=5e^{-3t}$
Obtain: $F(s)=\int^{\infty}_0 e^{-st}f(t)dt\\
=\int^{\infty}_0 e^{-st} (5e^{-3t})dt\\
=5\int^{\infty}_0 e^{-(s+3)t}dt\\
=5\lim e^{-(s+3)t}+\frac{5}{s+3}e^{-(s+3)}\\
=\frac{5}{s^3}$
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 - 10.10 Chapter Review - Additional Problems - Page 718: 4
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