Derive the following Laplace Transform using the definition: Assuming that IfCt)]= FG), find LFf4)] %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Derive the following Laplace Transform
using the definition:
Assuming that IFCH)]= FGS), findLff'G]
%3D
Transcribed Image Text:Derive the following Laplace Transform using the definition: Assuming that IFCH)]= FGS), findLff'G] %3D
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This does not make alot of sense. If applying the definition how does the e^-st get moved outside as a constant and back in. Where does the s outside the functionin the solution come from? If someone could rework with a little more explanation it would be appreciated. 

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