Determine £¹{F}. F(s) = 3s² + 42s + 119 (s + 5)² (s + 1) Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. L-1¹{F} =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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### Determine \( \mathcal{L}^{-1} \{ F \} \)

\[ 
F(s) = \frac{3s^2 + 42s + 119}{(s + 5)^2 (s + 1)} 
\]

[Click here to view the table of Laplace transforms.](#)

[Click here to view the table of properties of Laplace transforms.](#)

\[ 
\mathcal{L}^{-1} \{ F \} = \boxed{\ }
\]

---

This exercise asks you to determine the inverse Laplace transform of the given function \( F(s) \). It is often useful to refer to standard tables of Laplace transforms to find the inverse of more complex functions. The numerator of the function is \( 3s^2 + 42s + 119 \), and the denominator includes the terms \((s + 5)^2 (s + 1)\). Use the provided links to assist with finding the necessary transforms and their properties.
Transcribed Image Text:### Determine \( \mathcal{L}^{-1} \{ F \} \) \[ F(s) = \frac{3s^2 + 42s + 119}{(s + 5)^2 (s + 1)} \] [Click here to view the table of Laplace transforms.](#) [Click here to view the table of properties of Laplace transforms.](#) \[ \mathcal{L}^{-1} \{ F \} = \boxed{\ } \] --- This exercise asks you to determine the inverse Laplace transform of the given function \( F(s) \). It is often useful to refer to standard tables of Laplace transforms to find the inverse of more complex functions. The numerator of the function is \( 3s^2 + 42s + 119 \), and the denominator includes the terms \((s + 5)^2 (s + 1)\). Use the provided links to assist with finding the necessary transforms and their properties.
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