Inverse Laplace for (e)^-5t*(t)^4

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The discussion focuses on finding the Inverse Laplace Transform of the function x(t) = e^(-5t) * t^4 using Laplace tables and properties. The initial approach of separating the terms into individual Laplace transforms was deemed incorrect due to the multiplication of the two functions. The user expressed frustration after several days of attempting to solve the problem without success. They eventually discovered a more useful table for their calculations. The thread highlights the challenges faced when dealing with products of functions in Laplace transforms.
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Homework Statement



Find:

Inverse Laplace for x(t)= (e)^-5t*(t)^4 using laplace table and laplace properties.

Homework Equations





The Attempt at a Solution



Well, I have been working on this problem for a few days now and cannot seem to figure it out. The two functions are not separate terms being added together so I cannot simply say

L^-1{(e)^-5t} + L^-1{(t)^4} which I originally tried. This would result in

1/s+5 + 24/s^5 which would be easy but since the two functions are being multiplied it is throwing me off and I cannot find an answer through the tables.
 
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I found a better table, this post can be deleted
 

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