Inverse Laplace Transform homework

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SUMMARY

The forum discussion centers on the calculation of the Inverse Laplace Transform for the function 1/s^5. The user correctly identifies the need to apply the formula n!/s^(n+1) for n=4, resulting in 4! = 24. The transformation leads to the expression 1/s^5 = (1/24)(4!/s^(4+1)), confirming the relationship between the Laplace Transform and factorials in this context.

PREREQUISITES
  • Understanding of Laplace Transforms
  • Familiarity with factorial notation and calculations
  • Knowledge of inverse functions in calculus
  • Basic algebraic manipulation skills
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  • Study the properties of Laplace Transforms in detail
  • Learn about the application of factorials in differential equations
  • Explore examples of Inverse Laplace Transforms for various functions
  • Investigate the use of software tools for symbolic computation, such as MATLAB or Mathematica
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Students studying engineering or mathematics, particularly those focusing on differential equations and control systems, will benefit from this discussion.

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Homework Statement



1/s^5

Homework Equations



I was thinking I need to use n!/s^n+1

The Attempt at a Solution



But n would then be 4, so n! will be 24. Not sure what to do?
 
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n!, or in this case 4!= 24, is a constant!

1/s5= (1/24)(4!/s4+1)
 

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