The inverse Laplace transform of 1/s is equal to 1. In this post, we will learn how to find the inverse Laplace transform of 1 divided by s.

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## Find the Inverse Laplace of 1/s

We know that the Laplace transform of t^{n} is given by

L{t^{n}} = $\dfrac{n!}{s^{n+1}}$ where n=0, 1, 2, 3, …

Thus, taking the inverse Laplace transform on both sides, we get that

t^{n} = L^{-1}$\left(\dfrac{n!}{s^{n+1}} \right)$

⇒ t^{n} = n! L^{-1}$\left(\dfrac{1}{s^{n+1}} \right)$

Putting n=0 in the above formula, we obtain that

t^{0 }= 0! L^{-1}(1/s)

⇒ 1 = L^{-1}(1/s).

So the inverse Laplace transform formula of 1/s is given by L^{-1}(1/s) = 1, that is, 1 is the inverse Laplace of 1 by s.

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Inverse Laplace transform of a constant

## FAQs

**Q1: What is the inverse Laplace transform of 1/s?**

Answer: The inverse Laplace transform of 1/s is 1.

This article is written by Dr. T. Mandal, Ph.D in Mathematics. On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.