Inverse Laplace transform of 1/s | Inverse Laplace of 1/s

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.

Find the Inverse Laplace of 1/s

We know that the Laplace transform of tⁿ is given by

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

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

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

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

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

t⁰ = 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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