Inverse Laplace Transform of 1/s³

The inverse Laplace transform of 1/s³ is 1/2·t^2. See the partial fraction expansion and the transform pair used for each term, then edit F(s) to try your own.

L⁻¹{1/s³} = 1/2·t^2. L⁻¹{1/sⁿ⁺¹} = tⁿ/n!, so 1/s³ gives t²/2.

e.g. 2s+3

Expanded or factored, e.g. (s+1)(s^2+4)

Try an example

The result

L⁻¹{1/s³} = 1/2·t^2

Partial fractions: 1/s^3

  • Invert 1/s^3 — L⁻¹{A/(s − a)^3} = A·t^2e^(at)/2!

L⁻¹{1/sⁿ⁺¹} = tⁿ/n!, so 1/s³ gives t²/2.

More inverse transforms

Frequently asked questions

What is the inverse Laplace transform of 1/s³?

It is f(t) = 1/2·t^2. L⁻¹{1/sⁿ⁺¹} = tⁿ/n!, so 1/s³ gives t²/2.

What are the partial fractions here?

F(s) splits into 1/s^3, and each piece is inverted separately.

How can I check this answer?

Transform 1/2·t^2 forward again with the Laplace transform calculator — you should get back 1/s³.

About this Calculator

The inverse Laplace transform of 1/s³ is 1/2·t^2. See the partial fraction expansion and the transform pair used for each term, then edit F(s) to try your own.

Related Searches

inverse laplace transform of 1/s³inverse laplace 1/s³l inverse 1/s³inverse laplace transform calculator