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.
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