Laplace Transform of t³
The Laplace transform of t³ is 6/s^4. See the table rule behind it, then edit the function to transform anything else.
L{t³} = 6/s^4. 3! = 6, so the numerator is 6 and the denominator is s⁴.
Use t as the variable. Examples: t^3, e^(-2t), sin(3t), t*cos(2t), 4t^2+3. Write δ(t) as delta(t).
The result
L{t³} = 6/s^4
- L{t^3} = 6/s^4 Table rule: L{t^3} = 3!/s^4
3! = 6, so the numerator is 6 and the denominator is s⁴.
More powers transforms
Other transforms
Frequently asked questions
What is the Laplace transform of t³? ▾
L{t³} = 6/s^4. 3! = 6, so the numerator is 6 and the denominator is s⁴.
Which rule gives the transform of t³? ▾
L{t^3} = 3!/s^4 applied to t^3.
How do I get back from F(s) to f(t)? ▾
Use the inverse Laplace transform. Split F(s) into partial fractions and invert each piece with the same table read backwards — the inverse Laplace transform calculator does this step by step.
About this Calculator
The Laplace transform of t³ is 6/s^4. See the table rule behind it, then edit the function to transform anything else.