Laplace Transform of 3t² + 2t − 5
The Laplace transform of 3t² + 2t − 5 is 6/s^3 + 2/s^2 - 5/s. See the table rule behind it, then edit the function to transform anything else.
L{3t² + 2t − 5} = 6/s^3 + 2/s^2 - 5/s. Linearity lets you transform a polynomial term by term.
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{3t² + 2t − 5} = 6/s^3 + 2/s^2 - 5/s
- L{3·t^2} = 6/s^3 Table rule: L{t^2} = 2!/s^3
- L{2·t} = 2/s^2 Table rule: L{t^1} = 1!/s^2
- L{-5} = -5/s Table rule: L{1} = 1/s
Linearity lets you transform a polynomial term by term.
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Frequently asked questions
What is the Laplace transform of 3t² + 2t − 5? ▾
L{3t² + 2t − 5} = 6/s^3 + 2/s^2 - 5/s. Linearity lets you transform a polynomial term by term.
Which rule gives the transform of 3t² + 2t − 5? ▾
L{t^2} = 2!/s^3 applied to 3·t^2; L{t^1} = 1!/s^2 applied to 2·t; L{1} = 1/s applied to -5.
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 3t² + 2t − 5 is 6/s^3 + 2/s^2 - 5/s. See the table rule behind it, then edit the function to transform anything else.