Laplace Transform of t²·e^(at)
The Laplace transform of t²·e^(at) is 2/(s − a)³. See the table rule behind it, then edit the function to transform anything else.
L{t²·e^(at)} = 2/(s − a)³. The general rule is L{tⁿe^(at)} = n!/(s − a)ⁿ⁺¹.
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{t²·e^(at)} = 2/(s − a)³
Worked example with numbers: L{t^2·e^(3t)} = 2/(s - 3)^3
- L{t^2·e^(3t)} = 2/(s - 3)^3 Table rule: L{t^2e^(at)} = 2!/(s − a)^3
The general rule is L{tⁿe^(at)} = n!/(s − a)ⁿ⁺¹.
More products transforms
Other transforms
Frequently asked questions
What is the Laplace transform of t²·e^(at)? ▾
L{t²·e^(at)} = 2/(s − a)³. The general rule is L{tⁿe^(at)} = n!/(s − a)ⁿ⁺¹.
Which rule gives the transform of t²·e^(at)? ▾
L{t^2e^(at)} = 2!/(s − a)^3 applied to t^2·e^(3t).
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 t²·e^(at) is 2/(s − a)³. See the table rule behind it, then edit the function to transform anything else.