Laplace Transforms

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Here you will find the Laplace transform of functions as well as their inverse Laplace transform. The Laplace transform table, formula, properties, and applications to find the solution of an ODE will be discussed here.

Main Article: Laplace Transform: Definition, Table, Formulas, Properties

Table of Inverse Laplace Transformations

For the Laplace transforms of your desired functions, just click on the function, and we will get your answer.

Laplace transforms of Basic Functions:

Functions f(t) L{f(t)}
1L{1} = 1/s
tL{t} = 1/s2
t3L{t3} = 6/s4
tnL{tn} = n!/s^{n+1}
2tL{2t} =1/(s-ln2), s>ln2
eatL{eat} = 1/(s-a)
sintL{sint} = 1/(s2+1)
sinatL{sin at} = a/(s2+a2)
costL{cost} = s/(s2+1)
cosatL{cos at} = s/(s2+a2)

More Laplace transforms:

tett sintt cost
teatt sinatt cosat

Inverse Laplace transform of 1

Inverse Laplace transform of 1/s

Inverse Laplace of 1/s2