The inverse Laplace transform of the function is calculated by using Mellin inverse formula:
Where and .
This operation is the inverse of the direct Laplace transform, where the function is found for a given function .
The inverse Laplace transform is denoted as .
It should be noted, that the function can also be found based on the decomposition theorem. If function is decomposes into a Laurent series in the neighborhood of an infinity distant point, i.e.
At the same time, in practice, to find the function for a given function , one can use various techniques such as partial fraction decomposition operational calculus rules.
Our online calculator based on the Wolfram Alpha system finds inverse Laplace transform for almost any given function.