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^{-1}When solving differential equations using the Laplace transform, we need to be able to compute the inverse Laplace transform. For this we can resort to the use of the formula, but in most cases its use requires the execution of cumbersome and complex calculations. Due to the high level of complexity, tables of Laplace transforms are used to find the inverse transforms.

But don’t worry, so you don’t break your head, we present the Inverse Laplace Transform calculator, with which you can calculate the inverse Laplace transform with just two simple steps:

- Enter the Laplace transform F(s) and select the independent variable that has been used for the transform, by default the variable s is selected.
- Hit the “Calculate” button and you will automatically get the inverse Laplace transform f(t).

Usually, when we compute a Laplace transform, we start with a time-domain function, f(t), and end up with a frequency-domain function, F(s).

Obviously, an inverse Laplace transform is the opposite process, in which starting from a function in the frequency domain F(s) we obtain its corresponding function in the time domain, f(t).

Where is the operator commonly used to designate an inverse Laplace transform.

The following integral formula is used to obtain the inverse transform, which is also known as the Bromwich integral:

Here is a table with the most common inverse transforms: