The inverse Laplace transform is defined as $$\begin{equation}ℒ^{-1}\left[F(s)\right]=\frac{1}{2\pi j}\int_{\sigma_1-j\infty}^{\sigma_1+j\infty}F(s)e^{st} ds\end{equation}$$

Although it is possible to apply the above formula to compute the $ℒ^{-1}\left[F(s)\right]$, in electric circuits we usually compute the inverse Laplace transform using the method of partial fraction decomposition.

By partial fraction we understand a fraction in which the numerator is a number (real or complex) and the denominator is a linear polynomial raised to a positive power. Partial fractions are of the form $$\frac{A}{(\textcolor{blue}{s}+a)^n}$$ where $A$ and $a$ are real or complex numbers and $n$ is a positive integer.

It turns out that all polynomial fractions in which the degree of the numerator is less than the degree of the denominator can be writtes as sum of partial fractions using the method of partial fraction decomposition.