inverse Laplace | MATHalino reviewer about inverse Laplace

Problem 05
Find the inverse transform of $\dfrac{2s^2 + 5s - 6}{s^3 - 3s^2 - 13s + 15}$

Problem 04
Perform the indicated operation: $\mathcal{L}^{-1} \left[ \dfrac{s - 5}{s^2 + s - 6} \right]$

Problem 03
Find the inverse transform of $\dfrac{7}{s^2 + 6}$.

Problem 01
Find the inverse transform of $\dfrac{8 - 3s + s^2}{s^3}$.

Definition
From $\mathcal{L} \left\{ f(t) \right\} = F(s)$, the value $f(t)$ is called the inverse Laplace transform of $F(s)$. In symbol,

$\mathcal{L}^{-1}\left\{ F(s) \right\} = f(t)$

where $\mathcal{L}^{-1}$ is called the inverse Laplace transform operator.