Inverse Laplace Transform Calculator
The calculator will try to find the Inverse Laplace transform of the given function.
Recall that $$$\mathcal{L}^{-1}(F(s))$$$ is such a function $$$f(t)$$$ that $$$\mathcal{L}(f(t))=F(s)$$$.
Usually, to find the Inverse Laplace transform of a function, we use the property of linearity of the Laplace transform. Just perform partial fraction decomposition (if needed), and then consult the table of Laplace transforms.
Your input: find $$$\mathcal{L}^{-1}\left(\frac{5}{s^{2} + 2 s + 10}\right)$$$
Answer
$$$\mathcal{L}^{-1}\left(\frac{5}{s^{2} + 2 s + 10}\right)=\frac{5 e^{- t} \sin{\left(3 t \right)}}{3}$$$