Inverse Laplace Transform of $$$8 s^{2} - 4 s + 12$$$
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Your Input
Find $$$\mathcal{L}^{-1}_{s}\left(8 s^{2} - 4 s + 12\right)$$$.
Answer
The Inverse Laplace transform of $$$8 s^{2} - 4 s + 12$$$A is $$$12 \delta\left(t\right) - 4 \frac{d}{dt} \left(\delta\left(t\right)\right) + 8 \frac{d^{2}}{dt^{2}} \left(\delta\left(t\right)\right)$$$A.