Properties of The Laplace Transform

The properties of the Laplace transform help us to obtain transform pairs without directly using Eq. (1) $$\mathcal{L}[f(t)]=F(s)=\int_{0-}^{\infty} f(t) e^{-s t} d t \tag{1}$$ as we did in Examples 1 and 2. As we derive each of these properties, we should keep in mind the definition of the Laplace transform in Eq. (1).

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