Linear Combination of Laplace Transforms

Theorem
Let $\mathcal L$ be the Laplace transform.

Let $f, g$ be functions such that $\mathcal L f$ and $\mathcal L g$ exist.

Let $\lambda \in \C$ or $\R$ be constant.

Then:


 * $\mathcal L \left \{{\lambda f \left({t}\right) + g \left({t}\right)}\right\} = \lambda \mathcal L \left\{ {f \left({t}\right)}\right\} + \mathcal L \left\{ {g \left({t}\right)}\right\}$

everywhere all the above expressions are defined.