Linear Combination of Laplace Transforms

Theorem
Let $\laptrans f$ denote the Laplace transform of the real function $f$.

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

Let $\lambda, \mu \in \C$ or $\R$ be constants.

Then:


 * $\laptrans {\lambda \, \map f t + \mu \, \map g t} = \lambda \laptrans {\map f t} + \mu \laptrans {\map g t}$

everywhere all the above expressions are defined.