# Math Help - Laplace Transform

1. ## Laplace Transform

I have a Laplace transform to solve: [5e^-2t - 2e^-t + e^t]u(t).

I know that its relatively simple, but I'm new to Laplace transforms and I can't find another problem like it to model the approach. I know that the transform of e^-2t u(t), for example, is 1/(s+2), and that I can linearly combine the transforms of each of the given terms, but what do you do with the leading coefficients?

By the way, instructions are to find the transform using tables only.

2. The Laplace Transform is linear. That means that if you have functions $f(t)$ and $g(t)$ and constants $a$ and $b$, then

$\mathcal{L}[af(t)+bg(t)]=a\mathcal{L}[f(t)]+b\mathcal{L}[g(t)].$ So what do you suppose happens to the $5$ and the $-2$ you have there?