# Math Help - Laplace Transform

1. ## Laplace Transform

Just started a course on Laplace Transforms and I just want to check that I'm going about things in the right way.

Find the Laplace transform $X(s)$ of $x(t) = (1-e^{-3t}) h(t)$.

So, firstly we get:

$X(s) = \int_0^{\infty} (1-e^{-3t}) e^{-st} dt$

$= \int_0^{\infty} e^{-st} - e^{-(3+s)t} dt$

$= \left[ \frac{-e^{-st}}{s} + \frac{e^{-(3+s)t}}{3+s} \right]_0^{\infty}$

$= \left( 0 + 0 \right) - \left( \frac{-1}{s} + \frac{1}{3+s} \right)$

$= \frac{3}{s(s+3)}$

Does the above seem about right?