Let $f(t)$ be a function on $[0, \infty)$. The Laplace transform of $f$ is the function $F$ defined by the integral $F(s) = \int_0^{\infty} e^{-st}f(t)dt$. Use this definition to determine the Laplace transform of the following function.
$f(t) = \begin{cases} e^{2t}, & 0 < t < 3 \\ 1, & 3 < t \end{cases}$
Set up the integral $F(s)$.
F(s) = \\
The Laplace transform of $f(t)$ is $F(s) = $ for all positive $s \ne 5$, where $F(5) = $
(Type exact answers.)
