Let

f$($t$)=$

$\{3$t$0$ t $2$sin$(4$t$)2$ $<$ t $4$e$6($t$4$$)$t $>4$

$($a$)$f$($t$)$ can be written in the form

g$1($t$)+$ g$2($t$)$U$($t $2$$)+$ g$3($t$)$U$($t $4$$)$

where U$($t$)$ is the Heaviside function. Enter the functions g$1($t$),$ g$2($t$),$ and g$3($t$),$ into the answer box below $($in that order$),$ separated with commas.

$($b$)$Compute the Laplace transform of $$f$($t$).$