Compute the Laplace transform of $f(t) = \begin{cases} 6, & \mbox{if } 0\leq x < 5\\ 3 t, & \mbox{if } 5\leq x < \infty \end{cases}$

$\displaystyle L\lbrace f\rbrace(s)=$

$\displaystyle\int$

$dt +$

$\displaystyle\int$

$dt$

$\hskip 120pt\displaystyle u =$ $dv =$

$\hskip 120pt\displaystyle du =$ $v =$

$\hskip 40pt\displaystyle=$

$\Bigg\vert$

$-$

$\Bigg\vert$

$+$

$\displaystyle\int$

$dt$

$\hskip 40pt\displaystyle=$

$-$

$\Bigg\vert$

$\hskip 50pt\displaystyle =$