Use Definition $7\mathrm{.}1\mathrm{.}1,$

DEFINITION $7\mathrm{.}1\mathrm{.}1$ Laplace Transform

Let $fbe$ a function defined for $t0.$ Then the integral

$L\{f(t)\}={\displaystyle \underset{0}{\overset{}{}}}{e}^{-st}f(t)dt$

$is$ said $tobe$ the Laplace transform $off,$ provided that the integral converges.

$to$ find $L\{f(t)\}s.f(t)=t^2{e}^{-6t}$

$L\{f(t)\}=,(s>-6)$