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

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

Let $f$ be a function defined for $t0.$ Then the integral

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

is said to be the Laplace transform of $f,$ provided that the integral converges.

to find $L\{f(t)\}.($Write your answer as a function of $s.)$

$f(t)=tsin(t)$

$L\{f(t)\}=$

$(s>0)$