Multiplication by Power of t | Laplace Transform
Multiplication by Power of $t$
If $\mathcal{L} \left\{ f(t) \right\} = F(s)$, then,
$\mathcal{L} \left\{ t^n f(t) \right\} = (-1)^n \dfrac{d^n}{ds^n} F(s) = (-1)^n F^{(n)}(s)$
where $n = 1, \, 2, \, 3, \, ...$