Laplace Transform of Positive Integer Power

Theorem
Let $\laptrans f$ denote the Laplace transform of a function $f$.

Let $t^n: \R \to \R$ be $t$ to the $n$th power for some $n \in \N_{\ge 0}$.

Then:


 * $\laptrans {t^n} = \dfrac {n!} { s^{n + 1} }$

for $\map \Re s > 0$.

Also see

 * Laplace Transform of Complex Power