Laplace Transform of Real Power

Theorem
Let $n$ be a constant real number such that $n > -1$

Let $f: \R \to \R$ be the real function defined as:
 * $\map f t = t^n$

Then $f$ has a Laplace transform given by:


 * $\laptrans {\map f t} = \dfrac {\map \Gamma {n + 1} } {s^{n + 1} }$

where $\Gamma$ denotes the gamma function.