What is the Laplace transform of the function f(t) = t^n where n is a positive integer?

The Laplace transform of the function f(t) = t^n, where n is a positive integer, is given by L{t^n} = n! / s^(n+1).

This result is derived from the definition of the Laplace transform and involves integration by parts. The process leads to a reduction formula that ultimately shows that the transform of t^n can be expressed as n! divided by s raised to the power of (n+1).