Ex:           Find the following Laplace transform:

Sol'n:      Apply the scaling identity with a = 6 to ƒ(t) = e−tu(t):

The result:

The result we obtain when we simplify is the same as we would have if our original expression were written with u(t) in place of u(6t). This makes sense since scaling of t leaves u( ) unchanged.

To account for the integral, we multiply the previous answer by 1/s:

This problem is simple enough that we may easily check our answer by computing the integral before taking the Laplace transform:

or