Using the Table of Laplace Transforms, we have:

For

we think of it as

and use rule (4) from above:

Now,

so

Similarly,

So

= 2u(t − 2) + (t − 2) • u(t − 2) − 3u(t − 3) − (t − 3) • u(t − 3)

= 2u(t − 2) + t • u(t − 2) − 2 • u(t − 2) − 3 • u(t − 3) − t • u(t − 3) + 3 • u(t − 3)

= t • [u(t − 2) − u(t − 3)]

So

g(t) = t • (u(t − 2) − u(t − 3))