What is the laplace transform of t(sinh(3t))?

[thepatient]

Homework Statement

So I finally had my final today, and I was so worried because I needed a 90% at least to pass the class with an A. :\ So I'm really worried with a few of my answers.

One of those (that I can remember) was the laplace transform of: t(sinh(3t).

Homework Equations

laplace t = 1/s^2
Definition of: sinh(3t) = 1/2 (e^3t - e^-3t), I think.

The Attempt at a Solution

So I had no idea how to do this, since it wasn't in the table. XD What I did was multiply t by 1/2 (e^3x-e^-3x), then used the laplace of each one separately. Something like:

1/2* (1/(s-3)^2 - 1/(s+3)^2, or something like that. Was this the correct way to do this?

 

[thepatient]

Omg as I typed that last post I received my grade for the final by email. I got a 99%. :D I'm so excited woooo. :D :D :D That was so fast we just did the final this morning...