Laplace transform with time shift

[maxsthekat]

Homework Statement

I need to find the Laplace transform of t*e^-t*u(t-tau)

2. Homework Equations and attempt at solution

I know the general form of the transform, but my problem is in the time shift of the step function. If both parts of the expression were (t-tau), then I could just pull out an e^(s*tau), but I have no idea what I'm supposed to do when one part has it and the other does not.

Can anyone help get me started?

 

[vela]

Hint:

te^{-t} = (t-\tau+\tau)e^{-(t-\tau+\tau)}