Laplace of a Unit Step Function

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Homework Statement

f(t) = {0, if t<4 and (t-3)^3 if t$$\geq$$4

The Attempt at a Solution

I feel like its pretty basic but i can't get it down
I have u(t-4)(t-4)^3

Can i change it to u(t-4)^4?
Then do i multiply it out and take the laplace?
If someone can work it out for me that would be awesome, I have about 20 more and I just need an example, i appologize if that's against the rules.

I want to say the answer is (6/s^4 - 24/s^3 + 48/s^2 - 64/s)e^-4s but that's wrong.

 

[Dick]

I don't know if this is the 'laplace' way of doing things, but change the variable of integration to u=t-4. Then what does the integral that defines the laplace transform look like in terms of u?