Laplace Transform of 5{\delta (t-3)}+4{u(t-2)}+3{e^{-5(t-3)}u(t-4)}

[EugP]

Homework Statement

Find the Laplace Transform of the following:

$$5{\delta (t-3)}+4{u(t-2)}+3{e^{-5(t-3)}u(t-4)}$$

The Attempt at a Solution

I know how to do the first and second terms, but I'm having trouble with the third.

$$5e^{-3t}+4\frac{1}{s}e^{-2t} + ?$$

I think I should be using either

$$L\{ f(t-t_0)u(t-t_0) \} = e^{-st_0}F(s)$$

or

$$L\{ e^{-\alpha t}u(t) \} = \frac{1}{s+\alpha}$$

or both.

The problem is, in the first one, I don't know what to put for $$F(s)$$.

Any help would be appreciated.

 

[SlideMan]

Unfortunately, you can't use your first equation because $$t_0$$ in f and u are not the same.

Try breaking up the exponential using algebra first.