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## Homework Statement

Obtain the Laplace transformation of the fucntion defined by

f(t) = 0 t<0

= t

^{2}e

^{-at}t>=0

## Homework Equations

## The Attempt at a Solution

I'm a little unsure of what I'm doing here, so bear with me.

L {t

^{2}e

^{-at}} = ∫

^{inf}

_{0}t

^{2}e

^{-at}dt

= ∫

_{0}

^{inf}t

^{2}e

^{-(a+s)t}dt

How do I integrate this? I tried using my TI-89 but it told me it is undefined. Any help would be greatly appreciated.

EDIT: The complete solution is required, which I think means I can't just take it out of the Laplace tables