Laplace transform of exponential function

[jaejoon89]

I'm trying to find the laplace transform (if possible) of exp(-2r/a)r^2.

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I did integration by parts to check that the integral of exp(-2r/a)r^2 from 0 to infinity is a^3 / 4. but i cannot get the laplace transform to work out. the answer mathematica online gives would have to have the term in the denominator "as" = 0 for the whole thing to become a^3 / 4. I'm trying to figure out how this would happen, and if you can even do the laplace transform for this in the first place.

http://www.wolframalpha.com/input/?i=LT+e^(-2t/a)+t^2+

 

[Dick]

The whole thing isn't a^3/4. It's a function of s. I agree with Mathematica.