Series representation of x^2/(a^3-x^3)

Hi all,

I'm having trouble with the series representation of a function.

First I tried breaking this up into partial fractions, then I realized I'm not very good at doing partial fractions... But I think I found another path that maybe I'm supposed to use:

Consider that:

I think this somehow relates to the integral of the alternating geometric series (switching variable for clarity):

I know I can integrate the terms of the geometric series to get the natural log, but I also know I can't just plug , and now I'm not sure what to do. Am I headed down the right tree or barking up the wrong path? Do I need to return to the partial fractions approach instead?

Thanks again for any help,

Brian