Originally Posted by

**buckeye1973** Hi all,

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

$\displaystyle f(x) = \frac{x^2}{a^3-x^3}$

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:

$\displaystyle \int \frac{x^2}{a^3-x^3} dx = -\frac{1}{3} ln(a^3 - x^3) + C$

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

$\displaystyle \int \frac{1}{1+u} du = ln(1 + u) + C$

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 $\displaystyle u = a^3 - x^3 - 1$, 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