I was having a bit of trouble with this:

Use the power series $\displaystyle {1\over{1+x}}=\sum_{n=0}^{\infty}{(-1)^nx^n}$ to determine a power series, centered at 0, for the function:

$\displaystyle f(x) = ln(1-x^2) = \int{{1\over{1+x}}dx} - \int{{1\over{1-x}}dx}$