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**blgonz03** From the list of basic power series: $\displaystyle -ln(1-x) = x + \frac{x^2}{2} +\frac{x^3}{3} + \frac{x^4}{4} +...$

How do you write a power series for $\displaystyle f(x)= \frac{-ln(1-x)}{x}$ ?

Using the result how do you write a series expression for the $\displaystyle \int_{0}^{1} \frac{-ln(1-x)}{x}dx $ ?

I started out by looking at the theorem for power series expansion and finding the derivatives of f(x), but that turned out to be a mess. Help is much appreciated!