Chapter 11.9, Problem 3PT

Using $\frac{1}{1-x}={\displaystyle \underset{n=0}{\overset{\infty }{\sum }}{x}^n}$ for |x| < 1, ${\displaystyle \int \frac{x}{1-x^2}dx=}$

1. a) ${\displaystyle \underset{n=0}{\overset{\infty }{\sum }}\frac{x^{2n}}{2n}}$
2. b) ${\displaystyle \underset{n=0}{\overset{\infty }{\sum }}\frac{x^{2n+1}}{2n+1}}$
3. c) ${\displaystyle \underset{n=0}{\overset{\infty }{\sum }}\frac{x^{2n+2}}{2n+2}}$
4. d) ${\displaystyle \underset{n=0}{\overset{\infty }{\sum }}{x}^{2n+1}}$