// / 2 2*log(1 - x)\ \
||x*|- - - ------------| |
|| | x 2 | |
|| \ x / |
||---------------------- for And(x >= -1, x < 1)|
|| 2 |
|| |
|| oo |
x*|< ____ |
|| \ ` |
|| \ n |
|| \ x |
|| / ----- otherwise |
|| / 1 + n |
|| /___, |
|| n = 1 |
\\ /
$$x \left(\begin{cases} \frac{x \left(- \frac{2}{x} - \frac{2 \log{\left(1 - x \right)}}{x^{2}}\right)}{2} & \text{for}\: x \geq -1 \wedge x < 1 \\\sum_{n=1}^{\infty} \frac{x^{n}}{n + 1} & \text{otherwise} \end{cases}\right)$$
x*Piecewise((x*(-2/x - 2*log(1 - x)/x^2)/2, (x >= -1)∧(x < 1)), (Sum(x^n/(1 + n), (n, 1, oo)), True))