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