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