// /6 - 3*x (6 - 6*x)*log(1 - x)\ \
||x*|------- + --------------------| |
|| | 2 3 | |
|| \ x x / |
||---------------------------------- for |x| <= 1|
|| 6 |
|| |
|| oo |
x*|< ____ |
|| \ ` |
|| \ n |
|| \ x |
|| ) ------------ otherwise |
|| / 2 |
|| / 2 + n + 3*n |
|| /___, |
\\ n = 1 /
$$x \left(\begin{cases} \frac{x \left(\frac{6 - 3 x}{x^{2}} + \frac{\left(6 - 6 x\right) \log{\left(1 - x \right)}}{x^{3}}\right)}{6} & \text{for}\: \left|{x}\right| \leq 1 \\\sum_{n=1}^{\infty} \frac{x^{n}}{n^{2} + 3 n + 2} & \text{otherwise} \end{cases}\right)$$
x*Piecewise((x*((6 - 3*x)/x^2 + (6 - 6*x)*log(1 - x)/x^3)/6, |x| <= 1), (Sum(x^n/(2 + n^2 + 3*n), (n, 1, oo)), True))