Suma de la serie arctg(x)^n(n-1)/(n+1)

  ///     2      2*log(1 - atan(x))\                                           \   ///          2            2*log(1 - atan(x))\                           \
  |||- ------- - ------------------|*atan(x)                                   |   |||- ------------------ + ------------------|*atan(x)                   |
  |||  atan(x)            2        |                                           |   |||      2                         2        |                           |
  ||\                 atan (x)     /                                           |   ||\  atan (x) - atan(x)        atan (x)     /                           |
  ||----------------------------------------  for And(x >= -tan(1), x < tan(1))|   ||---------------------------------------------------  for |atan(x)| < 1|
  ||                   2                                                       |   ||                         2                                            |
  ||                                                                           |   ||                                                                      |
  ||               oo                                                          |   ||                   oo                                                 |
- |<             ____                                                          | + |<                 ____                                                 |
  ||             \   `                                                         |   ||                 \   `                                                |
  ||              \        n                                                   |   ||                  \          n                                        |
  ||               \   atan (x)                                                |   ||                   \   n*atan (x)                                     |
  ||               /   --------                           otherwise            |   ||                   /   ----------                        otherwise    |
  ||              /     1 + n                                                  |   ||                  /      1 + n                                        |
  ||             /___,                                                         |   ||                 /___,                                                |
  ||             n = 1                                                         |   ||                 n = 1                                                |
  \\                                                                           /   \\                                                                      /

$$- \begin{cases} \frac{\left(- \frac{2 \log{\left(1 - \operatorname{atan}{\left(x \right)} \right)}}{\operatorname{atan}^{2}{\left(x \right)}} - \frac{2}{\operatorname{atan}{\left(x \right)}}\right) \operatorname{atan}{\left(x \right)}}{2} & \text{for}\: x \geq - \tan{\left(1 \right)} \wedge x < \tan{\left(1 \right)} \\\sum_{n=1}^{\infty} \frac{\operatorname{atan}^{n}{\left(x \right)}}{n + 1} & \text{otherwise} \end{cases} + \begin{cases} \frac{\left(\frac{2 \log{\left(1 - \operatorname{atan}{\left(x \right)} \right)}}{\operatorname{atan}^{2}{\left(x \right)}} - \frac{2}{\operatorname{atan}^{2}{\left(x \right)} - \operatorname{atan}{\left(x \right)}}\right) \operatorname{atan}{\left(x \right)}}{2} & \text{for}\: \left|{\operatorname{atan}{\left(x \right)}}\right| < 1 \\\sum_{n=1}^{\infty} \frac{n \operatorname{atan}^{n}{\left(x \right)}}{n + 1} & \text{otherwise} \end{cases}$$

-Piecewise(((-2/atan(x) - 2*log(1 - atan(x))/atan(x)^2)*atan(x)/2, (x < tan(1))∧(x >= -tan(1))), (Sum(atan(x)^n/(1 + n), (n, 1, oo)), True)) + Piecewise(((-2/(atan(x)^2 - atan(x)) + 2*log(1 - atan(x))/atan(x)^2)*atan(x)/2, Abs(atan(x)) < 1), (Sum(n*atan(x)^n/(1 + n), (n, 1, oo)), True))