/ 2 \
|atan (x) -1 + 2*x*atan(x) 2*atan(x) |
2*|-------- - ---------------- - ----------|
| 2 2 / 2\|
| x / 2\ x*\1 + x /|
\ \1 + x / /
--------------------------------------------
x
$$\frac{2 \left(- \frac{2 x \operatorname{atan}{\left(x \right)} - 1}{\left(x^{2} + 1\right)^{2}} - \frac{2 \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{2}}\right)}{x}$$
/ / 2 \ \
| | 3*x 4*x *atan(x) | |
| 2*|------ - ------------ + atan(x)| |
| 2 | 2 2 | |
| 3*atan (x) \1 + x 1 + x / 3*(-1 + 2*x*atan(x)) 6*atan(x) |
2*|- ---------- - ----------------------------------- + -------------------- + -----------|
| 3 2 2 2 / 2\|
| x / 2\ / 2\ x *\1 + x /|
\ \1 + x / x*\1 + x / /
-------------------------------------------------------------------------------------------
x
$$\frac{2 \left(- \frac{2 \left(- \frac{4 x^{2} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} + \frac{3 x}{x^{2} + 1} + \operatorname{atan}{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}} + \frac{3 \left(2 x \operatorname{atan}{\left(x \right)} - 1\right)}{x \left(x^{2} + 1\right)^{2}} + \frac{6 \operatorname{atan}{\left(x \right)}}{x^{2} \left(x^{2} + 1\right)} - \frac{3 \operatorname{atan}^{2}{\left(x \right)}}{x^{3}}\right)}{x}$$