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