2 3
3 2 / 2 \ 3*atan (x)*cot (x)
atan (x)*cot (x)*\-3 - 3*cot (x)/ + ------------------
2
1 + x
$$\left(- 3 \cot^{2}{\left(x \right)} - 3\right) \cot^{2}{\left(x \right)} \operatorname{atan}^{3}{\left(x \right)} + \frac{3 \cot^{3}{\left(x \right)} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1}$$
/ 2 / 2 \ \
| 2 / 2 \ / 2 \ cot (x)*(-1 + x*atan(x)) 3*\1 + cot (x)/*atan(x)*cot(x)|
6*|atan (x)*\1 + cot (x)/*\1 + 2*cot (x)/ - ------------------------ - ------------------------------|*atan(x)*cot(x)
| 2 2 |
| / 2\ 1 + x |
\ \1 + x / /
$$6 \left(\left(\cot^{2}{\left(x \right)} + 1\right) \left(2 \cot^{2}{\left(x \right)} + 1\right) \operatorname{atan}^{2}{\left(x \right)} - \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \frac{\left(x \operatorname{atan}{\left(x \right)} - 1\right) \cot^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\right) \cot{\left(x \right)} \operatorname{atan}{\left(x \right)}$$
/ / 2 2 \ \
| 3 | 1 2 6*x*atan(x) 4*x *atan (x)| |
|cot (x)*|------ - atan (x) - ----------- + -------------| |
| | 2 2 2 | / 2 \ 2 / 2 \ / 2 \ 2 / 2 \ |
| \1 + x 1 + x 1 + x / 3 / 2 \ |/ 2 \ 4 2 / 2 \| 9*atan (x)*\1 + cot (x)/*\1 + 2*cot (x)/*cot(x) 9*cot (x)*\1 + cot (x)/*(-1 + x*atan(x))*atan(x)|
6*|--------------------------------------------------------- - atan (x)*\1 + cot (x)/*\\1 + cot (x)/ + 2*cot (x) + 7*cot (x)*\1 + cot (x)// + ----------------------------------------------- + ------------------------------------------------|
| 2 2 2 |
| / 2\ 1 + x / 2\ |
\ \1 + x / \1 + x / /
$$6 \left(- \left(\cot^{2}{\left(x \right)} + 1\right) \left(\left(\cot^{2}{\left(x \right)} + 1\right)^{2} + 7 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)} + 2 \cot^{4}{\left(x \right)}\right) \operatorname{atan}^{3}{\left(x \right)} + \frac{9 \left(\cot^{2}{\left(x \right)} + 1\right) \left(2 \cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{9 \left(x \operatorname{atan}{\left(x \right)} - 1\right) \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{2}{\left(x \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{\left(\frac{4 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{6 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \operatorname{atan}^{2}{\left(x \right)} + \frac{1}{x^{2} + 1}\right) \cot^{3}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\right)$$