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