/ / 2 \ \
|3*\1 + cot (3*x)/ x*cot(3*x) / 2 \ |
2*|----------------- + ---------- + 9*\1 + cot (3*x)/*acot(x)*cot(3*x)|
| 2 2 |
| 1 + x / 2\ |
\ \1 + x / /
$$2 \left(\frac{x \cot{\left(3 x \right)}}{\left(x^{2} + 1\right)^{2}} + 9 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cot{\left(3 x \right)} \operatorname{acot}{\left(x \right)} + \frac{3 \left(\cot^{2}{\left(3 x \right)} + 1\right)}{x^{2} + 1}\right)$$
// 2 \ \
|| 4*x | |
||-1 + ------|*cot(3*x) |
|| 2| / 2 \ / 2 \ |
|\ 1 + x / 9*x*\1 + cot (3*x)/ 27*\1 + cot (3*x)/*cot(3*x) / 2 \ / 2 \ |
-2*|---------------------- + ------------------- + --------------------------- + 27*\1 + cot (3*x)/*\1 + 3*cot (3*x)/*acot(x)|
| 2 2 2 |
| / 2\ / 2\ 1 + x |
\ \1 + x / \1 + x / /
$$- 2 \left(\frac{9 x \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}} + 27 \left(\cot^{2}{\left(3 x \right)} + 1\right) \left(3 \cot^{2}{\left(3 x \right)} + 1\right) \operatorname{acot}{\left(x \right)} + \frac{27 \left(\cot^{2}{\left(3 x \right)} + 1\right) \cot{\left(3 x \right)}}{x^{2} + 1} + \frac{\left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \cot{\left(3 x \right)}}{\left(x^{2} + 1\right)^{2}}\right)$$