/
| 3
| 4 cos (3*x) cos(3*x)
| cot (3*x) dx = C + x - ----------- + ----------
| 3 3*sin(3*x)
/ 9*sin (3*x)
$$\int \cot^{4}{\left(3 x \right)}\, dx = C + x + \frac{\cos{\left(3 x \right)}}{3 \sin{\left(3 x \right)}} - \frac{\cos^{3}{\left(3 x \right)}}{9 \sin^{3}{\left(3 x \right)}}$$