/ 2
| x acot(2*x) x *acot(2*x)
| x*acot(2*x) dx = C + - + --------- + ------------
| 4 8 2
/
$$\int x \operatorname{acot}{\left(2 x \right)}\, dx = C + \frac{x^{2} \operatorname{acot}{\left(2 x \right)}}{2} + \frac{x}{4} + \frac{\operatorname{acot}{\left(2 x \right)}}{8}$$