интxarcctgxdx
u=arcctgx dv=xdx du=-(1/1+x*2) v=x*2/2
или так u=x du=dx dv=arcctgxdx v?
какое правильно?

int x * arcctg x dx = int arcctg x d(1/2 * x^2) = 1/2 * x^2 * arccctg x - int 1/2 * x^2 d(arcctg x) =
= x^2/2 * arcctg x + 1/2 * int x^2/(1 + x^2) dx = x^2/2 * arcctg x + 1/2 * int (1 + x^2 - 1)/(1 + x^2) dx = x^2/2 * arcctg x + 1/2 * int dx - 1/2 * int dx/(1 + x^2) =
= x^2/2 * arcctg x + 1/2 * x + 1/2 * arcctg x + C
Вроде так.