/ 2\ -x + \1 + x /*acot(x) --------------------- / 2\ 2*\1 + x /
(-x + (1 + x^2)*acot(x))/(2*(1 + x^2))
2 -x + x *acot(x) + acot(x) ------------------------- / 2\ 2*\1 + x /
(-x + x^2*acot(x) + acot(x))/(2*(1 + x^2))
/ 2\ -2*x + \2 + 2*x /*acot(x) ------------------------- 2 4 + 4*x
(-2*x + (2 + 2*x^2)*acot(x))/(4 + 4*x^2)
/ 2\ -x + \1 + x /*acot(x) --------------------- / 2\ 2*\1 + x /
(-x + (1 + x^2)*acot(x))/(2*(1 + x^2))