arctan(x/2)/2=∫ 1 · 1/(x^2 + 4) dx = x · 1/(x^2 + 4) +∫ 2·x^2/(x^2 + 4)^2 dx
=x · 1/(x^2 + 4) +
∫ 2·(x^2+4-4)/(x^2 + 4)^2 dx
=x · 1/(x^2 + 4) +
∫ 2/(x^2 + 4)^2 dx-∫ 8/(x^2 + 4)^2 dx
=x · 1/(x^2 + 4) +
arctan(x/2)-∫ 8/(x^2 + 4)^2 dx
---> -1/2 arctan(x/2) -x/(x^2+4) =-∫ 8/(x^2 + 4)^2 dx
1/16 arctan(x/2) -x/[8(x^2+4)] (+C) =∫ 1/(x^2 + 4)^2 dx