Получается
int 1/(x + 3)^2 dx + int (x + 2)/(x^2 + 3) dx =
= -1/(x + 3) + int x/(x^2 + 3) dx + 2 * int 1/(x^2 + 3) dx =
= -1/(x + 3) + 1/2 * int d(x^2)/(x^2 + 3) + 2 * 1/3^(1/2) * arctg x/3^(1/2) =
= -1/(x + 3) + 1/2 * ln (x^2 + 3) + 2/3^(1/2) * arctg x/3^(1/2) + C