Интеграл dx/(x^2+3x+3)
Выделяем полный квадрат. x^2+3x+3=(x^2+2*x*(3/2)+(9/4))-(9/4)+3= =(x+(3/2))^2+(3/4) О т в е т. (1/sqrt(3/4))*arctg ((x+(3/2))/sqrt(3/4)+C= =(2/sqrt(3))*arctg((2x+3)/sqrt(3)) + C.