∫x/(x^2+3x+3)dx =∫(x+3/2-3/2)/(x^2+3x+3)dx =∫(x+3/2)/(x^2+3x+3)dx-3/2∫dx/(x^2+3x+3) =1/2∫d(x^2+3x+3)/(x^2+3x+3)-3/2∫dx/(x+3/2)^2+(√3/2)^2 =ln(x^2+3x+3)/2-√3arctan(√3x/2)+C