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