求不定積分∫x/(x²;+2x+2)dx

求不定積分∫x/(x²;+2x+2)dx

∫x/(x²;+2x+2)dx=1/2*∫(2x+2-2)/(x²;+2x+2)dx
=1/2*∫(2x+2)/(x²;+2x+2)dx-∫1/(x²;+2x+1+1)dx
=1/2ln(x²;+2x+2)+arctan(x+1)+C