求不定积分∫x/（x²+2x+2）dx

求不定积分∫x/（x²+2x+2）dx
求不定积分∫x/（x²+2x+2）dx

求不定积分∫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