Finding indefinite integral ∫ X / (X & # 178; + 2x + 2) DX

Finding indefinite integral ∫ X / (X & # 178; + 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