Integral of ((x+1)/(x^2+2x+2))dx

thanks for your help!

Integral of ((x+1)/(x^2+2x+2))dx
= Integral of ((1/2)/(x^2+2x+2))d(x^2+2x+2)
= (1/2)ln|x^2+2x+2| + c

subsititution!!
u=x^2+2x+2
du=2x+2
du/2=x+1

1/2 int (1/u)du
1/2 ln u
1/2 ln |x^2+2x+2|

I =(1/2) ∫ (2x + 2) dx / (x² + 2x + 2)
I = (1/2) log (x² + 2x + 2) + C