I doublechecked this but I'm a bit rusty lately so perhaps someone else can verify it,

int dx/(x+1)(x^2-x+1)

You have an irreducible quadratic factor so the equation is

a/(x+1) + (bx+c)/(x^2-x+1) = 1

x=0 -> a+c=1

x=1 -> a+2b+2c=1

x=-1 -> 3a=1

Solving that system, a=1/3, b=-1/3, c=2/3

Now all you have to do is to solve the last part:

int 1/(3(x+1)) + ((-1/3)x + (2/3))/(x^2-x+1)

Hope this helps