How do you integrate x/(x^3-1)

I've already done partial fraction decomposition and ended up with 3 integrals, but I do not know how to solve the integrals from there.
The integrals I got were:

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

Integral of 1/(x-1) dx = Ln (x-1)
Integral of 1 / (x^2 + x + 1) dx

x^2 + x + 1 = (x + 1/2)^2 + (3/4) . Apply trig substitution using (x + 1/2) = tan w

I'll let you think about the 3rd one, but consider that it is almost of the form of du / u