How can I integrate this rational function using partial fractions?

[demersal]

Homework Statement

$$\int$$$$\frac{\frac{1}{3}x+\frac{2}{3}}{x^{2}-x+1}$$

Homework Equations

This is the result of a partial fraction integration. I don't think a direct u-substitution will work or an integration by parts.

The Attempt at a Solution

I don't know which I should use! We learned so many and none seem to work nicely in this case. Should I try to do a trigonometric substitution? That is my best guess, but since there is no radical I have no idea how to implement it!

Any sort of hint would be great. I'm just not "seeing it" ;)

 

[Defennder]

Complete the square of the denominator then break it up using (a+b)(a-b) = a^2 - b^2. From here you can do it by partial fractions, though it appears tedious.