The math help thread

Ugh, I'm having a really dumb moment. Got all the way through a semi long question, and now i'm having a moron moment on what should be the easiest part of the question.

How does one integrate -1/(1-x+x^2) with respect to x? I have the anwser, but can't for the life of me work out which method was used for it.
(The anwser should be

)

Multiply by 4/4:
-4 / (4-4x+4x^2) dx

Complete the square:
-4 / ((2x-1)^2+3) dx

Substitute u = 2x-1, du = 2dx:
-2 / (u^2+3) du

Inverse tan integral:
-2 arctan(u/sqrt(3)) / sqrt(3)

De-substitute u = 2x-1:
-2 arctan((2x-1)/sqrt(3)) / sqrt(3)

That should be your answer.