Evaluate the following integral I got stuck with the integral below. I have tried to make it look like the derivative of arctan.
$$\int \frac{2-x}{x^2-x+1}\,dx$$
Thank you!

HINT: $$\int \frac{2-x}{x^2-x+1}\ dx=\frac{1}{2}\int \frac{3-(2x-1)}{x^2-x+1}$$
$$=\frac{1}{2}\int \frac{3}{x^2-x+1}\ dx-\frac 12\int \frac{(2x-1)}{x^2-x+1}\ dx$$
$$=\frac{3}{2}\int \frac{1}{\left(x-\frac 12\right)^2+\frac{3}{4}} dx-\frac 12\int \frac{d(x^2-x+1)}{x^2-x+1}$$
