How can I integrate this expression I looked over on the internet but I don't know hot to integrate this... Can someone give a hint 
$$ \int \frac {\sqrt x} {x^2 -x + 1} dx $$

$$\int\dfrac{\sqrt x dx}{x^2-x+1} =\int\dfrac{2xd\sqrt x}{x^2-x+dx} = \int \dfrac{2u^2du}{u^4-u^2+1}, \text { where } u = \sqrt x.$$
HINT:
$$\dfrac{2u^2}{u^4-u^2+1} = \dfrac{2u^2}{u^4+u^2+1 -3u^2} = $$$$\dfrac{2u^2}{(u^2 -\sqrt 3u +1)(u^2 + \sqrt3 u +1)}$$$$=\dfrac {Au+B}{u^2 -\sqrt 3u +1} + \dfrac {Cu+D}{u^2 + \sqrt 3u +1}.$$
