I got this question on an exam this morning and I didn't know how to answer it. I've been working on it the past hour trying to figure it out. Usually with rational functions, I factor to get it in a from that I can use partial fractions.

$\displaystyle \int{\frac{1}{x^2 + x + 1}}$

But this can't be factored and completing the square gives $\displaystyle (x+\frac{1}{2})^2+\frac{3}{4}$

Which doesn't look any easier to integrate.

Could someone point me in the right direction?

Thanks