Calculate $\int \frac{1}{x^2+x+1}\mathrm{d}x$ Define the integral $I$ as follow:
$$I=\int \dfrac{1}{x^2+x+1}\mathrm{d}x.$$
I do not know how to integrate it. Any suggestions please?
I tried a lot of methods:


*

*I substituted $x^2+x=u$.

*I modified the denominator $x^2+x+1=(x+1)^2-x$ and I substituted $x+1=u$.


I know that it is somewhat very easy to do it but I am stuck.
Thanks.

$(x+1/2)^2+3/4$  substitute $u=x+1/2$
