<s>[INST] How to evaluate $\int\frac{x}{\sqrt{x^2+x+1}}dx\;?$ How do you integrate,
$$\int \frac{x}{\sqrt{x^2+x+1}} dx $$
I am trying to use trig substitution, but I am having trouble finding a perfect square which works.
 [/INST] Hint: $$\frac{x}{x^2+x+1} = \frac{x}{x^2+x+\frac{1}{4} + \frac{3}{4}} = \frac{x}{\left(x+\frac{1}{2}\right)^2 + \frac{3}{4}}$$
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