Testing for convergence of this function For the integral 
$$\int_2^\infty \dfrac{x+1}{(x-1)(x^2+x+1)}dx .$$ 
Can I know if it's convergent or not?  If it does can I know how to evaluate it?
I tried to use $u$ substitution but it didn't work.

To see the convergence, just note that, the integrand behaves as
$$ \dfrac{x+1}{(x-1)(x^2+x+1)} \sim_{\infty} \frac{x}{x^3}=\frac{1}{x^2}. $$
