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.

According to The Limit Comparison Test we have $$\lim_{x\to\infty}x^{\mathbf{2}}f(x)=1<\infty$$ so the improper integral converges. 
