divergence of $\int_{2}^{\infty}\frac{dx}{x^{2}-x-2}$ i ran into this question and im sitting on it for a long time.
why does this integral diverge:
$$\int_{2}^{\infty}\frac{dx}{x^{2}-x-2}$$
thank you very much in advance.
yaron.

$$\frac1{x^2-x-2}=\frac13\left(\frac1{x-2}-\frac1{x+1}\right)\implies$$
$$\int\limits_2^\infty\frac{dx}{x^2-x-2}=\left.\lim_{b\to\infty\,,\,\epsilon\to +}\frac13\log\frac{x-2}{x+1}\right|_{2+\epsilon}^b=\frac13\left[\lim_{b\to\infty}\log\frac{b-2}{b+1}-\lim_{\epsilon\to 0^+}\log\frac{\epsilon}{3+\epsilon}\right]=\infty$$
