Help with the limit of an integral I am trying to evaluate this limit
$$\lim \limits_{x \to \infty} \frac {1}{\ln x} \int_{0}^{x^2} \frac{t^5-t^2+8}{2t^6+t^2+4}    dt=? $$
Any help will be appreciated.

Hint: Compare with the integral of just $t^5/(2 t^6)$ as $t$ goes to infinity. Show that the rest really doesn't matter.
