How to test convergence for $\int_{2}^{\infty}\frac{\sqrt{x^5}}{3x^2 +x +100}$?

Question

I'm new to these convergence tests, I've studied the quotient test and the comparison test for integrals, but I'm having difficulty using them, like for this integral $$\int_{2}^{\infty}\frac{\sqrt{x^5}}{3x^2 +x +100} .$$

Is there something in this integral that I immediately should pay attention to, to make me understand which test I should be using and which function I should be choosing for the test?

Answer 1

HINT

The numerator has $x^{2.5}$ so the entire fraction is roughly $$\frac{x^{2.5}}{3x^2} = \frac{\sqrt{x}}{3}$$