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## Homework Statement

Evaluate if the integral diverges or converges using the comparison theorem.

[tex]\int^ \infty_2 \frac{dx}{\sqrt{x^3+1}}[/tex]

Having trouble with this question, the exercises I have managed I generally guessed if it was convergent/divergent, and then found a smaller of bigger function at the interval and went by that. Here I assumed it was convergent and used [tex]\frac{1}{\sqrt{x^2+1}}[/tex], though that was divergent which says absolutely nothing. Ran into the same issue with other attempts.

Is my reasoning the issue or have I just not found the correct manipulation? Not really approaching with anything more involved than "Find something bigger and hope it converges".

Any help would be appreciated, thanks.