Convergence of ∫dx/sqrt(x^4+1): Explanation Needed

[MozAngeles]

Homework Statement

Does ∫dx/sqrt(x^4+1) from x=-∞ to x=∞ converge or diverge?
explain in detail if you can please.
thanks

Homework Equations

limit comparison test
direct comparison

The Attempt at a Solution

...well i have the answer, it converges. I just need a better explanation than the solutions manual gives.

the first thing i did was break it up into ... ∫dx/√(x⁴+1) from x=-∞ to x=0 +∫dx/√(x⁴+1) from x=0 to x=∞ then i was stuck, now I'm here...

 

[lanedance]

i think a comparison test would work well here...