Integral Convergence/Divergence: 0 to ∞, 1/(1+x^6)^(1/2)

[Lchan1]

Homework Statement

Determine if the integral converges or diverges?
it;s the integral of 0 to infinity
of 1/(1+x^6)^(1/2)

Homework Equations

so I compared it with 1/x^2

The Attempt at a Solution

the answer key says it converges but i think it diverges since the integral of 1/x^2 diverges from 0 to 1...

 

[Dick]

1/x^2 is WAY GREATER than 1/(1+x^6)^(1/2) near 0. In fact, the latter function is bounded on [0,1]. The fact 1/x^2 diverges near zero doesn't prove your function does.