Improper Integral

Lchan1

1. The problem statement, all variables and given/known data
Determine if the integral converges or diverges?
it;s the integral of 0 to infinity
of 1/(1+x^6)^(1/2)

2. Relevant equations

so I compared it with 1/x^2

3. 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.