Very confused about converging integral/direct comparison

[miniskus]

I'm supposed to prove that int(1/(x^(1/3)+x^(2/3))dx evaluated between -infinity and positive infinity converges. I understand direct comparison can be used in positive territory but have no idea how to start in negative. Please help. Thank you.

 

[Gene]

I'm not sure if I am completly confused or I don't understand the problem. Maybe this will catch the attention of someone else who will explain where I am wrong.

I start out with a substitution.
z = x^(1/3)
dz = 1/(3x^(2/3)) dx
dx = 3x^(2/3) dz = 3z^2 dz

dy = (1/(x^(1/3)+x^(2/3))dx =
(1/z+z^2)*3z^2*dz =
(3z+3z^4)dz

int(dy)= int_{-a to a} (3z+3z^4)dz =
y = {(3/2)z^2 + (3/5)z^5}_{-a to a} =
{(3/2)a^2+(3/5)a^5}-{(3/2)a^2-(3/5)a^5} =
(6/5)a^5

That doesn't appear to me to converge even if a doesn't approach infinity. HELP!
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Gene