Convergent or Divergent? 

$$\int\_0^1 \frac {dx}{(x+x^{5})^{1/2}} $$

I have problem with the fact that if we have integration from 0 to a say and a to infinity.
How does this change the way we do the comparison test ? 

I have in my textbook: If we have from 0 to a and compare with the function 

$$ \frac {1}{(x^{3})} $$ then the exponent of x should be less than 1 for it too be convergent. Which I would say is Divergent. But I am wrong?