Convergent or Divergent Integral 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? 

Set $x=y^2$, then $dx=2ydy$. So the integral becomes:
$$I=\int_0^1  \frac {1}{(x+x^{5})^{1/2}}dx=\int_0^1  \frac {2y}{(y^2+y^{10})^{1/2}}dy=\int_0^1  \frac {2}{(1+y^5)^{1/2}}dy$$
Thus the integral is convergent.
