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? 

$$\frac{1}{\sqrt{x+x^5}}=\frac{1}{\sqrt{x}\sqrt{1+x^4}}$$
Near $x\approx0$ you have $1+x^4 \approx 1$. And the integral of $1/\sqrt{x}$ converges near 0. Therefore your integral converges.
Moreover, the result, as computed by Mathematica, is:
$$\int_0^1\frac{\mathrm{d}x}{\sqrt{x+x^5}} = 2 \times\,  _2 F_1\left(\frac{1}{8},\frac{1}{2};\frac{9}{8};-1\right) \approx 1.91773$$
