I know that this is an integral problem, but I'm stuck on some algebra within it. I'm doing a u-substitution on this problem:

$\displaystyle \int \frac{\sqrt{x}}{x^2+x} dx$

$\displaystyle \displaystyle let u = \sqrt{x} \rightarrow du = \frac{dx}{2\sqrt{x}} \rightarrow 2 du = x^\frac{-1}{2} dx$

So far, so good. Here's where I am stuck. According to Wolfram Alpha, when I do my u-substitution, I should get:

$\displaystyle 2 \int \frac{u^2}{u^4 + u^2} du$

The denominator and the constant are obvious, but I can't see how they get from $\displaystyle 2 du = x^\frac{-1}{2} dx$ to $\displaystyle u^2 du$ in the numerator. Can somebody show this to me? Clearly I have a hole in my algebra abilities.

Thanks.