So I have $\displaystyle \displaystyle \int{\frac{\sqrt{x}}{x+1}\,dx}$

My initial attempts at u substitution failed because I couldn't see any clear derivatives of terms in the numerator or denominator.

I looked at Wolfram Alpha and it says to use $\displaystyle u = \sqrt{x}$ and $\displaystyle du=\frac{1}{2\sqrt{x}}$

But then, I'm not really sure where to go from there. It says to go right to

$\displaystyle \displaystyle \2\int{\frac{u^2}{u^2+1}\,du}$

but I can't figure out how they got that from the u and du.