This is on page 542 of Evans PDE book. The last inequality states that
$\int_{U}{C(|Du|+1)|u|dx} \leq \frac{1}{2}\int_{U}|Du|^2dx + C\int_{U}{|u|^2+1 \ dx}$
Where is this coming from? I think this is just young's inequality and then holder applied to $|Du|$ (since $u$ is assumed to be in $H_0^1[U]$) but why write it in such a weird way?