Central orbit differential equation problems

Question

I have a problem with the highlighted step in the example, i couldn't quite understand how did he integrate that ?

Answer 1

Both sides of the equation are multiplied by $du/d\theta$ and then integrated with respect to $\theta$ (and multiplied by 2).

I suppose you could call this procedure “integrating with respect to $u$”, but I think that's a rather unclear way of explaining it.