I've always separated mine but some swear by letting them brood with the rest of the flock (which is why I was cautious about mentioning separating her). It might make integration easier if your broody is high up in the pecking order, but it can all go horribly wrong with stroppy hens, as Mace Gill said, pushing the broody off her nest (because everyone has to use the same box!), breaking her eggs, and some may attack chicks or squash them by accident once they hatch. Personally I like to give the broody her own space where she feels safe and you can ensure the safety of her chicks with a safe, shallow waterer, the right feed, and a small space so no chick gets lost or left behind. But when you move her to her own space make sure it's at night, in the dark, and that she can't see her old run/nest site as otherwise she will try and get back to it. Cover the cage if need be so she can't see in that direction if you can't move her far. Leave her and make sure she's going to sit for a couple of days before you put the eggs under her.