If a member of a fireteam is unconscious then healed by a doctor: does he reintegrate the fireteam ? like this sentence would mean: " When one or more members leave the Fireteam, the player must recalculate the number of members to check if a Fireteam Cancellation occurs, or to determine the bonus available to the members during that Order if enough remain to compose a Fireteam. If the Fireteam has not been cancelled, then the troopers who left will automatically be able to rejoin it if they are again in Coherency with the Team Leader during the Order Count phase of their next Active Turn." or he's out of the fireteam because of the null state ? " In the Active Turn and Reactive Turn, a trooper stops being part of a Fireteam in the following cases: If the trooper enters or is in the Isolated or any Null state." http://infinitythewiki.com/en/Fireteam_Integrity
As soon as the trooper enters a Null state, they leave the Fireteam. Healing them does not let them rejoin the Fireteam. The bit you quoted won't apply until "the Order Count phase of their next Active Turn".
but he can freely rejoin the fireteam under this condition ... I never played this thing that's ... very very specific so I have to lose a member of my fireteam then revive him and wait one turn, while leaving him out of the fireteam why this option exist ? I don't get the usefulness of it ?
The main use of this rule is if one of your member declares an ARO that is different than the rest of the fireteam. They'll leave the fireteam for the duration of the reactive turn, but will rejoin for free at the beginning of your active turn. This allows you to declare different ARO without having such a harsh penalty.
Okay I see it now thx @Diphoration Does that mean that if I have 6 trooper that can be inside the same fireteam Can I change and choose the best suited 5 member each "order count" step ?
No, you can only rejoin the Fireteam, if a trooper want part of the team to begin with then you'll need to spend a Command Token to reform the link.
A trooper may only re-join if he was previously part of the fireteam. You can't add new members this way. (see conditions here http://infinitythewiki.com/en/Fireteam_Integrity)
The usefulness is for AROs, as Diphoration pointed out, and that it's free, without having to spend a Command Token.
Small addendum: start of the player's next active turn following the event which caused the unit to leave the Fireteam. If you get shot while in Reactive turn and get resuscitated during the following active turn, the chance to re-join has been missed.