TMZ has learned David Cook is out of the hospital and in his hotel, but his medical problem has not yet been resolved. Cook was examined by medics at the show and then taken to the hospital (not by ambulance) and treated by a private doctor to keep everything on the down low. The doctor gave Cook medication to bring his blood pressure down and he will monitored again Tuesday.

The "A.I." exec says the stress and anxiety from being on "Idol" and dealing with his brother's illness (see link) was just too much. - more on this story

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