Find the indefinite integral. 
Definitions:
REM Sleep
A unique phase of sleep characterized by rapid eye movement, increased brain activity, vivid dreams, and temporary paralysis of the muscles.
N1 Sleep
N1 sleep, or the first stage of non-REM sleep, is a transitional phase where one drifts in and out of sleep and can be easily awakened.
N2 Sleep
A stage of sleep characterized by sleep spindles and K-complexes, representing a deeper sleep than N1 and preceding the deeper N3 stage of sleep.
N3 Sleep
The third stage of non-REM sleep, characterized by deep sleep and the lowest levels of physiological activity within the sleep cycle.
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