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I too see much worse battery life on my iPhone 6. Updated through iTunes as I always do. Battery doesn't last a day now compared to normally ending on 30-40%
 
Seems that Apple music is a possible reason iOS 8.4 draining battery faster than expected. I recommend anyone with battery draining issue add comments on whether apple music and related service is activated on device or not, to help clearing possible root cause.
 
It's an issue on my old iP 5. Battery's already in bad shape. Checking out the new music app makes a difference. Otherwise, 8.4 seems the same.
 
I experienced drain until I disabled Apple music. Seems to get about one hour more than with 8.3 with the same usage.
 
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