NSAIDS interfere with the normal inflammation response, and thus protein synthesis and healing.
That being said, if you simply cannot move without them due to a chronic condition, you're better off taking them and training, than not training at all. Just be aware that injuries heal less well while using NSAIDS. The tissue remodeling tends to not set down in an ordered matrix, and you may tend to reinjure the area because of this.
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I've just been working out and sucking the back pain up without relying on anti inflamatories. You've just confirmed what I have been led to believe. It's been six weeks since my injury and rehab exercises aren't doing much to help, time to visit the chiro.