Ibuprofen, Naproxen, Diclofenac and dozens of other prescription drugs are NSAIDs: non-steroidal anti-inflammatory drugs. They relieve pain caused by inflammation, by reducing the inflammation. As a gout sufferer I know that large doses of these drugs are spectacularly successful on the right sort of problem. Crippling agony to mild ache in six hours. Magic that works!
But if you have back pain, it may very well be neurological: a trapped or pinched nerve. In which case an anti-inflammatory drug is useless. Which leaves Paracetamol, Aspirin and the all-too-addictive opiates.
Personally, the only thing I've found Paracetamol any use for is flu / bad colds (and I do wonder whether palliative interference with the natural self-curing of these ailments is wise) I used to find Aspirin much more effective, except it's contra-indicated for gout sufferers like me. Aspirin has a direct effect at the neurological level, as well as being an anti-inflammatory drug.
Another reason to avoid NSAIDs for back pain is that it's likely to be chronic, and long-term use of anti-inflammatories is rather bad for you. They appear to block your body's natural repair mechanisms, and if you take them long-term your risk of suffering a stroke or heart attack slowly rises. In some people they also cause stomach bleeding, which long-term can lead to ulcers or anaemia.