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so I was working on an integral that looks like this (sin\^n+1(ax)cos\^n(ax). I want to set u = cos\^n(ax) but I'm not sure that is legal lol. Was just wondering if that is a legal u sub.

not posting the actual question so i don't get in trouble btw
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Why did you choose that for u? It's legal (as in there's no rules in Algebra which prohibit that substitution).
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Usually you want simple u's with useful derivatives
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