Trig substitution with tangent

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This vid is a great example of a larger issue in terms of pattern recognition in learning, trying things and not worrying about being wrong, etc. Translating integrals into "integratable" forms, I believe is a much bigger issue than just a calc problem. It is in my not so humble opinion, teaching the essence of learning; i.e. mastery

JosephWisniewski
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Please do one requiring 'completing the square'

idiosyncraticidiott
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What if we substitute x by x=cot (theta)? the final answer would be different

Pouya