U-sub vs reverse chain rule (1 Viewer)

TheShy

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So im self-learning integration and im up to reverse chain rule. I done u sub before, and when I check my answers on wolframalpha, it often does it by u-subbing. So are they similar? And are there any qestions where reverse chain rule is better than u subbing?
 

blyatman

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Reverse chain rule can be derived using U-sub (or can be verified using basic differentiation), and is a specific formula which can be applied to integrals with a specific format, whereas U-sub is a more general-purpose tool. As a result, it's always faster to do reverse chain rule than U-sub if possible. E.g. Try and integrate 2x*(x^2+1)^5 using U-sub and reverse chain rule. Using reverse chain rule take less than a second to get the answer: simple inspection gives (1/6)*(x^2+1)^6 + C. U-sub will require a few extra lines and will require wasting a piece of paper for some actual working out. This is definitive proof that reverse chain rule is sustainable and environmentally friendly, whereas U-sub is a contributor to climate change.
 

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