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Wolfram Alpha:

I'll probably kick myself when someone explains it, but I can't understand where the 1/12 comes from after the re-substitution of u? I thought it would be 1/3, but it clearly isn't. Why is that?

Thanks for input on this.

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Just a word of warning: using Wolfram Alpha should be limited to checking answers (if it is used at all). I personally believe WA is a crutch that actually undermines ones ability to understand calculus fully. You have asked a few questions concerning standard trig-substitution. I would suggest that with this type of problem you put away the computer ( and WA alike), sit down with a sheet of paper and try as many examples from a textbook as you can. – JavaMan Aug 30 '11 at 3:14
Ok. I thought since it explained the steps it was better than not having someone to consult with questions, but I'll follow your advice then. Thanks. – ranonk Aug 30 '11 at 3:26
up vote 1 down vote accepted

Since x is cubed, when the 1/2 is factored it turns into 1/8. Then 2/3 times 1/8 is 1/12.

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Makes perfect sense now. Thanks – ranonk Aug 30 '11 at 3:27

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