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 2 years ago
Can someone explain to me why is there a "u^2" ?
Here's the solution in wolfram alpha http://www.wolframalpha.com/input/?i=integrate+sqrt+%2832x%29+x%5E2
I understand how it used substitution to get (3u^2)^2 and the 1/4 but i can't seem to know where the u^2 came from...help T_T
 2 years ago
Can someone explain to me why is there a "u^2" ? Here's the solution in wolfram alpha http://www.wolframalpha.com/input/?i=integrate+sqrt+%2832x%29+x%5E2 I understand how it used substitution to get (3u^2)^2 and the 1/4 but i can't seem to know where the u^2 came from...help T_T

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colorful
 2 years ago
Best ResponseYou've already chosen the best response.1\[u=\sqrt{32x}\implies du=\frac{dx}{\sqrt{32x}}=\frac{dx}u\]therefor\[dx=udu\]so then \[\sqrt{32x}dx=u\cdot(udu)=u^2du\]
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