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anonymous
 5 years ago
How do you antiderive x(2x)^2?
anonymous
 5 years ago
How do you antiderive x(2x)^2?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you have to take the integral

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Would you mind showing me step by step?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I'm a little rough at this but I can try to help. I would go ahead and multiply through before calculating the integral. So you would have \[x(2x)(2x)\] then you would foil and multiply through by x. You end up with an integral that looks like this \[\int\limits 4x4x ^{2}+x^3 dx\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Check my work... Like I said I'm a little rough at this. I believe you use a basic integration formula for each of those numbers...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits 4x dx = 4(1/2)x ^{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You can make it much simpler by letting u=2x and du=1*dx. Then, you get ∫u^2*(2u) du which expands to ∫2u^2u^3 du = [2u^3/3  u^4/4] + c = 2(2x)^2/3 + (2x)^4/4 + c, if I'm not mistaken. MtHaleyGirl's solution is correct, but just seems like a lot more tedious multiplication than is necessary.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I DO take the long way... Scared of substitution but I just need a little practice. Good tip. Maybe it will make MY life easier.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yesss, substitution makes life so much easier later on, once you get confident with it. It's an absolute must for a lot, if not all, of advanced techniques of integration.
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