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Alright so I've got the question:

$\int2\sin^2(x)\cos^2(x)dx$

And in class I learned:

$\sin^2(x) = ((1-\cos(2x))/2)$

$\cos^2(x) = ((1+\cos(2x))/2)$

So when I substitute I get:

$\int2((1-\cos(2x))/2)((1+\cos(2x))/2)dx$

But according to the almighty wolfram, those two aren't the same integral. What did I do wrong? And furthermore, how to I proceed?

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    @InBetween - I would also recommend htt$p$://en.wikibooks.org/wiki/LaTeX2011-06-23

1 Answers 1

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When I put each of them into WolframAlpha, I got the same thing:

original integral

second integral

However, if I were evaluating your original integral by hand, I'd probably have used the identity $\sin 2x=2\sin x\cos x$ first (any time I see $\sin x\cos x$, that identity comes to mind).

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    @InBetween: Wolfram Alpha gives yo$u$ a fairly nicely formatted display of what it "thinks" you mean. It pays to look carefully at that display.2011-06-23