# Calculus question - Trig Identities

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?

• You should use LaTeX for the math parts of your questions. It makes people answer faster. – user12205 Jun 23 '11 at 0:46
• $\int 2 sin^{2}x cos^{2}xdx$? do you know $2 sin x cos x = sin 2x$? – newbie Jun 23 '11 at 0:49
• I'm having trouble finding a LaTeX tutorial online. Could you point me to one? – InBetween Jun 23 '11 at 0:53
• Ah nvm, someone edited my post and I looked at the edits, pretty straight forward. – InBetween Jun 23 '11 at 0:55
• @InBetween: tobi.oetiker.ch/lshort/lshort.pdf – user12205 Jun 23 '11 at 1:00  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).