## anonymous 3 years ago integrate sin^3X

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1. anonymous

$\sin^3x=\sin x \sin^2x$

2. anonymous

i think the gimmick is to rewrite this as $\sin^2(x)\sin(x)=(1-\cos^2(x))\sin(x)$

3. anonymous

then $\sin(x)-\sin(x)\cos^2(x)$ first integral is easy, second is a u - sub

4. anonymous

or you can look at the "reduction" formula for sine on the inside cover of the back off your text and use $$n=3$$

5. anonymous

HMMMM.. Tnx guys.. can u give me a site for online lessons

6. UnkleRhaukus

$\sin^3x=\sin x \sin^2x\\\qquad=\sin x\frac{1-\cos(2x)}2\\\qquad=\tfrac12\big(\sin x-\sin x\cos(2x)\big)\\\qquad=\tfrac12\Big(\sin x-\frac{\sin(3x)+\sin(-x)}{2}\Big)\\\qquad=\frac {\sin x}2-\frac{\sin(3x)}{4}+\frac{\sin(x)}{4}$

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