integrate sin^3X

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integrate sin^3X

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[\sin^3x=\sin x \sin^2x\]
i think the gimmick is to rewrite this as \[\sin^2(x)\sin(x)=(1-\cos^2(x))\sin(x)\]
then \[\sin(x)-\sin(x)\cos^2(x)\] first integral is easy, second is a u - sub

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or you can look at the "reduction" formula for sine on the inside cover of the back off your text and use \(n=3\)
HMMMM.. Tnx guys.. can u give me a site for online lessons
\[\sin^3x=\sin x \sin^2x\\\qquad=\sin x\frac{1-\cos(2x)}2\\\qquad=\tfrac12\big(\sin x-\sin x\cos(2x)\big)\\\qquad=\tfrac12\Big(\sin x-\frac{\sin(3x)+\sin(-x)}{2}\Big)\\\qquad=\frac {\sin x}2-\frac{\sin(3x)}{4}+\frac{\sin(x)}{4}\]

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