Question

integrate sin^3X

Answer 1

\[\sin^3x=\sin x \sin^2x\]

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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