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Question Number 102001 by hardylanes last updated on 06/Jul/20

$$evaluate\int \cos {}^{3}x\sin {}^{3}xdx.$$

Answered by bobhans last updated on 06/Jul/20

$$\int (1-\sin {}^{2}x)\sin {}^{3}xd\left(\sin x\right)=$$$$\int (\sin {}^{3}x-\sin {}^{5}x)d\left(\sin x\right)=$$$$\frac{1}{4}\sin {}^{4}x-\frac{1}{6}\sin {}^{6}x+C$$$$(Bob-◻)$$

Commented by hardylanes last updated on 06/Jul/20

that's it??

Commented by bobhans last updated on 06/Jul/20

$$what?$$

Answered by bobhans last updated on 06/Jul/20

$$\int \cos {}^{3}x(\cos {}^{2}x-1)d\left(\cos x\right)=$$$$\int (\cos {}^{5}x-\cos {}^{3}x)d\left(\cos x\right)=$$$$\frac{1}{6}\cos {}^{6}x-\frac{1}{4}\cos {}^{4}x+C$$

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