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Question Number 21965 by j.masanja06@gmail.com last updated on 07/Oct/17

$$integrate$$$$\int {sin}^{3}xdx$$

Answered by Tikufly last updated on 07/Oct/17

$$=\int \left({\sin }^{2}x\right)\sin xdx$$$$=\int (1-{\cos }^{2}x)\sin xdx$$$$\mathrm{Put}u=\cos x\to du=-\sin xdx$$$$I=-\int (1-u^2)du=-\int 1du+\int u^{2}du$$$$=-u+\frac{1}{3}{u}^3+C$$$$=-\cos x+\frac{1}{3}{\cos }^{3}x+C$$

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