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Question Number 63566 by aliesam last updated on 05/Jul/19

$$provethat$$$$$$$$\int {sin}^n\left(x\right)dx,p\in n,p⩾2=-\frac{1}{n}cos\left(x\right){sin}^{n-1}\left(x\right)+(p-1)\int {sin}^{n-2}\left(x\right)dx$$

Commented by aliesam last updated on 05/Jul/19

$$thatsrightitwasatypo$$

Commented by MJS last updated on 05/Jul/19

$${\mathrm{it}}^{\prime }\mathrm{s}\mathrm{not}\mathrm{true}.\mathrm{the}\mathrm{formula}\mathrm{is}\mathrm{for}(n⩾2)\in \mathbb{N}$$$$\int {\sin }^{n}xdx=-\frac{1}{n}\cos x{\sin }^{n-1}x+\frac{n-1}{n}\int {\sin }^{n-2}xdx$$$$\Rightarrow p-1=\frac{n-1}{n}\iff p=2-\frac{1}{n}\Rightarrow p\notin \mathbb{N}\wedge p<2$$

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