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Question Number 177913 by infinityaction last updated on 11/Oct/22

$$\mathbf{if}{\mathbf{I}}_{\mathbf{n}}=\int {\mathbf{xsin}}^{\mathbf{n}}\mathbf{x}\mathbf{dx}\mathbf{and}$$$${\mathbf{I}}_{\mathbf{n}}=-\frac{{\mathbf{xsin}}^{\mathbf{n}-1}\mathbf{x}\mathbf{cosx}}{\mathbf{n}}+\frac{{\mathbf{sin}}^{\mathbf{n}}\mathbf{x}}{{\mathbf{n}}^2}+\mathrm{f}\left(\mathrm{n}\right){\mathrm{I}}_{\mathrm{n}-2}$$$$\mathrm{then}\mathrm{f}\left(\mathrm{n}\right)=?$$

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