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Question Number 60938 by aliesam last updated on 27/May/19

$$\int \frac{{csc}^{2019}\left(x\right)}{{sec}^5\left(x\right)}{tan}^2\left(x\right)dx$$

Commented by Prithwish sen last updated on 27/May/19

$$\int \frac{{\cos }^3\mathrm{x}}{{\sin }^{2017}\mathrm{x}}\mathrm{dx}=\int \frac{(1-{\sin }^2\mathrm{x})\mathrm{cosx}}{{\sin }^{2017}\mathrm{x}}\mathrm{dx}$$$$\mathrm{put}\mathrm{sinx}=\mathrm{v}$$$$\mathrm{then}\mathrm{cosx}\mathrm{dx}=\mathrm{dv}$$$$=\int \frac{(1-{\mathrm{v}}^2)\mathrm{dv}}{{\mathrm{v}}^{2017}}$$$$=\int ({\mathrm{v}}^{-2017}-{\mathrm{v}}^{-2015})\mathrm{dv}$$$$$$

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