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Question Number 162512 by vishal1234 last updated on 30/Dec/21

$$solve\int \sqrt{{cosec}^{2}x-2}dx$$

Commented by MJS_new last updated on 30/Dec/21

$$2\mathrm{steps}\mathrm{are}\mathrm{necessary}$$$$\left(1\right)t=\cos x$$$$\left(2\right)u=\sqrt{2}t+\sqrt{2t^2-1}$$$$\mathrm{the}\mathrm{rest}\mathrm{is}\mathrm{decomposition}...$$$$\mathrm{I}\mathrm{get}$$$$\sqrt{2}\int \frac{{(u^2-1)}^2}{u(u^2-2u-1)(u^2+2u-1)}du=$$$$=\sqrt{2}(\int \frac{du}{u}+\int \frac{du}{u^2-2u-2}-\int \frac{du}{u^2+2u+1)})$$

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