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(A) We have the integral: $\int \operatorname{cosec} x(\operatorname{cosec} x + \cot x) \, dx$ Distributing the $\operatorname{cosec} x$ term,we get:

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$-\cot x - \operatorname{cosec} x + C$

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(A) We have the integral: $\int \operatorname{cosec} x(\operatorname{cosec} x + \cot x) \, dx$ Distributing the $\operatorname{cosec} x$ term,we get: $\int (\operatorname{cosec}^2 x + \operatorname{cosec} x \cot x) \, dx$ Using the linearity property of integration,we split the integral: $\int \operatorname{cosec}^2 x \, dx + \int \operatorname{cosec} x \cot x \, dx$ We know the standard integration formulas: $\int \operatorname{cosec}^2 x \, dx = -\cot x + C_1$ $\int \operatorname{cosec} x \cot x \, dx = -\operatorname{cosec} x + C_2$ Combining these results,we get: $-\cot x - \operatorname{cosec} x + C$,where $C = C_1 + C_2$.

Find the following integral: $\int \operatorname{cosec} x(\operatorname{cosec} x + \cot x) \, dx$

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