Question 44

What is the integral of $$\cosec^{2} x$$ with respect to $$x$$?

Solution

The integral of $$\operatorname{cosec}^{2x}$$ with respect to x is -cot(x) + C, where C is the constant of integration. This integral can be obtained by using the trigonometric identity:

$$\operatorname{cosec}^{2x}$$ = 1 + cot^2(x),

and then integrating term by term. So, integrating 1 gives x, and integrating cot^2(x) gives -cot(x). Adding the constant of integration, we get -cot(x) + C.


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