Find the Integral csc(x)^2

Problem

(∫_^)(csc2(x)*d(x))

Solution

1. Identify the standard trigonometric integral form for the squared cosecant function.

2. Recall the basic differentiation rule for the cotangent function, which states that d(cot(x))/d(x)=−csc2(x)

3. Apply the reverse power rule or trigonometric identity for integration, noting that the integral of csc2(x) is the negative of the cotangent function.

4. Add the constant of integration C to represent the family of antiderivatives.

Final Answer

(∫_^)(csc2(x)*d(x))=−cot(x)+C

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