Evaluate the Integral integral of cot(x)^2 with respect to x

Problem

(∫_^)(cot2(x)*d(x))

Solution

1. Apply the trigonometric identity to rewrite the integrand using the identity cot2(x)=csc2(x)−1

(∫_^)((csc2(x)−1)*d(x))

2. Split the integral into two separate terms using the linearity property of integration.

(∫_^)(csc2(x)*d(x))−(∫_^)(1*d(x))

3. Evaluate the integrals using standard integration rules, where (∫_^)(csc2(x)*d(x))=−cot(x) and (∫_^)(1*d(x))=x

−cot(x)−x+C

Final Answer

(∫_^)(cot2(x)*d(x))=−cot(x)−x+C

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