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The problem shown involves the integral of \( \csc^2(x) \, dx \). The integral is a standard trigonometric integral. Let's solve it step-by-step.

### Problem:
\[
\int \csc^2(x) \, dx
\]

### Solution:
The antiderivative of \( \csc^2(x) \) is \( -\cot(x) \). Therefore:

\[
\int \csc^2(x) \, dx = -\cot(x) + C
\]

### Answer:
From the provided options, the correct answer is:

- **a. -Cot(x)**

Would you like more details on the steps, or have any other questions?

### Related Questions:
1. What is the integral of \( \sec^2(x) \)?
2. How is the derivative of \( \cot(x) \) calculated?
3. Why is the constant of integration necessary?
4. How does the integral of \( \csc^2(x) \) relate to real-world applications?
5. What other integrals of trigonometric functions are commonly used?

**Tip:** Always check the result of your integration by differentiating the answer!

¿Cuál es el resultado de la integral ∫csc²(x)dx?

Learn how to solve the integral of csc²(x) with a detailed step-by-step solution. This calculus problem demonstrates the integral of trigonometric functions, specifically yielding -cot(x) as the result. Suitable for advanced high school students or early university-level calculus learners.

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