Evaluate the following integrals and show the details of
your work.

It looks like you want to evaluate some integrals with detailed steps. However, you didn't provide the specific integrals you want to evaluate. Please provide the integrals you'd like to solve, and I will show you the detailed steps for each one!

For now, here are some examples of integrals that I can help with:

1. **Definite Integral:**  
   \[
   \int_{0}^{1} x^2 \, dx
   \]

2. **Indefinite Integral:**  
   \[
   \int e^x \sin(x) \, dx
   \]

3. **Improper Integral:**  
   \[
   \int_{1}^{\infty} \frac{1}{x^2} \, dx
   \]

4. **Integral involving trigonometric functions:**  
   \[
   \int \sin^2(x) \, dx
   \]

5. **Complex Integral:**  
   \[
   \oint_C \frac{1}{z^2 + 1} \, dz
   \]

Feel free to specify any integral you'd like to evaluate or any topic you'd like to focus on!

Explore detailed steps and examples for evaluating integrals, including definite, indefinite, improper, and trigonometric integrals. Learn key formulas and theorems used in integration techniques.

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