To integrate a function, Brian would typically follow these steps:

1. **Identify the function to be integrated**: This could be a polynomial, trigonometric, exponential, or any other type of function.

2. **Determine the type of integration**: Decide whether the problem requires an indefinite integral (finding the antiderivative) or a definite integral (finding the area under the curve between two points).

3. **Apply the appropriate integration rules**:
   - **Basic power rule**: \(\int x^n \, dx = \frac{x^{n+1}}{n+1} + C\), where \(n \neq -1\).
   - **Trigonometric functions**: For example, \(\int \sin(x) \, dx = -\cos(x) + C\) or \(\int \cos(x) \, dx = \sin(x) + C\).
   - **Exponential functions**: \(\int e^x \, dx = e^x + C\).
   - **Integration by parts**: For functions that are a product of two functions, use the formula \(\int u \, dv = uv - \int v \, du\).
   - **Substitution method**: Useful when the function is composite, where substitution simplifies the integral.

4. **Solve the integral**: After applying the rules, Brian would solve the integral step by step.

5. **Simplify the result**: If possible, the result is simplified to its simplest form.

6. **For definite integrals**: After finding the antiderivative, substitute the upper and lower limits and compute the difference.

If you provide the specific function you're referring to, I can guide you through the integration process in detail.

Would you like to see how to integrate a specific function, or do you have any further questions on the integration process?

### Related Questions:
1. How do you integrate the function \( x^2 \)?
2. What is the integral of \( \sin(x) \)?
3. How do you apply integration by parts to the function \( x \ln(x) \)?
4. What is the difference between definite and indefinite integrals?
5. Can you explain the substitution method with an example?
6. How do you integrate a function that involves an exponential?
7. What is the integral of \( \frac{1}{x} \)?
8. How do you integrate a trigonometric function like \( \cos^2(x) \)?

**Tip:** When integrating, always check if the function can be simplified first, as this can make the integration process much easier.

Discover how to integrate a function step-by-step with Brian's guide. Learn about integration techniques, including the basic power rule, trigonometric functions, exponential functions, and integration by parts. Suitable for advanced high school students and beyond.

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