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The image you've uploaded contains a set of mathematical problems. Here are the problems as I interpret them:

1. \( \int_{0}^{2} x^2 - 6x + 5 \, dx \)
2. \( \int x e^{2x} \, dx \) 
3. \( \int x \ln(2x) \, dx \)
4. \( \int \frac{1}{x^2} \cos \left( \frac{1}{x} \right) \, dx \)
5. \( \int \frac{1}{x} e^{x^2} \, dx \)

Would you like solutions and explanations for these integrals, or is there a specific problem you want to focus on? 

Please let me know if you want to dive deeper into any of the specific problems.

### Here are 8 related questions:
1. What is the technique of integration by parts, and how can it be applied to these problems?
2. How can substitution be used to solve these integrals?
3. What are definite integrals and how do they differ from indefinite integrals?
4. How is the Fundamental Theorem of Calculus applied in solving definite integrals?
5. What are common integration strategies for dealing with integrals involving logarithms?
6. What are some common pitfalls when solving integrals involving trigonometric functions?
7. How does one approach integrals that involve exponential functions, such as \( e^{2x} \)?
8. How can improper integrals be evaluated if the integrand is undefined at certain points?

### Tip:
When solving integrals, it's often helpful to identify patterns that match known integral forms or to break down the integrand into simpler components that can be integrated separately.

Explore advanced calculus integrals with detailed step-by-step solutions. Topics include integration by parts, substitution methods, and the application of the Fundamental Theorem of Calculus. Suitable for advanced high school and college students.

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