The uploaded document appears to contain a list of integral problems that likely involve substitution and integration techniques. Below are the listed problems:

1. $\int \frac{dx}{\sqrt{x^2 - x + 1}}$
2. $\int \sqrt{\frac{1 + x}{1 - x}} \, dx$
3. $\int \frac{6x^2 - 2x - 1}{4x^3 - x} \, dx$
4. $\int \frac{1}{x^2 - 3x + 2} \, dx$
5. $\int \frac{2x^2 - 3x - 5}{(x - 1)(x - 2)(x - 3)(x - 4)} \, dx$
6. $\int \frac{1}{9 - 8x - x^2} \, dx$
7. $\int \frac{1}{9 + 8x + 2x^2} \, dx$
8. $\int \frac{1}{2\cos x + 3\sin x} \, dx$
9. $\int \frac{2x^2 + x + 1}{(x - 1)(x^2 + 1)} \, dx$
10. $\int \frac{1}{1 - \cos x + \sin x} \, dx$

Would you like solutions for all or any specific ones? Let me know, and I can solve them in detail.

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Here are five questions to guide further exploration:

1. Would you like detailed steps for solving these integrals?
2. Do you want explanations of specific techniques (e.g., substitution, partial fractions)?
3. Should the solutions include graphical interpretations or related concepts?
4. Are these exercises part of a larger set of study material you’d like help with?
5. Would you like summaries of the integration techniques after solving?

Tip: When solving integrals, identify symmetry or simplifications in the function to reduce complexity before applying substitution or decomposition.