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I see that you've uploaded a page from a math exam or worksheet. It contains problems related to calculus and partial fractions, including:

1. Decomposition of rational expressions.
2. Indefinite and definite integrals.
3. Natural logarithms in integral solutions.

Would you like assistance with any specific problem from this page? Let me know which one, and I can walk you through its solution.

Here are some related questions that may expand your understanding:

1. How do you decompose a rational function into partial fractions?
2. What methods are used to solve integrals involving logarithmic expressions?
3. Can indefinite integrals involving rational functions always be solved using partial fractions?
4. How do you find the constants in partial fraction decomposition?
5. What are some techniques for evaluating definite integrals involving logarithms?

**Tip:** When solving indefinite integrals, always check if you can simplify the integrand (the function being integrated) through algebraic manipulation or substitution first!

Various calculus problems involving integrals, partial fractions, and logarithmic functions. The problems include partial fraction decomposition, indefinite integrals, definite integrals, and logarithmic functions in integral solutions.

This page provides a step-by-step solution to calculus problems involving indefinite and definite integrals, logarithmic functions, and partial fraction decomposition. Suitable for undergraduate students in calculus courses.

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