Unit 04 Honors / Extended Practice

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Honors / Extended pathway

Rational Integration & Partial Fractions

Deeper proof, synthesis, parameter analysis, and unfamiliar applications.

1. Evaluate ∫(x³+1)/(x²+1) dx.

2. Which statement best describes the central reasoning in Polynomial Division Before Decomposition?

3. Evaluate ∫1/[(x−1)(x+2)]dx.

4. Which statement best describes the central reasoning in Distinct Linear Factors?

5. Decompose 1/[x(x−1)²].

6. Which statement best describes the central reasoning in Repeated Linear Factors?

7. Evaluate ∫(2x+3)/(x²+4)dx.

8. Which statement best describes the central reasoning in Irreducible Quadratic Factors?

9. State the form for (3x+1)/(x²+1)².

10. Which statement best describes the central reasoning in Repeated Irreducible Quadratics?

11. Set up the decomposition of 1/[x(x²+1)].

12. Which statement best describes the central reasoning in Mixed Factorizations & Coefficient Systems?

13. A CAS returns ln(x−1)−ln(x+2) for an integral across x<1. What is missing?

14. Which statement best describes the central reasoning in Strategy, CAS Comparison & Domain-Safe Verification?

β Beta Program