Unit route
Complete lessons in sequence, use diagnostic evidence to select a pathway, conduct the investigation, submit corrected work, and demonstrate mastery at 80% or above.
Weeks 9, 10, 11 · 7 college lessons
Rational Integration & Partial Fractions
How does algebraic decomposition expose the logarithmic, inverse-trigonometric, and rational pieces hidden inside a rational function?
Pathways
Lesson 01 · Week 9
Polynomial Division Before Decomposition
Separating polynomial and proper-rational parts.
Lesson 02 · Week 9Distinct Linear Factors
Decomposing into simple logarithmic pieces.
Lesson 03 · Week 9Repeated Linear Factors
Including every power through the multiplicity.
Lesson 04 · Week 10Irreducible Quadratic Factors
Using linear numerators over irreducible quadratics.
Lesson 05 · Week 10Repeated Irreducible Quadratics
Building all required numerator layers.
Lesson 06 · Week 11Mixed Factorizations & Coefficient Systems
Coordinating linear and quadratic components.
Lesson 07 · Week 11Strategy, CAS Comparison & Domain-Safe Verification
Using technology to check—not replace—algebraic decomposition.