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 3, 4, 5 · 7 college lessons
Integration by Parts, Reduction & Cyclic Structure
How does reversing the product rule transform products, recursive integrals, and cyclic structures into solvable forms?
Pathways
Lesson 01 · Week 3
Reversing the Product Rule
Deriving and applying integration by parts from the product rule.
Lesson 02 · Week 3Choosing u and dv Strategically
Selecting factors so differentiation simplifies and integration remains possible.
Lesson 03 · Week 3Repeated and Tabular Integration by Parts
Organizing repeated product-rule reversal efficiently.
Lesson 04 · Week 4Definite Integration by Parts
Tracking boundary terms and exact values in definite products.
Lesson 05 · Week 4Reduction Formulas & Recursive Integrals
Building recurrences that lower powers or complexity.
Lesson 06 · Week 5Cyclic Exponential–Trigonometric Integrals
Solving integrals that return to themselves after repeated integration by parts.
Lesson 07 · Week 5Applications, Method Comparison & Proof of Verification
Defending method choice and validating integration-by-parts results.