ยง7.1: Integration by Parts
Library, Handouts & Tools
| Resource Name | Type | Description | Link |
|---|---|---|---|
| Paul's Notes: Integration by Parts | Study Guide | Derivation of the formula and standard examples involving $e^x$, logs, and trig. | Read Notes |
| Paul's Notes: IBP Problem Set | Worksheet | Extensive list of problems with full solutions available online. | View Problems |
| LIATE Strategy Guide | Handout | A heuristic guide (Log, InvTrig, Alg, Trig, Exp) for choosing $u$ and $dv$. | Download PDF |
| LIATE Rule Worksheet | PDF Handout | CU Boulder worksheet on choosing $u$ and $dv$. | Download PDF |
Video Lectures
| Topic | Source | Description | Link |
|---|---|---|---|
| Integration by Parts | Univ. of Houston | Comprehensive lecture covering the formula derivation and standard examples. | Watch |
| Deriving the Formula | Khan Academy | Connecting the Product Rule to the Integration by Parts formula. | Watch |
| Definite Integrals | Khan Academy | Applying the Fundamental Theorem of Calculus within the IBP framework. | Watch |
| Deriving the Formula | Houston Math Prep | Connecting the Product Rule to the Integration by Parts formula. | Watch |
| Basic Examples (x sin x) | Houston Math Prep | Walkthrough of a standard example where algebraic meets trigonometric. | Watch |
| Advanced Cases (Inverse Trig) | Houston Math Prep | Handling integrals like $\int x \arctan(x) \, dx$ or $\int \ln(x) \, dx$. | Watch |
| Cyclic Integrals | YouTube | Solving integrals that loop back on themselves (e.g., $e^x \sin x$). | Watch |