Chapter 8

Section 8.1

  • Lesson: Review of “Basic” Integration Techniques

  • Examples: Using Completing the Square to Integrate

  • Review: A Review of Completing the Square for Calc Students

  • Examples: Multiplying by a Fraction

  • Examples: Improper Fractions and Integration

  • Examples: Separating Fractions to Integrate

  • Examples: Creatively Using Substitution to Integrate

Section 8.2

  • Lesson: Integration by Parts and an Overview of Examples

  • Lesson: Integration by Parts with Definite Integrals

  • Examples: Using the Integration by Parts Formula Multiple Times

  • Examples: Integration by Parts when the Integral Cycles Back to Itself

  • Examples: Using both Substitution AND Integration by Parts

Section 8.3

  • Lesson: Trigonometric Integrals with Powers of Sines and Cosines

  • Examples: Integrals with Powers of Sines and Cosines

  • Lesson: Trigonometric Integrals with Square Roots or Products of Sines and Cosines

  • Examples: Integrals with Trig Functions and Square Roots

  • Examples: Integrals with Products of Sines and Cosines

  • Lesson: Trignometric Integrals with Powers of Tangent, Secant, Cotangent, and Cosecant

  • Examples: Integrals with Powers of Tangent and Secant

Section 8.4

  • Lesson: Trigonometric Substitution

  • Examples: “Basic” Trig Substitution

  • Examples: More Complicated Trig Substitution Problems

  • Examples: Problems Where You Have to Use U-Substitution and Trig Substitution

  • Review: A Review of Completing the Square for Calc Students

  • Examples: Problems where You Have to Complete the Square Before Integrating (and maybe also Trig Substitution)

Section 8.5

  • Lesson: Partial Fractions with Integration

  • Examples: Partial Fractions with Linear Factors Only

  • Examples: Partial Fractions with Irreducible Quadratic Factors

  • Examples: Improper Fractions

  • Examples: Partial Fractions where Significant Creativity is Required

Section 8.7

Section 8.8

  • Lesson: Improper Integrals Type I

  • Lesson: Improper Integrals Type II

  • Lesson: Comparison Tests for Integrals

  • Review of Everything About L’Hopital’s Rule in 14 Minutes

  • Summary: A Summary of How to Study for the Advanced Integration Exam and a Few Randomly Hard Integrals