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Home › Courses › Calculus 1/AB/BC › Archive for Chapter 8 – Advanced Integration Techniques and Improper Integrals
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Chapter 8 – Advanced Integration Techniques and Improper Integrals

This chapter begins with tricky yet neat manipulations of integrands to make integrating those very difficult functions much easier.  From there, it is off to learn all about a staple in Calculus 2 / BC, integration by parts.  Next, you will learn how to integrate by partial fraction decomposition – sounds fancy…it’s just fun!  Then you will master the art of using trigonometric identities and some nifty manipulations to solve trigonometric integrals.  The second to last lesson is all about trigonometric substitution taught in a way you can understand!  This chapter on integration wraps up with a thorough study of improper integrals.  What are you waiting for?  Get integrating!

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Lesson 1 – Tricky Integrand Manipulations

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Lesson 1 – Tricky Integrand Manipulations (Part 2)

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Lesson 2 – Integration By Parts

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Lesson 2 – Integration By Parts (Part 2)

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Lesson 3 – Integration by Partial Fractions

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Lesson 3 – Integration by Partial Fractions (Part 2)

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Lesson 4 – Manipulation of Trig Integrals

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Lesson 4 – Manipulation of Trig Integrals (Part 2)

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Lesson 5 – Trigonometric Substitution

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Lesson 6 – Improper Integrals

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Lesson 6 – Improper Integrals (Part 2)

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        • Chapter 12: Two-Step Equations and Inequalities
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        ▼
        • Course Overview
        • How to Maximize Your Learning Experience!
        • Chapter 1: Algebraic Expressions & Operations with Integers
        • Chapter 2: One-Step Equations & Inequalities
        • Chapter 3: Operations and Equations With Decimals
        • Chapter 4: Factors, Simplifying Fractions, and Exponent Rules
        • Chapter 5: Fraction Operations & Solving Equations with Fractions
        • Chapter 6: Operations and Uses of Ratios, Proportions, & Percents
        • Chapter 7: Solving Equations and Inequalities
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        • Chapter 10: Areas of Two- & Three-Dimensional Figures and Volume
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        • Chapter 1: Algebraic Expressions and Operations with Real Numbers
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        • Chapter 4: Solving Inequalities
        • Chapter 5: Introduction to Graphs and Functions
        • Chapter 6: Linear Functions and Graphing Lines
        • Chapter 7: Systems of Linear Equations and Linear Inequalities
        • Chapter 8: Exponent Rules & Exponential Functions
        • Chapter 9: Polynomials
        • Chapter 10: Graphing and Solving Quadratic Equations
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        • Chapter 14: Probability, Combinations, and Permutations
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        • Chapter 1 – Limits
        • Chapter 2 – Derivatives
        • Chapter 3 – Uses of the Derivative
        • Chapter 4 – Integration
        • Chapter 5 – Derivatives and Integrals of Exponential Functions, Logarithms, and Inverse Trigonometry
        • Chapter 6 – Differential Equations and Exponential & Logistic Growth
        • Chapter 7 – Area, Volume, and Arc Length
        • Chapter 8 – Advanced Integration Techniques and Improper Integrals
        • Chapter 9 – Series and Tests for Convergence and Divergence
        • Chapter 10 – Taylor Polynomials and Power Series
        • Chapter 11 – The Calculus of Parametric and Polar Equations
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