Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Calculus I
Topic: Antiderivatives
Subtopic: Integration by Substitution & Indefinite Integrals

Overview

Integration by substitution is a method that allows us to “undo” the chain rule. The process involves making a u-substitution that enables a somewhat complicated integral to be rewritten as one that is simpler and can be easily integrated. The key lies in making the correct substitution!

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 4.6.1 Recognize that u-substitution is required and find an appropriate u-substitution
• 4.6.2 Using u-substitution with INDEFINITE integrals: Rewrite the integral from in terms of x to an equivalent integral in terms of u and du, then evaluate the new integral with respect to u and remember to convert back to in terms of x for the final answer
• 4.6.3 Use algebraic techniques (e.g. complete the square, use trig identities) to transform the integrand to an expression where the u-substitution method will work

Terminology

Terms you should be able to define: u-substitution method of integration

Mini-Lectures and Examples

Supplemental Resources (optional)

Lesson: Finding Antiderivatives, Dale Hoffman's Contemporary Calculus provides a nice review of processes (properties of integrals, u-subs) from Calc I in preparation for Calc II.

rev. 2020-11-27