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Calculus III

Course: Calculus II
Topic: Integration Techniques
Subtopic: Integration by Parts

Overview

Integration by parts is an integration technique used to integrate products. Essentially it reduces the product rule of differentiation. For instance the derivative of xe^x is e^x(x+1). Integration by parts enables us to find int e^x(x+1) dx to get back to the xe^x. This technique is one of the most useful in the course!

Objectives

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

• 8.1.1 Apply the integration by parts formula identifying u, du, v, dv
• 8.1.2 Understand how to choose the right u for the integration by parts formula
• 8.1.3 Use the integration by parts formula to evaluate integrals
• 8.1.4 Know the integral of ln(x), log(x), and log_b(x)
• 8.1.5 Perform integration by parts multiple times on a single problem when needed
• 8.1.6 Evaluate integrals by parts that require one to add an integral to both sides

Terminology

Terms you should be able to define: "by parts"

Mini-Lectures and Examples

Supplemental Resources (recommended)

Integ. by Parts "LIATE" method: David Lippman, creator of WAMAP, has a video on the LIATE method of choosing u and dv in Integration By Parts that you might find useful: Integration by parts - choosing u and dv

Supplemental Resources (optional)

Lesson: Finding Antiderivatives - A Review, Dale Hoffman's Contemporary Calculus provides a review of finding basic antiderivaties. Worth skimming before starting more complicated techniques of integration.

rev. 2021-01-30