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S = contains supplemental resources
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 xex is ex(x+1). Integration by parts enables us to find ∫ex(x+1)dx to get back to the xex. 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 logb(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

Define: "by parts"

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.