# Integration by Parts

Taught by Houston
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Meets NCTM Standards:
Lesson Summary:

In this lesson on Integration by Parts, you’ll learn how to simplify difficult integrals using the product rule. This technique involves letting u equal one factor and dv equal the other, anti-differentiating both sides, and then rearranging the formula to isolate the integral. The lesson includes examples of integrating x*sin(x), x*e^(-x/2), and the natural log of x. You’ll also learn how to use integration by parts on definite integrals and reduction formulas to reduce the power of x as well as powers of sine and cosine.

Lesson Description:

Integration by parts. Derivation of reduction formulas.

Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.

• What is integration by parts?
• How do you do integration by parts?
• What is the integral of u dv?
• Why does the integral of u dv = uv - integral of v du?
• What is the integral of x cos x?
• How do you find an integral without ever taking an integral?
• How do you use integration by parts of a definite integral?
• What are reduction formulas?
• What is the integral of x^n cos(kx)?
• What is the integral of (cos x)^n?
• #### Staff Review

• Currently 4.0/5 Stars.
This video does a very thorough job of explaining integration by parts. It explains where the formula comes from and shows many example problems using this formula, including how to pick u and dv so it works. There are also reduction formulas that use integration by parts to make certain problems with high powers of x much easier and faster. An incredibly useful technique vital to integration in Calculus.