Integration by Parts
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.
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?
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Staff Review
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.
