RedAssigh4[1].3 - Subtract ( ) ( ) f x g x from both sides....

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Unit: Techniques of Integration Module: Integration by Parts Introduction to Integration by Parts Copyright 2001, Thinkwell Corp. All Rights Reserved. 1479 –rev 06/14/2001 Integration by parts reverses the product rule . Integration by parts requires a product of two functions: one with a simple derivative and one with a simple integral. The integral of ln x is a tough nut to crack. The techniques of integration that you’ve studied, u -substitution and partial fraction decomposition, don’t apply. A new technique must be used. This technique is called integration by parts . Recall the product rule . It is used to differentiate the product of two functions.
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Unformatted text preview: Subtract ( ) ( ) f x g x from both sides. Integrate both sides. Note that one antiderivative of [ ] ( ) ( ) f x g x is ( ) ( ) f x g x . The equation in the box is the formula for integration by parts. Use integration by parts to integrate a function that has two parts, one part that is easy to differentiate and one part that is easy to integrate. The formula for integration by parts is often rewritten so that = ( ) g x u and = ( ) f x v . In this case, u is easily differentiable and dv is easily integrable. When written this way, integration by parts can be thought of as a love affair between the two functions, u and v ....
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This note was uploaded on 04/27/2010 for the course MATH 172 taught by Professor Hyon during the Spring '10 term at Community College of Denver.

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