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# PP 8.1_1 - Techniques of Integration We already have a list...

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Techniques of Integration We already have a list of basic integration formulas learned in Calculus I. We want to create new tools to evaluate the integrals of more complicated functions using those formulas. Please, memorize the formulas on page 488 of the textbook.

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Integration by Parts
Integration by parts is used to integrate products of functions. The formula is derived from the product rule for derivatives: + = ) ( ) ( ) ( ) ( )] ( ) ( [ x g dx d x f x g x f dx d x g x f dx d dx x g dx d x f x g x f dx d x g x f + = ) ( ) ( ) ( ) ( ) ( ) (

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= = - = - = = - ) ( and ) ( where , OR ) ( ) ( ) ( ) ( ) ( ) ( OR ) ( ) ( ) ( ) ( ) ( ) ( x v v x u u vdu uv udv dx x f x g x g x f dx x g x f dx x g x f dx d dx x g dx d x f x g x f
Examples -

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PP 8.1_1 - Techniques of Integration We already have a list...

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