{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-28T14:38:38+00:00","modifiedTime":"2016-03-28T14:38:38+00:00","timestamp":"2022-09-09T18:15:43+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Calculus","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33723"},"slug":"calculus","categoryId":33723}],"title":"How to Integrate by Parts","strippedTitle":"how to integrate by parts","slug":"how-to-integrate-by-parts","canonicalUrl":"","seo":{"metaDescription":"Integrating by parts is a complicated calculus procedure. 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This video uses example problems to show you how to put the calculus formulas to work to integrate by parts.","item_vector":null},"titleHighlight":null,"descriptionHighlights":null,"headers":null},{"objectType":"article","id":188471,"data":{"title":"Calculus: Techniques of Integration","slug":"calculus-techniques-of-integration","update_time":"2016-03-26T20:41:22+00:00","object_type":"article","image":null,"breadcrumbs":[{"name":"Academics & The Arts","slug":"academics-the-arts","categoryId":33662},{"name":"Math","slug":"math","categoryId":33720},{"name":"Calculus","slug":"calculus","categoryId":33723}],"description":"You'll find that there are many ways to solve an integration problem in calculus. The following list contains some handy points to remember when using different integration techniques:\n\n Guess and Check. This technique works when the integrand is close to a simple backward derivative.\n \n u-substitution. The integration counterpart to the chain rule; use this technique when the argument of the function you're integrating is more than a simple x.\n \n Integration by Parts. Integration's counterpart to the product rule.\n1. Use this technique when the integrand contains a product of functions.\n2. Pick your u according to LIATE, box it, \"7\" it, finish it.\n \n Trig Integrals\n1. Use Pythagorean identities.\n\n2. Use half-angle formulas.\n\n \n Trigonometric Substitution. This method works when the integrand contains radicals of the forms\n\n (or powers of these roots), where a is a constant and u is an expression in x.\n\n \n Partial Fractions. This technique works for rational functions (one polynomial over another).\n\n \n","item_vector":null},"titleHighlight":null,"descriptionHighlights":null,"headers":null},{"objectType":"article","id":188542,"data":{"title":"How to Use Integration by Parts","slug":"how-to-use-integration-by-parts","update_time":"2016-03-26T20:41:57+00:00","object_type":"article","image":null,"breadcrumbs":[{"name":"Academics & The Arts","slug":"academics-the-arts","categoryId":33662},{"name":"Math","slug":"math","categoryId":33720},{"name":"Calculus","slug":"calculus","categoryId":33723}],"description":"When doing Calculus, the formula for integration by parts gives you the option to break down the product of two functions to its factors and integrate it in an altered form. 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If you’re stumped by any of them, full explanations of the solution techniques can be found in Calculus Workbook For Dummies, 2nd Edition, or Calculus For Dummies, 2nd Edition. \n\n \n\n \n \n\n \n \n\n \n \n\n \n \n\n \n \n\n \n \n\n \n \n\n \n \n\n \n \n\n \n\nHere are the answers to the quick integration problems:\n\n \n\n \n \n\n \n 100. (Did you use calculus for this? No need. 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Integrating by parts is a complicated calculus procedure. This video uses example problems to show you how to put the calculus formulas to work to integrate by parts. About This Article
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