{"id":46,"date":"2021-03-25T02:20:44","date_gmt":"2021-03-25T02:20:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/calculus2\/chapter\/integration-by-parts\/"},"modified":"2021-11-17T02:23:31","modified_gmt":"2021-11-17T02:23:31","slug":"integration-by-parts","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/calculus2\/chapter\/integration-by-parts\/","title":{"raw":"Introduction to Integration by Parts","rendered":"Introduction to Integration by Parts"},"content":{"raw":"

By now we have a fairly thorough procedure for how to evaluate many basic integrals. However, although we can integrate [latex]\\displaystyle\\int x\\sin\\left({x}^{2}\\right)dx[\/latex] by using the substitution, [latex]u={x}^{2}[\/latex], something as simple looking as [latex]\\displaystyle\\int x\\sin{x}dx[\/latex] defies us. Many students want to know whether there is a product rule for integration. There isn\u2019t, but there is a technique based on the product rule for differentiation that allows us to exchange one integral for another. We call this technique integration by parts<\/span>.<\/p>","rendered":"

By now we have a fairly thorough procedure for how to evaluate many basic integrals. However, although we can integrate [latex]\\displaystyle\\int x\\sin\\left({x}^{2}\\right)dx[\/latex] by using the substitution, [latex]u={x}^{2}[\/latex], something as simple looking as [latex]\\displaystyle\\int x\\sin{x}dx[\/latex] defies us. Many students want to know whether there is a product rule for integration. There isn\u2019t, but there is a technique based on the product rule for differentiation that allows us to exchange one integral for another. We call this technique integration by parts<\/span>.<\/p>\n\n\t\t\t

\n\t\t\t

Candela Citations<\/h3>\n\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t\t
CC licensed content, Shared previously<\/div>