7.1 Integration by Parts Review the integrals shown on page 469 and integration by substitution. Examples: 1( )( )(sin)(cos)xxeeadxbxx+∫∫dxRemember - integration is done by various techniques and is not as straightforward as differentiation. Typically, selecting the proper technique is the most difficult aspect of integration. Large numbers of practice problems is the best solution to the difficulty you may encounter. The integration rule that corresponds to the product rule for differentiation is integration by parts. INTEGRATION BY PARTS. u dvuvv du=−∫∫OBJECT:select a substitution that yields a simplerintegral. GENERALLY:select u = f(x)to be a function that becomes simpler when differentiated (or at least not more complicated). Examples (Note Example 2 on page 471) ( )cos( )xaxx dbxe dx
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