MAT136H1 Lecture Notes - Product Rule
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MAT136H1 Full Course Notes
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Integration by parts is useful when the integral contains two seemingly different function that cannot further be simplified, so that: ( ) ( ) ( ) ( ) ( ) ( ) . This is after the form of the product rule. Assign simpler variables like ( ) and let ( ) , then by taking derivative of , ( ) and by taking the anti-derivative of , ( ). Evaluate the indefinite integral using integration by parts. The functions cannot be combined or simplified in any other way. So let since it gets simpler through derivation. And since this does not change much with derivation. For the second integral, integration by parts is needed again. Then plug into the form of integration by parts: . Plug into the first part of the answer: Therefore, the indefinite integral is evaluated as: .
