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## TECHNIQUES OF INTEGRATION

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**TECHNIQUES OF**INTEGRATION In this chapter we develop techniques for using these basic integration formulas to obtain indefinite integrals of more complicated functions.**INTEGRATION BY PARTS**formula for integration by parts. Example Example Find Find**INTEGRATION BY PARTS**formula for integration by parts. REMARK1: aim in using integration by parts is to obtain a simpler integral than the one we started with. REMARK2: How to choose u and dv to obtain simpler integral Example Find**INTEGRATION BY PARTS**Example REMARK2: in some integral, we may need to apply integration by parts many times. Find**INTEGRATION BY PARTS**Example REMARK2: in some integral, we may need to apply integration by parts many times. Find Example Find Example Find**INTEGRATION BY PARTS**formula for integration by parts. Example Find REMARK3: sometimes a repeated application of integration by parts leads back to an integral similar to our original one. If so, this expression can be combined with original integral.**INTEGRATION BY PARTS**Exam2 Term082 Exam2 Term102**Exam2**Term092**INTEGRATION BY PARTS**Observe: Reduction Formula REMARK3: sometimes The reduction formula is useful because by using it repeatedly we could eventually express our integral.**INTEGRATION BY PARTS**Reduction Formula Example Example**INTEGRATION BY PARTS**Reduction Formula Example Example Reduction Formula**INTEGRATION BY PARTS**Most of the time ln(x) is easier by parts Reduction Formula Integration by Parts Repeated Applications Term 0 (diff) tabular integration Back to original