Section 5.6: Integration by Parts

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Section 5.6 Integration by Parts

• Practice HW from Stewart Textbook
• (not to hand in)
• p. 398 1-23 odd, 29, 31

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Integration by Parts

• Integration by parts undoes the product rule of
• differentiation.
• Suppose the have two functions u and v.
• Differentiating the product of these two
  functions
• by the product rule gives

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• Integrating both sides with respect to x gives
• or
• Solving for gives the following integration by
  parts
• formula.

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Integration by Parts Formula

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• Example 1 Integrate .
• Solution

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• Example 2 Integrate
• Solution

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Repeated Use of Integration by Parts

• Example 3 Integrate
• Solution

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• Example 4 Integrate
• Solution

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• Example 5 Integrate
• Solution

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