Section 7.2 Integration by Parts

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Section 7.2Integration by Parts
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• Consider the function
• Use substitution to find the antiderivative
• Let u x2, u 2 x
• Consider the function
• We cant use substitution
• Let u x, but u 1 ? x
• Use the product rule to integrate by part

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• While integration by substitution is based on the
  chain rule, integration by parts is based on the
  product rule
• We know
• So integrate both sides and get
• After switching things around we get

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Integration by parts
Even more complex!

• How to choose u and v
• Easy to find the antiderivative of v
• u is not more complicated than u
• v is not more complicated than v

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Exchange u and v, and compare the results
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