MATH 2B Study Guide - Midterm Guide: Product RulePremium
Course CodeMATH 2B
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Section 7.1 - Integration by Parts
What is the derivative of ()()?
●(()()) = ()() + ()()
●This kind of answer is difficult to see if you want to take the integral of something
●How can we rewrite it?
○First take the integral
■ The integral of the left side is the same as ()()
()() = ()()
●What does this mean?
○Replacing () , () , you can get this formula
○This is integration by parts
○ = , which means that = 1
■ From the integral, replace with which parts look easiest to derive
○ = , then =
■ From the integral, replace with which parts look easiest to integrate
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How do we know which to set to and which to set to ?
●Going down the list means that it is easier to take the integral of
○In other words, logs are the easiest to take the derivative of while exponentials
are the easiest to take the integral of
○ = , so = 1
○ = (2), so =
■ Here, we have to use substitution to further integrate
■ = 2, (
■ Plug in ,,
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