Difference between revisions of "Integration by parts"
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Revision as of 01:00, 11 July 2006
The purpose of integration by parts is to replace a difficult integral with an easier one. The formula is
Now, given an integrand, what should be u and what should be dv? Since u will show up as du and dv as v in the integral on the RHS, u should be chosen such that it has an "easy" (or "easier") derivative and dv so that it has a easy antiderivative.
A mnemonic for when to substitute u for what is LIATE:
If any two of these types of functions are in the function to be integrated, the type higher on the list should be substituted as u.
x has a pretty simple derivative, so let's say . Then , , and . We have
. You can take the derivative to see that it is indeed our desired result.