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July 18th, 2009, 05:20 AM   #1
 
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Integration by Parts ... the LIATE heuristic

When you apply integration by parts, there is usually a choice of what to call u and what to call dv. The "LIATE" heuristic provides a suggestion of how to do that. It doesn't always work, but it works so often that it is worth remembering and using it as the first attempt.

LIATE stands for:
Logarithmic
Inverse trigonometric
Algebraic
Trigonometric
Exponential

The heuristic says: when there are two factors in the integrand, choose u as the one furthest to the left in LIATE and choose dv as the one furthest to the right.

Example... ... Here is algebraic, is exponential. So use

... Here is algebraic, is logarithmic. So use

Try this...
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