A common example of integration by parts used in many Calculus II classes has students compute

by integrating by parts *twice*, then rearranging terms to arrive at a solution. This technique is handy for many functions whose derivatives eventually repeat, that is, functions satisfying

for some integer *n* and some constant *c*. (Question: Is there a name for such functions? I feel like I should know this.) When does this technique fail?

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