Integration by parts: Always use “LIATE”?

My student was trying out the following question that requires integration by parts:

\int{\cos {{(\ln x)}_{{}}}}dx

where she chose u=1,dv=\cos (\ln x). The reason was she interprets “1” as {{x}^{0}} which is under “A” of the LIATE method. Since “A” is before “T”, she chose to differentiate one instead and got stuck.

This is one reason why the topic of techniques of integration, especially by parts, requires some foresight. One should consider what happens to the working upon his / her choice for “u”. This example shows us that we should not learn techniques of integration by memorising formulas blindly.

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