Ah, the ILATE order is a fine helper for choosing which function to differentiate when integrating by parts: Inverse, Logarithmic, Algebraic, Trigonometric, Exponential. One starts differentiating from the top of that list. But I must say, in practice, the heart of the problem often reveals itself better than any list. This reminds me of my son, who follows all the modern business rules for our shop, yet it is the old stories shared over *chai* on the bench that truly teach him what to keep and what to let go.
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