ILATE order is for choosing which function to differentiate first — it stands for Inverse trig, Logarithmic, Algebraic, Trigonometric, Exponential. You take the one that comes earlier as "u" to differentiate.
I'm writing this on the back of a power bill envelope, because our tuition sir made us memorize it yesterday.
But honestly, when you're doing integration past midnight, with the rain dripping into the bucket next to your desk, you remember the roof repair cost comes before any exponential function in your personal priority list.
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