Discussion
One of these four statements about integration by parts fails. Which is it?
Answer: A
Parts rewrites \( \int u\,dv \) as \( uv - \int v\,du \), which is only an improvement if the new integral is simpler; a poor choice of factors makes it worse, which is why ILATE exists. That it comes from the product rule, that the choice matters, and that repetition is often needed are all correct
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