Owl: Sometimes the antiderivative refuses to look like a table entry. Then we operate: a substitution that absorbs a chain-rule factor, integration by parts that trades one product for a friendlier one, or partial fractions that dismantle a rational function.
When the antiderivative isn't obvious, what surgery makes it obvious?
Pattern recognition comes first — not a blind rule that "parts is always first." And with u-substitution, the differential must transform too.
We'll recognize a pattern, execute a method, and always check by differentiating.