Integration By Parts: Meaning, Notation, and Example
Reverses the product rule for integration.
Definition and meaning
Choose u so differentiation simplifies it and dv so it can be integrated cleanly.
The term integration by parts names a precise mathematical idea, not merely a visual pattern. Read its notation as a statement with hypotheses, quantities, and a conclusion.
Notation
Read every symbol with its domain and hypotheses; notation compresses an argument but does not remove its conditions.
Worked example
Identify the quantities in the notation, state the relevant hypothesis, and explain what conclusion the integration by parts statement permits.
Common confusion
Do not treat integration by parts as a keyword that automatically selects a formula; its hypotheses and domain still control the conclusion.