This concept covers the strategy for choosing which factor to designate as u and which as v' (v-prime) when applying integration by parts, within single-variable calculus integration techniques. The general principle is to choose u such that differentiating it simplifies the expression (e.g., reduces a power, eliminates a transcendental function whose derivative is algebraic) and to choose v' such that it remains readily integrable, sometimes requiring an integrand to be split or rewritten (or treated as a product with 1) in a non-obvious way to enable the method. This formalizes the integration-by-parts formula as the product-rule analog for integration, and situates the selection heuristic within the broader toolkit of integration techniques (substitution, algebraic manipulation).
This concept covers the strategy for choosing which factor to designate as u and which as v' (v-prime) when applying integration by parts, within single-variable calculus integration techniques. The …