Integralglied

Integralglied is a term that appears in the context of integral calculus, specifically when discussing the process of integration by parts. It refers to the term that remains after performing one step of the integration by parts formula. The integration by parts formula is derived from the product rule for differentiation and is stated as: ∫ u dv = uv - ∫ v du. In this formula, ∫ u dv is the integral we want to evaluate. The term uv is the "first part" of the result, and ∫ v du is the remaining integral that still needs to be evaluated. This remaining integral, ∫ v du, is referred to as the integralglied or the integral part. The goal of integration by parts is to choose u and dv such that the new integral, ∫ v du, is simpler to solve than the original integral, ∫ u dv. Often, ∫ v du will be an integral that can be solved directly or by further application of integration by parts. The effectiveness of integration by parts hinges on making a judicious choice for u and dv to simplify the integralglied.