Integration by Parts/Also presented as
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Integration by Parts: Also presented as
Integration by Parts is often seen presented in this sort of form:
- $\ds \int u \frac {\d v} {\d x} \rd x = u v - \int v \frac {\d u} {\d x} \rd x$
or:
- $\ds \int u \rd v = u v - \int v \rd u$
where it is understood that $u$ and $v$ are functions of the independent variable.
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text {II}$. Calculus: Integration: Integration by Parts
- 1960: Margaret M. Gow: A Course in Pure Mathematics ... (previous) ... (next): Chapter $10$: Integration: $10.4$. Standard integrals: General Rules: $\text {VI}$.
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of Mathematical Functions ... (previous) ... (next): $3$: Elementary Analytic Methods: $3.3$ Rules for Differentiation and Integration: Integration by Parts: $3.3.12$
- 1967: Michael Spivak: Calculus ... (previous) ... (next): Part $\text {III}$: Derivatives and Integrals: Chapter $18$: Integration in Elementary Terms: Theorem $1$ (Integration by Parts)
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 14$: General Rules of Integration: $14.4$
- 1968: George B. Thomas, Jr.: Calculus and Analytic Geometry (4th ed.) ... (next): Front endpapers: A Brief Table of Integrals: $1$.
- 1971: Wilfred Kaplan and Donald J. Lewis: Calculus and Linear Algebra ... (previous) ... (next): Appendix $\text I$: Table of Indefinite Integrals $4$.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): integration by parts
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Appendix: Table $2$: Integrals
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): integration by parts
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Appendix: Table $2$: Integrals