Tabel integral: Perbedaan antara revisi
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Baris 46:
Rumus-rumus berikut hanya menyatakan dalam bentuk lain pernyataan-pernyataan dalam [[tabel turunan]].
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===Integrals with a singularity===
When there is a singularity in the function being integrated such that the antiderivative becomes undefined or at some point (the singularity), then ''C'' does not need to be the same on both sides of the singularity. The forms below normally assume the [[Cauchy principal value]] around a singularity in the value of ''C'' but this is not in general necessary. For instance in
::<math>\int {1 \over x}\,dx = \ln \left|x \right| + C</math>
there is a singularity at 0 and the antiderivative becomes infinite there. If the integral above would be used to compute a definite integral between -1 and 1, one would get the wrong answer 0. This however is the Cauchy principal value of the integral around the singularity. If the integration is done in the complex plane the result depends on the path around the origin, in this case the singularity contributes −''i''{{pi}} when using a path above the origin and ''i''{{pi}} for a path below the origin. A function on the real line could use a completely different value of ''C'' on either side of the origin as in:
: <math> \int {1 \over x}\,dx = \ln|x| + \begin{cases} A & \text{if }x>0; \\ B & \text{if }x < 0. \end{cases} </math>
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=== Fungsi rasional ===
{{main|Daftar integral dari fungsi rasional}}
Baris 105 ⟶ 113:
: <math>\int \operatorname{arsech}\,x \, dx = x \operatorname{arsech} x- \arctan{\left(\frac{x}{x-1}\sqrt{\frac{1-x}{1+x}}\right)} + C</math>
: <math>\int \operatorname{arcoth} \, dx = x \operatorname{arcoth} x+ \frac{1}{2}\log{(x^2-1)} + C</math>
"[[Sophomore's dream]]"
:<math>\begin{align}
\int_0^1 x^{-x}\,dx &= \sum_{n=1}^\infty n^{-n} &&(= 1.29128599706266\dots)\\
\int_0^1 x^x \,dx &= -\sum_{n=1}^\infty (-n)^{-n} &&(= 0.78343051071213\dots)
\end{align}</math>
diyakini berasal dari [[Johann Bernoulli]].
== Lihat pula ==
* [[Integral]]
* [[Kalkulus]]
* [[Incomplete gamma function]]
* [[Indefinite sum]]
* [[List of limits]]
* [[List of mathematical series]]
* [[Symbolic integration]]
{{Lists of integrals}}
== Referensi ==
{{reflist}}
== Pustaka ==
* [[Milton Abramowitz|M. Abramowitz]] and [[Irene Stegun|I.A. Stegun]], editors. ''[[Abramowitz and Stegun|Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables]]''.
* I.S. Gradshteyn (И.С. Градштейн), I.M. Ryzhik (И.М. Рыжик); Alan Jeffrey, Daniel Zwillinger, editors. ''Table of Integrals, Series, and Products'', seventh edition. Academic Press, 2007. ISBN 978-0-12-373637-6. [http://www.mathtable.com/gr Errata.] ''(Several previous editions as well.)''
* A.P. Prudnikov (А.П. Прудников), Yu.A. Brychkov (Ю.А. Брычков), O.I. Marichev (О.И. Маричев). ''Integrals and Series''. First edition (Russian), volume 1–5, [[Nauka (publisher)|Nauka]], 1981−1986. First edition (English, translated from the Russian by N.M. Queen), volume 1–5, Gordon & Breach Science Publishers/[[CRC Press]], 1988–1992, ISBN 2-88124-097-6. Second revised edition (Russian), volume 1–3, Fiziko-Matematicheskaya Literatura, 2003.
* Yu.A. Brychkov (Ю.А. Брычков), ''Handbook of Special Functions: Derivatives, Integrals, Series and Other Formulas''. Russian edition, Fiziko-Matematicheskaya Literatura, 2006. English edition, Chapman & Hall/CRC Press, 2008, ISBN 1-58488-956-X.
* Daniel Zwillinger. ''CRC Standard Mathematical Tables and Formulae'', 31st edition. Chapman & Hall/CRC Press, 2002. ISBN 1-58488-291-3. ''(Many earlier editions as well.)''
=== Sejarah ===
* Meyer Hirsch, [http://books.google.com/books?id=Cdg2AAAAMAAJ Integraltafeln, oder, Sammlung von Integralformeln] (Duncker und Humblot, Berlin, 1810)
* Meyer Hirsch, [http://books.google.com/books?id=NsI2AAAAMAAJ Integral Tables, Or, A Collection of Integral Formulae] (Baynes and son, London, 1823) [English translation of ''Integraltafeln'']
* David Bierens de Haan, [http://www.archive.org/details/nouvetaintegral00haanrich Nouvelles Tables d'Intégrales définies] (Engels, Leiden, 1862)
* Benjamin O. Pierce [http://books.google.com/books?id=pYMRAAAAYAAJ A short table of integrals - revised edition] (Ginn & co., Boston, 1899)
== Pranala luar ==
=== Tabel integral ===
* [http://tutorial.math.lamar.edu/pdf/Common_Derivatives_Integrals.pdf Paul's Online Math Notes]
* A. Dieckmann, Table of Integrals (Elliptic Functions, Square Roots, Inverse Tangents and More Exotic Functions): [http://pi.physik.uni-bonn.de/~dieckman/IntegralsIndefinite/IndefInt.html Indefinite Integrals] [http://pi.physik.uni-bonn.de/~dieckman/IntegralsDefinite/DefInt.html Definite Integrals]
* [http://mathmajor.org/calculus-and-analysis/table-of-integrals/ Math Major: A Table of Integrals]
* {{cite web | last1=O'Brien |first1=Francis J. Jr. | url=http://www.docstoc.com/docs/23969109/500-Integrals-of-Elementary-and-Special-Functions |title=500 Integrals}} Derived integrals of exponential and logarithmic functions
* [http://www.apmaths.uwo.ca/RuleBasedMathematics/index.html Rule-based Mathematics] Precisely defined indefinite integration rules covering a wide class of integrands
* {{cite arxiv| first1= Richard J. | last1=Mathar | title=Yet another table of integrals | eprint=1207.5845 |year=2012}}
=== Derivasi ===
* [http://www.math.tulane.edu/~vhm/Table.html V. H. Moll, The Integrals in Gradshteyn and Ryzhik]
=== Layanan Online ===
* [http://www.wolframalpha.com/examples/Integrals.html Integration examples for Wolfram Alpha]
=== Program open source ===
*[http://wxmaxima.sourceforge.net/wiki/index.php/Main_Page wxmaxima gui for Symbolic and numeric resolution of many mathematical problems]
[[Category:Integrals|*]]
[[Category:Mathematics-related lists|Integrals]]
[[Category:Mathematical tables|Integrals]]
[[Kategori:Kalkulus]]
[[Kategori:Integral|Integral]]
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