[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2pl\/wiki27\/tabela-primisives-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2pl\/wiki27\/tabela-primisives-wikipedia\/","headline":"Tabela Primisives – Wikipedia","name":"Tabela Primisives – Wikipedia","description":"before-content-x4 Artyku\u0142 w Wikipedii, Free L’Encyclop\u00e9i. after-content-x4 Obliczenie prymitywny Funkcja jest jedn\u0105 z dw\u00f3ch podstawowych operacji analizy, a poniewa\u017c operacja","datePublished":"2019-05-15","dateModified":"2019-05-15","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2pl\/wiki27\/author\/lordneo\/#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2pl\/wiki27\/author\/lordneo\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/e40873840318b1117d28117841282ac1e2d1d01b","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/e40873840318b1117d28117841282ac1e2d1d01b","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2pl\/wiki27\/tabela-primisives-wikipedia\/","wordCount":7278,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4Artyku\u0142 w Wikipedii, Free L’Encyclop\u00e9i.        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4Obliczenie prymitywny Funkcja jest jedn\u0105 z dw\u00f3ch podstawowych operacji analizy, a poniewa\u017c operacja ta jest delikatna, w przeciwie\u0144stwie do wyprowadzania, znane tabele prymitywne s\u0105 cz\u0119sto przydatne. Wiemy, \u017ce ci\u0105g\u0142a funkcja w przedziale przyznaje niesko\u0144czono\u015b\u0107 prymityw\u00f3w i \u017ce te prymitywy r\u00f3\u017cni\u0105 si\u0119 od sta\u0142ej; Wyznaczamy przez C A dowolna sta\u0142a kt\u00f3re mo\u017cna ustali\u0107 tylko wtedy, gdy znamy warto\u015b\u0107 prymitywnego w jednym punkcie.        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u222b F ( X ) D X {DisplayStyle int f (x), Mathrm {d} x} – nazywany nieokre\u015blon\u0105 ca\u0142k\u0105 F – wyznacza wszystkie prymitywy funkcji F do sta\u0142ej addytywnej.   Liniowo\u015b\u0107: \u222b (af(x)+bg(x))dX = a\u222b f(x)dX + b\u222b g(x)dX {displayStyle int lewy ({color {blue} a}, {color {blue} f (x)}+{color {blue} b}, {color {blue} g (x)} right) mathrm {d} x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x = x =} {color {blue} a} int {color {blue} f (x)}, mathrm {d} x+{color {blue} b} int {color {blue} g (x)}, mathrm {d} x} Zwi\u0105zek Chasles: \u222bacF ( X ) dX = \u222babF ( X ) dX + \u222bbcF ( X ) dX {displayStyle int _ {a}^{c} f (x), mathrm {d} x = int _ {a}^{color {blue} b} f (x), mathrm {d} x+int _ {kolorowy kolor {kolorowy {blue} b}^{c} f (x), Mathrm {d} x} a szczeg\u00f3lnie : \u222babF ( X ) dX = \u2212\u222bbaF ( X ) dX {displayStyle int _ {color {blue} a}^{color {blue} b} f (x), mathrm {d} x = {color {blue}-} int _ {color {blue} b}^{color {color {color { Blue} a} f (x), mathrm {d} x} Integracja przez cz\u0119\u015bci: \u222b f(x)g\u2032(x)dX = [[[ f(x)g(x)] – \u222b f\u2032(x)g(x)dX {displayStyle int {color {blue} f (x)}, {color {blue} g ‘(x)}, mathrm {d} x = [{color {blue} f (x)}, {color {blue} g (x)}]-int {color {blue} f ‘(x)}, {color {blue} g (x)}, mathrm {d} x} MEDIU MEMOTECHNICAL: \u222b uv\u2032= [[[ uv]  – \u222b u\u2032v{displayStyle int {color {blue} u} {color {blue} v ‘} = [{color {blue} u} {color {blue} v}] -int {color {blue} u’} {color {blue}} v}} z        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4W = F ( X ) W  W \u2032 = F \u2032 ( X ) W  W = G ( X ) W  W \u2032 = G \u2032 ( X ) {DisplayStyle u = f (x), ~ u ‘= f’ (x), ~ v = g (x), ~ v ‘= g’ (x)} I D X domniemany. Integracja przez zmian\u0119 zmiennej (je\u015bli F I Phi ‘ s\u0105 ci\u0105g\u0142e): \u222babF ( \u03c6(t)) \u03c6\u2032(t)dt= \u222b\u03c6(a)\u03c6(b)F ( x) dx{displayStyle int _ {a}^{b} f ({color {blue} varphi (t)}), {color {blue} varphi ‘(t)}, mathrm {d} {color {blue} t} = int int int int int int int int int int int int int int int} = int int int int} = int int int} = int _ {color {blue} varphi (a)}^{color {blue} varphi (b)} f ({color {blue} x}), mathrm {d} {color {blue} x}} . \u222b dX = X + C \u2200 X \u2208 R{DisplayStyle int, Mathrm {d} x = x+cqquad forall xin mathbb {r}} Table of ContentsPrymitywy racjonalnych funkcji [[[ modyfikator |. Modyfikator i kod ] Prymitywy funkcji logarytm\u00f3w [[[ modyfikator |. Modyfikator i kod ] Prymitywy funkcji wyk\u0142adniczych [[[ modyfikator |. Modyfikator i kod ] Prymitywy funkcji irracjonalnych [[[ modyfikator |. Modyfikator i kod ] Prymitywy funkcji trygonometrycznych [[[ modyfikator |. Modyfikator i kod ] Prymitywy funkcji hiperbolicznych [[[ modyfikator |. Modyfikator i kod ] Prymitywy wzajemnych funkcji ko\u0142owych [[[ modyfikator |. Modyfikator i kod ] Prymitywy wzajemnych funkcji hiperbolicznych [[[ modyfikator |. Modyfikator i kod ] Bibliografia [[[ modyfikator |. Modyfikator i kod ] Powi\u0105zane artyku\u0142y [[[ modyfikator |. Modyfikator i kod ] Link zewn\u0119trzny [[[ modyfikator |. Modyfikator i kod ] Prymitywy racjonalnych funkcji [[[ modyfikator |. Modyfikator i kod ] \u222b xndX = xn+1n+1+ C \u00a0si\u00a0N \u2260 – Pierwszy {DisplayStyle int x^{n}, Mathrm {d} x = {frac {x^{n+1}} {n+1}}+cqquad {si}} nneq -1} \u222b 1xdX = Ln \u2061 |x|+ C \u00a0si\u00a0X \u2260 0 {DisplayStyle int {frac {1} {x}}, mathrm {d} x = ln lewy | xright |+cqquad {text {si}} xneq 0} \u222b 1x\u2212adX = Ln \u2061 |X – A |+ C \u00a0si\u00a0X \u2260 A {displayStyle int {frac {1} {x-a}}, mathrm {d} x = ln | x-a |+cqquad {text {si}} xneq a} \u222b 1(x\u2212a)ndX = – 1(n\u22121)(x\u2212a)n\u22121+ C \u00a0si\u00a0N \u2260 Pierwszy \u00a0et\u00a0X \u2260 A {displayStyle int {frac {1} {(x-a)^{n}}}, mathrm {d} x =-{frac {1} {(n-1) (x-a)^{n-1}}}+cqquad {text {si}} nneq 1 {text {et}} xneq a} \u222b 11+x2dX = Arctan \u2061 X + C \u2200 X \u2208 R{DisplayStyle int {frac {1} {1+x^{2}}}, mathrm {d} x = operatorname {arctan} x+cqquad forall xin mathbb {r}} \u222b 1a2+x2dX = 1aArctan \u2061 xa+ C \u00a0si\u00a0A \u2260 0 {displayStyle int {frac {1} {a^{2}+x^{2}}}, mathrm {d} x = {frac {1} {a}} operatorname {arctan} {frac {x} {a} {a} }+Cqquad {text {si}} aneq 0} \u222b 11\u2212x2dX = 12Ln \u2061 |x+1x\u22121|+ C = {artanh\u2061x+C\u00a0sur\u00a0]\u22121,1[arcoth\u2061x+C\u00a0sur\u00a0]\u2212\u221e,\u22121[\u00a0et sur\u00a0]1,+\u221e[.{DisplayStyle int {frac {1} {1-x^{2}}}, mathrm {d} x = {frac {1} {2}} ln {left | {frac {x+1} {x-1} } right |}+c = {start {cases} operatorname {artanh} x+c & {text {sur}}]-1,1 [\\ operatorname {arcoth} x+c & {sur {sur}}]-infty,- 1 [{text {et sur}}] 1,+infty [.end {case}}} Prymitywy funkcji logarytm\u00f3w [[[ modyfikator |. Modyfikator i kod ] \u2200 X \u2208 R+\u2217{DisplayStyle forall xin Mathbb {r} _ {+}^{*}} \u222b Ln \u2061 X dX = X Ln \u2061 X – X + C {DisplayStyle int ln x, Mathrm {d} x = xln x-x+c} Bardziej og\u00f3lnie, prymitywny N -th of Ln {DisplayStyle ln} Wsch\u00f3d : xnn!(ln\u2061x\u2212\u2211k=1n1k){displayStyle {frac {x^{n}} {n!}} lewy (ln x-suum _ {k = 1}^{n} {frac {1} {k}} po prawej)} . Prymitywy funkcji wyk\u0142adniczych [[[ modyfikator |. Modyfikator i kod ] \u2200 X \u2208 R{DisplayStyle forall xin Mathbb {r}} \u222b eaxD X = 1aeax+ C {DisplayStyle int e^{ax}, dx = {frac {1} {a}} e^{ax}+c} \u222b f\u2032( X ) ef(x)D X = ef(x)+ C {DisplayStyle int f ‘(x) e^{f (x)}, dx = e^{f (x)}+c} "},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2pl\/wiki27\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2pl\/wiki27\/tabela-primisives-wikipedia\/#breadcrumbitem","name":"Tabela Primisives – Wikipedia"}}]}]