İnteqral — Vikipediya

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href="/w/index.php?title=%C4%B0nteqral&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Vikipediya (az)"> <link rel="EditURI" type="application/rsd+xml" href="//az.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://az.wikipedia.org/wiki/%C4%B0nteqral"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.az"> <link rel="alternate" type="application/atom+xml" title="Vikipediya — Atom-lent" href="/w/index.php?title=X%C3%BCsusi:SonD%C9%99yi%C5%9Fiklikl%C9%99r&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin-vector-legacy mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-İnteqral rootpage-İnteqral skin-vector action-view"><div id="mw-page-base" class="noprint"></div> <div id="mw-head-base" class="noprint"></div> <div id="content" class="mw-body" role="main"> <a id="top"></a> <div id="siteNotice"></div> <div class="mw-indicators"> </div> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">İnteqral</span></h1> <div id="bodyContent" class="vector-body"> <div id="siteSub" class="noprint">Vikipediya, azad ensiklopediya</div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="contentSub2"></div> <div id="jump-to-nav"></div> <a class="mw-jump-link" href="#mw-head">Naviqasiyaya keç</a> <a class="mw-jump-link" href="#searchInput">Axtarışa keç</a> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="az" dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/Fayl:Integral_as_region_under_curve.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Integral_as_region_under_curve.png/234px-Integral_as_region_under_curve.png" decoding="async" width="234" height="205" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Integral_as_region_under_curve.png/351px-Integral_as_region_under_curve.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/90/Integral_as_region_under_curve.png/468px-Integral_as_region_under_curve.png 2x" data-file-width="782" data-file-height="685" /></a><figcaption>f(x)-in a dan b'yə qədər olan inteqralı, y=f(x) funksiyasının a ilə b arasındakı fiqurun sahәsinә bәrabәrdir.</figcaption></figure> <p><b>İnteqral</b> – kəsilməz <i>f(x)</i> <a href="/wiki/Funksiya" class="mw-disambig" title="Funksiya">funksiyasının</a> ibtidai funksiyalarının ümumi şəklinə <i>f(x)</i> funksiyasının <b>inteqralı</b> deyilir. </p> <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none" /><div class="toctitle" lang="az" dir="ltr"><h2 id="mw-toc-heading">Mündəricat</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#Tarixi"><span class="tocnumber">1</span> <span class="toctext">Tarixi</span></a></li> <li class="toclevel-1 tocsection-2"><a href="#İnteqral_hesabına_aid_nümunə"><span class="tocnumber">2</span> <span class="toctext">İnteqral hesabına aid nümunə</span></a></li> <li class="toclevel-1 tocsection-3"><a href="#Bəsit_funksiyaların_inteqralları"><span class="tocnumber">3</span> <span class="toctext">Bəsit funksiyaların inteqralları</span></a> <ul> <li class="toclevel-2 tocsection-4"><a href="#Rasional_funksiyalar"><span class="tocnumber">3.1</span> <span class="toctext">Rasional funksiyalar</span></a></li> <li class="toclevel-2 tocsection-5"><a href="#İrrasional_funksiyalar"><span class="tocnumber">3.2</span> <span class="toctext">İrrasional funksiyalar</span></a></li> <li class="toclevel-2 tocsection-6"><a href="#Loqarifmik_funksiyalar"><span class="tocnumber">3.3</span> <span class="toctext">Loqarifmik funksiyalar</span></a></li> <li class="toclevel-2 tocsection-7"><a href="#Üstlü_funksiyalar"><span class="tocnumber">3.4</span> <span class="toctext">Üstlü funksiyalar</span></a></li> <li class="toclevel-2 tocsection-8"><a href="#Triqonometrik_funksiyalar"><span class="tocnumber">3.5</span> <span class="toctext">Triqonometrik funksiyalar</span></a></li> <li class="toclevel-2 tocsection-9"><a href="#Hiperbolik_funksiyalar"><span class="tocnumber">3.6</span> <span class="toctext">Hiperbolik funksiyalar</span></a></li> <li class="toclevel-2 tocsection-10"><a href="#Tərs_hiperbolik_funksiyalar"><span class="tocnumber">3.7</span> <span class="toctext">Tərs hiperbolik funksiyalar</span></a></li> </ul> </li> <li class="toclevel-1 tocsection-11"><a href="#Xarici_keçidlər"><span class="tocnumber">4</span> <span class="toctext">Xarici keçidlər</span></a></li> </ul> </div> <div class="mw-heading mw-heading2"><h2 id="Tarixi">Tarixi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%B0nteqral&veaction=edit&section=1" title="Tarixi bölməsini redaktə et" class="mw-editsection-visualeditor"><span>redaktə</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%B0nteqral&action=edit&section=1" title="Bölmənin mənbə kodunu redaktə et: Tarixi"><span>mənbəni redaktə et</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>İnteqral sahəsində ən böyük işləri <a href="/wiki/Qotfrid_Leybnits" title="Qotfrid Leybnits">Qotfrid Leybnits</a> və <a href="/wiki/%C4%B0saak_Nyuton" title="İsaak Nyuton">İsaak Nyuton</a> görmüşlər. "İnteqral" sözünü və işarəsini ilk dəfə elmə alman alimi <a href="/wiki/Qotfrid_Leybnits" title="Qotfrid Leybnits">Qotfrid Leybnits</a> daxil etmişdir. Bu söz latıncadan "Cəm" ("ſumma", "summa") mənasını verir. İnteqral <b>∫</b> hərfi ilə işarə edilir: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F(x)=\int f(x)+c,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>∫</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>c</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(x)=\int f(x)+c,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a7733aaf6ff829ce229009e5b85f2014b37f410e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:19.471ex; height:5.676ex;" alt="{\displaystyle F(x)=\int f(x)+c,}"></span></dd></dl> <p>[a, b] parçasında götürülmüş <i>f(x)</i> funksiyasının müəyyən inteqralın düsturu belədir: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{a}^{b}\!f(x)\,dx\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mspace width="negativethinmathspace" /> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{a}^{b}\!f(x)\,dx\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b7e414cdf22f8da119c72c2ffddfcc8f1b3febf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.139ex; height:6.343ex;" alt="{\displaystyle \int _{a}^{b}\!f(x)\,dx\,}"></span></dd></dl> <p>Qeyri-müəyyən inteqralın isə düsturu belədir: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=\int f(x)\,dx+c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mo>∫</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>+</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=\int f(x)\,dx+c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b006f391e57e2456e78eb2860e2f700090ccd11f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:18.617ex; height:5.676ex;" alt="{\displaystyle F=\int f(x)\,dx+c}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="İnteqral_hesabına_aid_nümunə"><span id=".C4.B0nteqral_hesab.C4.B1na_aid_n.C3.BCmun.C9.99"></span>İnteqral hesabına aid nümunə</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%B0nteqral&veaction=edit&section=2" title="İnteqral hesabına aid nümunə bölməsini redaktə et" class="mw-editsection-visualeditor"><span>redaktə</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%B0nteqral&action=edit&section=2" title="Bölmənin mənbə kodunu redaktə et: İnteqral hesabına aid nümunə"><span>mənbəni redaktə et</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x)=5x^{2}+9x+15\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>5</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>9</mn> <mi>x</mi> <mo>+</mo> <mn>15</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)=5x^{2}+9x+15\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5845d747977cc3d23aa05617ac61defc061a1e07" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.947ex; height:3.176ex;" alt="{\displaystyle f(x)=5x^{2}+9x+15\,}"></span>.</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f'(x)=10x+9+0\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>10</mn> <mi>x</mi> <mo>+</mo> <mn>9</mn> <mo>+</mo> <mn>0</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f'(x)=10x+9+0\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09d73109fdd1c05a5235cc8962ba0c8a59dd11e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.29ex; height:3.009ex;" alt="{\displaystyle f'(x)=10x+9+0\,}"></span>.</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int (10x+9)\,dx=5x^{2}+9x+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mo stretchy="false">(</mo> <mn>10</mn> <mi>x</mi> <mo>+</mo> <mn>9</mn> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mn>5</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>9</mn> <mi>x</mi> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int (10x+9)\,dx=5x^{2}+9x+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0236e675c0949c74841eac7f33f0c69843d36c33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:31.177ex; height:5.676ex;" alt="{\displaystyle \int (10x+9)\,dx=5x^{2}+9x+C}"></span>.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Bəsit_funksiyaların_inteqralları"><span id="B.C9.99sit_funksiyalar.C4.B1n_inteqrallar.C4.B1"></span>Bəsit funksiyaların inteqralları</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%B0nteqral&veaction=edit&section=3" title="Bəsit funksiyaların inteqralları bölməsini redaktə et" class="mw-editsection-visualeditor"><span>redaktə</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%B0nteqral&action=edit&section=3" title="Bölmənin mənbə kodunu redaktə et: Bəsit funksiyaların inteqralları"><span>mənbəni redaktə et</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Rasional_funksiyalar">Rasional funksiyalar</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%B0nteqral&veaction=edit&section=4" title="Rasional funksiyalar bölməsini redaktə et" class="mw-editsection-visualeditor"><span>redaktə</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%B0nteqral&action=edit&section=4" title="Bölmənin mənbə kodunu redaktə et: Rasional funksiyalar"><span>mənbəni redaktə et</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int dx=x+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int dx=x+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6871c63878d57e21529e7055eb803323be89668f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.161ex; height:5.676ex;" alt="{\displaystyle \int dx=x+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {dx \over x}=\ln {\left|x\right|}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mi>x</mi> </mfrac> </mrow> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>|</mo> <mi>x</mi> <mo>|</mo> </mrow> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {dx \over x}=\ln {\left|x\right|}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/edb5ab1e32f9a2f75ba9e523693f3968bcec5da6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:18.617ex; height:5.843ex;" alt="{\displaystyle \int {dx \over x}=\ln {\left|x\right|}+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {dx \over {a^{2}+x^{2}}}={1 \over a}\arctan {x \over a}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>a</mi> </mfrac> </mrow> <mi>arctan</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mi>a</mi> </mfrac> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {dx \over {a^{2}+x^{2}}}={1 \over a}\arctan {x \over a}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0d3b35622824d182fcb81f2a04777f7687e1aed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:30.103ex; height:5.843ex;" alt="{\displaystyle \int {dx \over {a^{2}+x^{2}}}={1 \over a}\arctan {x \over a}+C}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="İrrasional_funksiyalar"><span id=".C4.B0rrasional_funksiyalar"></span>İrrasional funksiyalar</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%B0nteqral&veaction=edit&section=5" title="İrrasional funksiyalar bölməsini redaktə et" class="mw-editsection-visualeditor"><span>redaktə</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%B0nteqral&action=edit&section=5" title="Bölmənin mənbə kodunu redaktə et: İrrasional funksiyalar"><span>mənbəni redaktə et</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {dx \over {\sqrt {a^{2}-x^{2}}}}=\arcsin {x \over a}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>arcsin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mi>a</mi> </mfrac> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {dx \over {\sqrt {a^{2}-x^{2}}}}=\arcsin {x \over a}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5ad19eec79c1d490e5e93d51369b90119650921" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:29.469ex; height:6.676ex;" alt="{\displaystyle \int {dx \over {\sqrt {a^{2}-x^{2}}}}=\arcsin {x \over a}+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {-dx \over {\sqrt {a^{2}-x^{2}}}}=\arccos {x \over a}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo>−</mo> <mi>d</mi> <mi>x</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>arccos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mi>a</mi> </mfrac> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {-dx \over {\sqrt {a^{2}-x^{2}}}}=\arccos {x \over a}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c355f67efb240295f8e62bc906fe2f62eda4970" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:29.725ex; height:6.676ex;" alt="{\displaystyle \int {-dx \over {\sqrt {a^{2}-x^{2}}}}=\arccos {x \over a}+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {dx \over x{\sqrt {x^{2}-a^{2}}}}={1 \over a}\sec {|x| \over a}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>a</mi> </mfrac> </mrow> <mi>sec</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <mi>a</mi> </mfrac> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {dx \over x{\sqrt {x^{2}-a^{2}}}}={1 \over a}\sec {|x| \over a}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/284ebb56d2b9f4fa41d28ca48630074e27be4527" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:31.565ex; height:7.009ex;" alt="{\displaystyle \int {dx \over x{\sqrt {x^{2}-a^{2}}}}={1 \over a}\sec {|x| \over a}+C}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Loqarifmik_funksiyalar">Loqarifmik funksiyalar</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%B0nteqral&veaction=edit&section=6" title="Loqarifmik funksiyalar bölməsini redaktə et" class="mw-editsection-visualeditor"><span>redaktə</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%B0nteqral&action=edit&section=6" title="Bölmənin mənbə kodunu redaktə et: Loqarifmik funksiyalar"><span>mənbəni redaktə et</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \ln(x)\,dx=x\ln(x)-x+C,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mi>ln</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>x</mi> <mo>+</mo> <mi>C</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \ln(x)\,dx=x\ln(x)-x+C,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7a9303ea743652c5215449d013715062c956ae7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:29.909ex; height:5.676ex;" alt="{\displaystyle \int \ln(x)\,dx=x\ln(x)-x+C,}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \log _{b}{x}\,dx=x\log _{b}{x}-x\log _{b}{e}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>x</mi> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mo>−</mo> <mi>x</mi> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msub> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>e</mi> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \log _{b}{x}\,dx=x\log _{b}{x}-x\log _{b}{e}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7e25004a52b2a654b87396ddf2ff3fc8a5041f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:36.125ex; height:5.676ex;" alt="{\displaystyle \int \log _{b}{x}\,dx=x\log _{b}{x}-x\log _{b}{e}+C}"></span>:)</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Üstlü_funksiyalar"><span id=".C3.9Cstl.C3.BC_funksiyalar"></span>Üstlü funksiyalar</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%B0nteqral&veaction=edit&section=7" title="Üstlü funksiyalar bölməsini redaktə et" class="mw-editsection-visualeditor"><span>redaktə</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%B0nteqral&action=edit&section=7" title="Bölmənin mənbə kodunu redaktə et: Üstlü funksiyalar"><span>mənbəni redaktə et</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int e^{x}\,dx=e^{x}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int e^{x}\,dx=e^{x}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e6d31e8ad38cc40b4e3d18ad17b756efa483abd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:17.731ex; height:5.676ex;" alt="{\displaystyle \int e^{x}\,dx=e^{x}+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int a^{x}\,dx={\frac {a^{x}}{\ln {a}}}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msup> <mrow> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int a^{x}\,dx={\frac {a^{x}}{\ln {a}}}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/816dde2034e43093b2a85e3dcc1ef2f39779f860" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:20.013ex; height:5.676ex;" alt="{\displaystyle \int a^{x}\,dx={\frac {a^{x}}{\ln {a}}}+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int a^{ln(x)}\,dx=\int x^{ln(a)}\,dx={\frac {x\,a^{ln(x)}}{\ln {a}+1}}+C={\frac {x\,x^{ln(a)}}{\ln {a}+1}}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>n</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>∫</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>n</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>x</mi> <mspace width="thinmathspace" /> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>n</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mrow> <mrow> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>C</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>x</mi> <mspace width="thinmathspace" /> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>n</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mrow> <mrow> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int a^{ln(x)}\,dx=\int x^{ln(a)}\,dx={\frac {x\,a^{ln(x)}}{\ln {a}+1}}+C={\frac {x\,x^{ln(a)}}{\ln {a}+1}}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/662b1d3a3bd78cc42b684542e9e63fbb3944b6bb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:56.672ex; height:6.176ex;" alt="{\displaystyle \int a^{ln(x)}\,dx=\int x^{ln(a)}\,dx={\frac {x\,a^{ln(x)}}{\ln {a}+1}}+C={\frac {x\,x^{ln(a)}}{\ln {a}+1}}+C}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Triqonometrik_funksiyalar">Triqonometrik funksiyalar</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%B0nteqral&veaction=edit&section=8" title="Triqonometrik funksiyalar bölməsini redaktə et" class="mw-editsection-visualeditor"><span>redaktə</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%B0nteqral&action=edit&section=8" title="Bölmənin mənbə kodunu redaktə et: Triqonometrik funksiyalar"><span>mənbəni redaktə et</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fayl:Gottfried_Wilhelm_von_Leibniz.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Gottfried_Wilhelm_von_Leibniz.jpg/200px-Gottfried_Wilhelm_von_Leibniz.jpg" decoding="async" width="200" height="253" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Gottfried_Wilhelm_von_Leibniz.jpg/300px-Gottfried_Wilhelm_von_Leibniz.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/6/6a/Gottfried_Wilhelm_von_Leibniz.jpg 2x" data-file-width="316" data-file-height="400" /></a><figcaption><a href="/wiki/Qotfrid_Leybnits" title="Qotfrid Leybnits">Qotfrid Leybnits</a></figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fayl:Sir_Isaac_Newton_by_Sir_Godfrey_Kneller,_Bt.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Sir_Isaac_Newton_by_Sir_Godfrey_Kneller%2C_Bt.jpg/200px-Sir_Isaac_Newton_by_Sir_Godfrey_Kneller%2C_Bt.jpg" decoding="async" width="200" height="243" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Sir_Isaac_Newton_by_Sir_Godfrey_Kneller%2C_Bt.jpg/300px-Sir_Isaac_Newton_by_Sir_Godfrey_Kneller%2C_Bt.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/50/Sir_Isaac_Newton_by_Sir_Godfrey_Kneller%2C_Bt.jpg/400px-Sir_Isaac_Newton_by_Sir_Godfrey_Kneller%2C_Bt.jpg 2x" data-file-width="2400" data-file-height="2912" /></a><figcaption>Ser <a href="/wiki/%C4%B0saak_Nyuton" title="İsaak Nyuton">İsaak Nyuton</a></figcaption></figure> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \sin {x}\,dx=-\cos {x}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \sin {x}\,dx=-\cos {x}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/537de256cbb401203900fd3623cdbc85e31cc70b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:24.814ex; height:5.676ex;" alt="{\displaystyle \int \sin {x}\,dx=-\cos {x}+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \cos {x}\,dx=\sin {x}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \cos {x}\,dx=\sin {x}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e1aae2ec756513ea8f93deb874803c61e291dd8a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:22.619ex; height:5.676ex;" alt="{\displaystyle \int \cos {x}\,dx=\sin {x}+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \tan {x}\,dx=-\ln {\left|\cos {x}\right|}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>tan</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>|</mo> <mrow> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </mrow> <mo>|</mo> </mrow> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \tan {x}\,dx=-\ln {\left|\cos {x}\right|}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db65697f06c5abbe10e8ff7dbf78d1213439495f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:28.938ex; height:5.676ex;" alt="{\displaystyle \int \tan {x}\,dx=-\ln {\left|\cos {x}\right|}+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \cot {x}\,dx=\ln {\left|\sin {x}\right|}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>cot</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>|</mo> <mrow> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </mrow> <mo>|</mo> </mrow> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \cot {x}\,dx=\ln {\left|\sin {x}\right|}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a79422c3c1bc1b58e8a1623920b50fb4ff87f907" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:26.227ex; height:5.676ex;" alt="{\displaystyle \int \cot {x}\,dx=\ln {\left|\sin {x}\right|}+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \sec {x}\,dx=\ln {\left|\sec {x}+\tan {x}\right|}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>sec</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>|</mo> <mrow> <mi>sec</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mo>+</mo> <mi>tan</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </mrow> <mo>|</mo> </mrow> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \sec {x}\,dx=\ln {\left|\sec {x}+\tan {x}\right|}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/378b45f5cd66c9fb7560eb362481df12ce77fa51" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:34.151ex; height:5.676ex;" alt="{\displaystyle \int \sec {x}\,dx=\ln {\left|\sec {x}+\tan {x}\right|}+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \csc {x}\,dx=\ln {\left|\csc {x}-\cot {x}\right|}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>csc</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>|</mo> <mrow> <mi>csc</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mo>−</mo> <mi>cot</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </mrow> <mo>|</mo> </mrow> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \csc {x}\,dx=\ln {\left|\csc {x}-\cot {x}\right|}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/912b48f413446f1ea54ceeec71a2f7a4f6808e42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:33.891ex; height:5.676ex;" alt="{\displaystyle \int \csc {x}\,dx=\ln {\left|\csc {x}-\cot {x}\right|}+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \sec ^{2}x\,dx=\tan x+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <msup> <mi>sec</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>tan</mi> <mo>⁡</mo> <mi>x</mi> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \sec ^{2}x\,dx=\tan x+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f8fbfacf62d7130b7bf000e226b07f8c599bf1c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:24.047ex; height:5.676ex;" alt="{\displaystyle \int \sec ^{2}x\,dx=\tan x+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \csc ^{2}x\,dx=-\cot x+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <msup> <mi>csc</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mi>cot</mi> <mo>⁡</mo> <mi>x</mi> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \csc ^{2}x\,dx=-\cot x+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/364c3afec409bb6bfbb787276d7cfd884040b07a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:25.982ex; height:5.676ex;" alt="{\displaystyle \int \csc ^{2}x\,dx=-\cot x+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \sec {x}\,\tan {x}\,dx=\sec {x}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>sec</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mspace width="thinmathspace" /> <mi>tan</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>sec</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \sec {x}\,\tan {x}\,dx=\sec {x}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/385d180bf75e276f8b0cafb1fdc1f584554be54f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:28.465ex; height:5.676ex;" alt="{\displaystyle \int \sec {x}\,\tan {x}\,dx=\sec {x}+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \csc {x}\,\cot {x}\,dx=-\csc {x}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>csc</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mspace width="thinmathspace" /> <mi>cot</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mi>csc</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \csc {x}\,\cot {x}\,dx=-\csc {x}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/038c3e132b5c6826b7be055d24fa617842c493d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:30.4ex; height:5.676ex;" alt="{\displaystyle \int \csc {x}\,\cot {x}\,dx=-\csc {x}+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \sin ^{2}x\,dx={\frac {1}{2}}(x-\sin x\cos x)+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mi>x</mi> <mi>cos</mi> <mo>⁡</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \sin ^{2}x\,dx={\frac {1}{2}}(x-\sin x\cos x)+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f51b216b7c2533bf9ceb78b278f162070ccd2f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:36.611ex; height:5.676ex;" alt="{\displaystyle \int \sin ^{2}x\,dx={\frac {1}{2}}(x-\sin x\cos x)+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \cos ^{2}x\,dx={\frac {1}{2}}(x+\sin x\cos x)+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mi>sin</mi> <mo>⁡</mo> <mi>x</mi> <mi>cos</mi> <mo>⁡</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \cos ^{2}x\,dx={\frac {1}{2}}(x+\sin x\cos x)+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f423c27f97e0cac690bdb3e0faf09dea37772362" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:36.866ex; height:5.676ex;" alt="{\displaystyle \int \cos ^{2}x\,dx={\frac {1}{2}}(x+\sin x\cos x)+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \sec ^{3}x\,dx={\frac {1}{2}}\sec x\tan x+{\frac {1}{2}}\ln |\sec x+\tan x|+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <msup> <mi>sec</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>⁡</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>sec</mi> <mo>⁡</mo> <mi>x</mi> <mi>tan</mi> <mo>⁡</mo> <mi>x</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>sec</mi> <mo>⁡</mo> <mi>x</mi> <mo>+</mo> <mi>tan</mi> <mo>⁡</mo> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \sec ^{3}x\,dx={\frac {1}{2}}\sec x\tan x+{\frac {1}{2}}\ln |\sec x+\tan x|+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e685542d54058f2defcf20dad355de10535d8d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:53.366ex; height:5.676ex;" alt="{\displaystyle \int \sec ^{3}x\,dx={\frac {1}{2}}\sec x\tan x+{\frac {1}{2}}\ln |\sec x+\tan x|+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \sin ^{n}x\,dx=-{\frac {\sin ^{n-1}{x}\cos {x}}{n}}+{\frac {n-1}{n}}\int \sin ^{n-2}{x}\,dx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>⁡</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </mrow> <mi>n</mi> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> <mi>n</mi> </mfrac> </mrow> <mo>∫</mo> <msup> <mi>sin</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \sin ^{n}x\,dx=-{\frac {\sin ^{n-1}{x}\cos {x}}{n}}+{\frac {n-1}{n}}\int \sin ^{n-2}{x}\,dx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c15d560c4a9f07da5aa62b1adc435b6e785ea33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:53.019ex; height:6.176ex;" alt="{\displaystyle \int \sin ^{n}x\,dx=-{\frac {\sin ^{n-1}{x}\cos {x}}{n}}+{\frac {n-1}{n}}\int \sin ^{n-2}{x}\,dx}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \cos ^{n}x\,dx={\frac {\cos ^{n-1}{x}\sin {x}}{n}}+{\frac {n-1}{n}}\int \cos ^{n-2}{x}\,dx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>⁡</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </mrow> <mi>n</mi> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> <mi>n</mi> </mfrac> </mrow> <mo>∫</mo> <msup> <mi>cos</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \cos ^{n}x\,dx={\frac {\cos ^{n-1}{x}\sin {x}}{n}}+{\frac {n-1}{n}}\int \cos ^{n-2}{x}\,dx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/307e19c74642ddbed625e25265cb0ee59638d286" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:51.722ex; height:6.176ex;" alt="{\displaystyle \int \cos ^{n}x\,dx={\frac {\cos ^{n-1}{x}\sin {x}}{n}}+{\frac {n-1}{n}}\int \cos ^{n-2}{x}\,dx}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \arctan {x}\,dx=x\,\arctan {x}-{\frac {1}{2}}\ln {\left|1+x^{2}\right|}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>arctan</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mi>arctan</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>|</mo> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>|</mo> </mrow> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \arctan {x}\,dx=x\,\arctan {x}-{\frac {1}{2}}\ln {\left|1+x^{2}\right|}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cf3499100d93064704955a0addfbfaf2f9726b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:46.921ex; height:5.676ex;" alt="{\displaystyle \int \arctan {x}\,dx=x\,\arctan {x}-{\frac {1}{2}}\ln {\left|1+x^{2}\right|}+C}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Hiperbolik_funksiyalar">Hiperbolik funksiyalar</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%B0nteqral&veaction=edit&section=9" title="Hiperbolik funksiyalar bölməsini redaktə et" class="mw-editsection-visualeditor"><span>redaktə</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%B0nteqral&action=edit&section=9" title="Bölmənin mənbə kodunu redaktə et: Hiperbolik funksiyalar"><span>mənbəni redaktə et</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \sinh x\,dx=\,coshx+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>sinh</mi> <mo>⁡</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mspace width="thinmathspace" /> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>h</mi> <mi>x</mi> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \sinh x\,dx=\,coshx+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4737049586c07193cc0ab287b81b0ee80e101035" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:25.364ex; height:5.676ex;" alt="{\displaystyle \int \sinh x\,dx=\,coshx+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \cosh x\,dx=\sinh x+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>cosh</mi> <mo>⁡</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>sinh</mi> <mo>⁡</mo> <mi>x</mi> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \cosh x\,dx=\sinh x+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/529344aa89d4a7732c58734fa5134612b73aaa19" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:25.204ex; height:5.676ex;" alt="{\displaystyle \int \cosh x\,dx=\sinh x+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \tanh x\,dx=\ln |\cosh x|+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>tanh</mi> <mo>⁡</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>cosh</mi> <mo>⁡</mo> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \tanh x\,dx=\ln |\cosh x|+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e448d5b96361c98f3d0af72e0a9e860261bfe9d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:29.715ex; height:5.676ex;" alt="{\displaystyle \int \tanh x\,dx=\ln |\cosh x|+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\mbox{csch}}\,x\,dx=\ln \left|\tanh {x \over 2}\right|+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>csch</mtext> </mstyle> </mrow> <mspace width="thinmathspace" /> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mrow> <mo>|</mo> <mrow> <mi>tanh</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>|</mo> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\mbox{csch}}\,x\,dx=\ln \left|\tanh {x \over 2}\right|+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53e784b82203b2db8d3bb9435d677aa204705ef1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:29.647ex; height:5.676ex;" alt="{\displaystyle \int {\mbox{csch}}\,x\,dx=\ln \left|\tanh {x \over 2}\right|+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\mbox{sech}}\,x\,dx=\arctan(\sinh x)+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>sech</mtext> </mstyle> </mrow> <mspace width="thinmathspace" /> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>arctan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>sinh</mi> <mo>⁡</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\mbox{sech}}\,x\,dx=\arctan(\sinh x)+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cba1e31fd35b44ba1cd78d5ec48f68be1d5f7a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:33.349ex; height:5.676ex;" alt="{\displaystyle \int {\mbox{sech}}\,x\,dx=\arctan(\sinh x)+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \coth x\,dx=\ln |\sinh x|+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>coth</mi> <mo>⁡</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>sinh</mi> <mo>⁡</mo> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \coth x\,dx=\ln |\sinh x|+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd7bd1bfe08e160d8d488e245bd13c42a16c91d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:29.2ex; height:5.676ex;" alt="{\displaystyle \int \coth x\,dx=\ln |\sinh x|+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int {\mbox{sech}}^{2}x\,dx=\tanh x+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>sech</mtext> </mstyle> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>tanh</mi> <mo>⁡</mo> <mi>x</mi> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int {\mbox{sech}}^{2}x\,dx=\tanh x+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17999bca1d5255acc4b6955e067f2e3b0169f017" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:26.245ex; height:5.676ex;" alt="{\displaystyle \int {\mbox{sech}}^{2}x\,dx=\tanh x+C}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Tərs_hiperbolik_funksiyalar"><span id="T.C9.99rs_hiperbolik_funksiyalar"></span>Tərs hiperbolik funksiyalar</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%B0nteqral&veaction=edit&section=10" title="Tərs hiperbolik funksiyalar bölməsini redaktə et" class="mw-editsection-visualeditor"><span>redaktə</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%B0nteqral&action=edit&section=10" title="Bölmənin mənbə kodunu redaktə et: Tərs hiperbolik funksiyalar"><span>mənbəni redaktə et</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \operatorname {arcsinh} x\,dx=x\operatorname {arcsinh} x-{\sqrt {x^{2}+1}}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>arcsinh</mi> <mo>⁡</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mi>arcsinh</mi> <mo>⁡</mo> <mi>x</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>1</mn> </msqrt> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \operatorname {arcsinh} x\,dx=x\operatorname {arcsinh} x-{\sqrt {x^{2}+1}}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/848be352ba3525d2b7eae4dd33243b30f40f6675" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:44.429ex; height:5.676ex;" alt="{\displaystyle \int \operatorname {arcsinh} x\,dx=x\operatorname {arcsinh} x-{\sqrt {x^{2}+1}}+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \operatorname {arccosh} x\,dx=x\operatorname {arccosh} x-{\sqrt {x^{2}-1}}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>arccosh</mi> <mo>⁡</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mi>arccosh</mi> <mo>⁡</mo> <mi>x</mi> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>1</mn> </msqrt> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \operatorname {arccosh} x\,dx=x\operatorname {arccosh} x-{\sqrt {x^{2}-1}}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b1f44dececc8a2ccba0f76b0b719d8f01cf30f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:44.94ex; height:5.676ex;" alt="{\displaystyle \int \operatorname {arccosh} x\,dx=x\operatorname {arccosh} x-{\sqrt {x^{2}-1}}+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \operatorname {arctanh} x\,dx=x\operatorname {arctanh} x+{\frac {1}{2}}\log {(1-x^{2})}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>arctanh</mi> <mo>⁡</mo> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mi>arctanh</mi> <mo>⁡</mo> <mi>x</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>log</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \operatorname {arctanh} x\,dx=x\operatorname {arctanh} x+{\frac {1}{2}}\log {(1-x^{2})}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/557ca65008b3a86245a9ac574417901823e6e6b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:50.667ex; height:5.676ex;" alt="{\displaystyle \int \operatorname {arctanh} x\,dx=x\operatorname {arctanh} x+{\frac {1}{2}}\log {(1-x^{2})}+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \operatorname {arccsch} \,x\,dx=x\operatorname {arccsch} x+\log {\left[x\left({\sqrt {1+{\frac {1}{x^{2}}}}}+1\right)\right]}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>arccsch</mi> <mspace width="thinmathspace" /> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mi>arccsch</mi> <mo>⁡</mo> <mi>x</mi> <mo>+</mo> <mi>log</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>[</mo> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </msqrt> </mrow> <mo>+</mo> <mn>1</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \operatorname {arccsch} \,x\,dx=x\operatorname {arccsch} x+\log {\left[x\left({\sqrt {1+{\frac {1}{x^{2}}}}}+1\right)\right]}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a61a885e4028e489ca59b0ee403f46d21155bd9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:60.858ex; height:6.343ex;" alt="{\displaystyle \int \operatorname {arccsch} \,x\,dx=x\operatorname {arccsch} x+\log {\left[x\left({\sqrt {1+{\frac {1}{x^{2}}}}}+1\right)\right]}+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \operatorname {arcsech} \,x\,dx=x\operatorname {arcsech} x-\arctan {\left({\frac {x}{x-1}}{\sqrt {\frac {1-x}{1+x}}}\right)}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>arcsech</mi> <mspace width="thinmathspace" /> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mi>arcsech</mi> <mo>⁡</mo> <mi>x</mi> <mo>−</mo> <mi>arctan</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mrow> <mi>x</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <mi>x</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mi>x</mi> </mrow> </mfrac> </msqrt> </mrow> </mrow> <mo>)</mo> </mrow> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \operatorname {arcsech} \,x\,dx=x\operatorname {arcsech} x-\arctan {\left({\frac {x}{x-1}}{\sqrt {\frac {1-x}{1+x}}}\right)}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58241a402b18f137cf9a6828e05dad58625e4890" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:61.292ex; height:6.343ex;" alt="{\displaystyle \int \operatorname {arcsech} \,x\,dx=x\operatorname {arcsech} x-\arctan {\left({\frac {x}{x-1}}{\sqrt {\frac {1-x}{1+x}}}\right)}+C}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int \operatorname {arccoth} \,x\,dx=x\operatorname {arccoth} x+{\frac {1}{2}}\log {(x^{2}-1)}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>arccoth</mi> <mspace width="thinmathspace" /> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>x</mi> <mi>arccoth</mi> <mo>⁡</mo> <mi>x</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>log</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int \operatorname {arccoth} \,x\,dx=x\operatorname {arccoth} x+{\frac {1}{2}}\log {(x^{2}-1)}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be6ab64732c6ed99feb485738c6defcfeccdea74" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:50.534ex; height:5.676ex;" alt="{\displaystyle \int \operatorname {arccoth} \,x\,dx=x\operatorname {arccoth} x+{\frac {1}{2}}\log {(x^{2}-1)}+C}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Xarici_keçidlər"><span id="Xarici_ke.C3.A7idl.C9.99r"></span>Xarici keçidlər</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%B0nteqral&veaction=edit&section=11" title="Xarici keçidlər bölməsini redaktə et" class="mw-editsection-visualeditor"><span>redaktə</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%B0nteqral&action=edit&section=11" title="Bölmənin mənbə kodunu redaktə et: Xarici keçidlər"><span>mənbəni redaktə et</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://integrals.wolfram.com">Wolfram Integrator</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; 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[o]" accesskey="o"><span>Daxil ol</span></a></li> </ul> </div> </nav> <div id="left-navigation"> <nav id="p-namespaces" class="mw-portlet mw-portlet-namespaces vector-menu-tabs vector-menu-tabs-legacy vector-menu" aria-labelledby="p-namespaces-label" > <h3 id="p-namespaces-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Ad fəzaları</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected mw-list-item"><a href="/wiki/%C4%B0nteqral" title="Məqalənin məzmununu göstər [c]" accesskey="c"><span>Məqalə</span></a></li><li id="ca-talk" class="new mw-list-item"><a href="/w/index.php?title=M%C3%BCzakir%C9%99:%C4%B0nteqral&action=edit&redlink=1" rel="discussion" class="new" title="Səhifə barədə müzakirə (səhifə mövcud deyil) [t]" accesskey="t"><span>Müzakirə</span></a></li> </ul> </div> </nav> <nav id="p-variants" class="mw-portlet mw-portlet-variants emptyPortlet vector-menu-dropdown vector-menu" aria-labelledby="p-variants-label" > <input type="checkbox" id="p-variants-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-variants" class="vector-menu-checkbox" aria-labelledby="p-variants-label" > <label id="p-variants-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">azərbaycanca</span> </label> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </nav> </div> <div id="right-navigation"> <nav id="p-views" class="mw-portlet mw-portlet-views vector-menu-tabs vector-menu-tabs-legacy vector-menu" aria-labelledby="p-views-label" > <h3 id="p-views-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Görünüş</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected mw-list-item"><a href="/wiki/%C4%B0nteqral"><span>Oxu</span></a></li><li id="ca-ve-edit" class="mw-list-item"><a href="/w/index.php?title=%C4%B0nteqral&veaction=edit" title="Bu səhifəni redaktə et [v]" accesskey="v"><span>Redaktə</span></a></li><li id="ca-edit" class="collapsible mw-list-item"><a href="/w/index.php?title=%C4%B0nteqral&action=edit" title="Səhifənin mənbə kodunu redaktə et [e]" accesskey="e"><span>Mənbəni redaktə et</span></a></li><li id="ca-history" class="mw-list-item"><a href="/w/index.php?title=%C4%B0nteqral&action=history" title="Bu səhifənin keçmiş nüsxələri. [h]" accesskey="h"><span>Tarixçəyə bax</span></a></li> </ul> </div> </nav> <nav id="p-cactions" class="mw-portlet mw-portlet-cactions emptyPortlet vector-menu-dropdown vector-menu" aria-labelledby="p-cactions-label" title="Daha çox seçim" > <input type="checkbox" id="p-cactions-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-cactions" class="vector-menu-checkbox" aria-labelledby="p-cactions-label" > <label id="p-cactions-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Daha çox</span> </label> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </nav> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <h3 >Axtar</h3> <form action="/w/index.php" id="searchform" class="vector-search-box-form"> <div id="simpleSearch" class="vector-search-box-inner" data-search-loc="header-navigation"> <input class="vector-search-box-input" type="search" name="search" placeholder="Vikipediyada axtar" aria-label="Vikipediyada axtar" autocapitalize="sentences" title="Vikipediya saytında axtar [f]" accesskey="f" id="searchInput" > <input type="hidden" name="title" value="Xüsusi:Axtar"> <input id="mw-searchButton" class="searchButton mw-fallbackSearchButton" type="submit" name="fulltext" title="Bu mətnin olduğu səhifələri axtar" value="Axtar"> <input id="searchButton" class="searchButton" type="submit" name="go" title="Əgər varsa, eyni adı daşıyan səhifəyə keç" value="Get"> </div> </form> </div> </div> </div> <div id="mw-panel" class="vector-legacy-sidebar"> <div id="p-logo" role="banner"> <a class="mw-wiki-logo" href="/wiki/Ana_s%C9%99hif%C9%99" title="Ana səhifə"></a> </div> <nav id="p-navigation" class="mw-portlet mw-portlet-navigation vector-menu-portal portal vector-menu" aria-labelledby="p-navigation-label" > <h3 id="p-navigation-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Naviqasiya</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage" class="mw-list-item"><a href="/wiki/Ana_s%C9%99hif%C9%99" title="Ana səhifəni ziyarət edin [z]" accesskey="z"><span>Ana səhifə</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Vikipediya:K%C9%99nd_meydan%C4%B1" title="Layihə haqqında, nələr edəbilərsiniz, axtardıqlarınızı harda tapmaq olar"><span>Kənd meydanı</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Vikipediya:%C4%B0cma_portal%C4%B1" title="Gündəlik xəbərlər ilə əlaqəli məlumatlar"><span>İcma portalı</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/X%C3%BCsusi:SonD%C9%99yi%C5%9Fiklikl%C9%99r" title="Vikidəki son dəyişikliklər siyahısı [r]" accesskey="r"><span>Son dəyişikliklər</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/X%C3%BCsusi:T%C9%99sad%C3%BCfi" title="Təsadüfi məqaləyə keç [x]" accesskey="x"><span>Təsadüfi məqalə</span></a></li> </ul> </div> </nav> <nav id="p-Layihələr" class="mw-portlet mw-portlet-Layihələr vector-menu-portal portal vector-menu" aria-labelledby="p-Layihələr-label" > <h3 id="p-Layihələr-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Layihələr</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-Seçilmiş-məqalələr" class="mw-list-item"><a href="/wiki/Vikipediya:Se%C3%A7ilmi%C5%9F_m%C9%99qal%C9%99l%C9%99r"><span>Seçilmiş məqalələr</span></a></li><li id="n-Seçilmiş-siyahılar" class="mw-list-item"><a href="/wiki/Vikipediya:Se%C3%A7ilmi%C5%9F_siyah%C4%B1lar"><span>Seçilmiş siyahılar</span></a></li><li id="n-Yaxşı-məqalələr" class="mw-list-item"><a href="/wiki/Vikipediya:Yax%C5%9F%C4%B1_m%C9%99qal%C9%99l%C9%99r"><span>Yaxşı məqalələr</span></a></li><li id="n-Məqalə-namizədləri" class="mw-list-item"><a href="/wiki/Vikipediya:M%C9%99qal%C9%99_namiz%C9%99dl%C9%99ri"><span>Məqalə namizədləri</span></a></li><li id="n-Mövzulu-ay" class="mw-list-item"><a href="/wiki/Vikipediya:M%C3%B6vzulu_ay"><span>Mövzulu ay</span></a></li> </ul> </div> </nav> <nav id="p-Xüsusi" class="mw-portlet mw-portlet-Xüsusi vector-menu-portal portal vector-menu" aria-labelledby="p-Xüsusi-label" > <h3 id="p-Xüsusi-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Xüsusi</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-contactpage" class="mw-list-item"><a href="/wiki/Vikipediya:Biziml%C9%99_%C9%99laq%C9%99"><span>Bizimlə əlaqə</span></a></li><li id="n-sitesupport" class="mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=az.wikipedia.org&uselang=az" title="Bizə dəstək verin"><span>İanə et</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/K%C3%B6m%C9%99k:M%C3%BCnd%C9%99ricat" title="Yardım almaq üçün."><span>Kömək</span></a></li> </ul> </div> </nav> <nav id="p-tb" class="mw-portlet mw-portlet-tb vector-menu-portal portal vector-menu" aria-labelledby="p-tb-label" > <h3 id="p-tb-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Alətlər</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/X%C3%BCsusi:S%C9%99hif%C9%99y%C9%99Ke%C3%A7idl%C9%99r/%C4%B0nteqral" title="Vikidə bu məqaləyə bağlantılar [j]" accesskey="j"><span>Səhifəyə keçidlər</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/X%C3%BCsusi:%C6%8Flaq%C9%99liD%C9%99yi%C5%9Fiklikl%C9%99r/%C4%B0nteqral" rel="nofollow" title="Bu məqaləyə aid başqa səhifələrdə yeni dəyişikliklər [k]" accesskey="k"><span>Əlaqəli redaktələr</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Vikipediya:Yükləmə_sehrbazı" title="Yeni şəkil və ya multimedia faylı yüklə [u]" accesskey="u"><span>Fayl yüklə</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/X%C3%BCsusi:X%C3%BCsusiS%C9%99hif%C9%99l%C9%99r" title="Xüsusi səhifələrin siyahısı [q]" accesskey="q"><span>Xüsusi səhifələr</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%C4%B0nteqral&oldid=7619803" title="Bu səhifənin bu versiyasına daimi keçid"><span>Daimi keçid</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%C4%B0nteqral&action=info" title="Bu səhifə haqqında ətraflı məlumat"><span>Səhifə məlumatları</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=X%C3%BCsusi:CiteThisPage&page=%C4%B0nteqral&id=7619803&wpFormIdentifier=titleform" title="Bu səhifəyə necə istinad etmək barədə məlumat"><span>Bu səhifəyə istinad et</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=X%C3%BCsusi:UrlShortener&url=https%3A%2F%2Faz.wikipedia.org%2Fwiki%2F%25C4%25B0nteqral"><span>Qısaldılmış URL əldə et</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=X%C3%BCsusi:QrCode&url=https%3A%2F%2Faz.wikipedia.org%2Fwiki%2F%25C4%25B0nteqral"><span>QR-kodu endir</span></a></li> </ul> </div> </nav> <nav id="p-coll-print_export" class="mw-portlet mw-portlet-coll-print_export vector-menu-portal portal vector-menu" aria-labelledby="p-coll-print_export-label" > <h3 id="p-coll-print_export-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Çap et/ixrac</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=X%C3%BCsusi:Book&bookcmd=book_creator&referer=%C4%B0nteqral"><span>Kitab yarat</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=X%C3%BCsusi:DownloadAsPdf&page=%C4%B0nteqral&action=show-download-screen"><span>PDF kimi yüklə</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%C4%B0nteqral&printable=yes" title="Səhifənin çap versiyası [p]" accesskey="p"><span>Çap versiyası</span></a></li> </ul> </div> </nav> <nav id="p-wikibase-otherprojects" class="mw-portlet mw-portlet-wikibase-otherprojects vector-menu-portal portal vector-menu" aria-labelledby="p-wikibase-otherprojects-label" > <h3 id="p-wikibase-otherprojects-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Digər layihələrdə</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Integration_(mathematics)" hreflang="en"><span>Vikianbar</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q80091" title="Bağlanan məlumatların saxlanması elementinə keçid [g]" accesskey="g"><span>Vikidata elementi</span></a></li> </ul> </div> </nav> <nav id="p-lang" class="mw-portlet mw-portlet-lang vector-menu-portal portal vector-menu" aria-labelledby="p-lang-label" > <h3 id="p-lang-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Digər dillərdə</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%A0%E1%8C%A0%E1%88%AB%E1%89%83%E1%88%9A" title="አጠራቃሚ – amhar" lang="am" hreflang="am" data-title="አጠራቃሚ" data-language-autonym="አማርኛ" data-language-local-name="amhar" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Integraci%C3%B3n" title="Integración – araqon" lang="an" hreflang="an" data-title="Integración" data-language-autonym="Aragonés" data-language-local-name="araqon" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D9%83%D8%A7%D9%85%D9%84" title="تكامل – ərəb" lang="ar" hreflang="ar" data-title="تكامل" data-language-autonym="العربية" data-language-local-name="ərəb" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Integraci%C3%B3n" title="Integración – asturiya" lang="ast" hreflang="ast" data-title="Integración" data-language-autonym="Asturianu" data-language-local-name="asturiya" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A7%D9%86%D8%AA%D9%82%D8%B1%D8%A7%D9%84" title="انتقرال – South Azerbaijani" lang="azb" hreflang="azb" data-title="انتقرال" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Интеграл – başqırd" lang="ba" hreflang="ba" data-title="Интеграл" data-language-autonym="Башҡортса" data-language-local-name="başqırd" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%86%D0%BD%D1%82%D1%8D%D0%B3%D1%80%D0%B0%D0%BB" title="Інтэграл – belarus" lang="be" hreflang="be" data-title="Інтэграл" data-language-autonym="Беларуская" data-language-local-name="belarus" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Интеграл – bolqar" lang="bg" hreflang="bg" data-title="Интеграл" data-language-autonym="Български" data-language-local-name="bolqar" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AF%E0%A7%8B%E0%A6%97%E0%A6%9C%E0%A7%80%E0%A6%95%E0%A6%B0%E0%A6%A3" title="যোগজীকরণ – benqal" lang="bn" hreflang="bn" data-title="যোগজীকরণ" data-language-autonym="বাংলা" data-language-local-name="benqal" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Integral" title="Integral – bosniya" lang="bs" hreflang="bs" data-title="Integral" data-language-autonym="Bosanski" data-language-local-name="bosniya" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca badge-Q17437796 badge-featuredarticle mw-list-item" title="seçilmiş məqalə"><a href="https://ca.wikipedia.org/wiki/Integraci%C3%B3" title="Integració – katalan" lang="ca" hreflang="ca" data-title="Integració" data-language-autonym="Català" data-language-local-name="katalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AA%DB%95%D9%88%D8%A7%D9%88%DA%A9%D8%A7%D8%B1%DB%8C" title="تەواوکاری – Mərkəzi kürdcə" lang="ckb" hreflang="ckb" data-title="تەواوکاری" data-language-autonym="کوردی" data-language-local-name="Mərkəzi kürdcə" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Integr%C3%A1l" title="Integrál – çex" lang="cs" hreflang="cs" data-title="Integrál" data-language-autonym="Čeština" data-language-local-name="çex" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Интеграл – çuvaş" lang="cv" hreflang="cv" data-title="Интеграл" data-language-autonym="Чӑвашла" data-language-local-name="çuvaş" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Integryn" title="Integryn – uels" lang="cy" hreflang="cy" data-title="Integryn" data-language-autonym="Cymraeg" data-language-local-name="uels" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Integral" title="Integral – alman" lang="de" hreflang="de" data-title="Integral" data-language-autonym="Deutsch" data-language-local-name="alman" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/%C4%B0ntegral" title="İntegral – Zazaki" lang="diq" hreflang="diq" data-title="İntegral" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-dtp mw-list-item"><a href="https://dtp.wikipedia.org/wiki/Ponompuuvan" title="Ponompuuvan – Central Dusun" lang="dtp" hreflang="dtp" data-title="Ponompuuvan" data-language-autonym="Kadazandusun" data-language-local-name="Central Dusun" class="interlanguage-link-target"><span>Kadazandusun</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9F%CE%BB%CE%BF%CE%BA%CE%BB%CE%AE%CF%81%CF%89%CE%BC%CE%B1" title="Ολοκλήρωμα – yunan" lang="el" hreflang="el" data-title="Ολοκλήρωμα" data-language-autonym="Ελληνικά" data-language-local-name="yunan" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Integral" title="Integral – ingilis" lang="en" hreflang="en" data-title="Integral" data-language-autonym="English" data-language-local-name="ingilis" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Integralo" title="Integralo – esperanto" lang="eo" hreflang="eo" data-title="Integralo" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Integraci%C3%B3n" title="Integración – ispan" lang="es" hreflang="es" data-title="Integración" data-language-autonym="Español" data-language-local-name="ispan" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Integraal" title="Integraal – eston" lang="et" hreflang="et" data-title="Integraal" data-language-autonym="Eesti" data-language-local-name="eston" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu badge-Q17437796 badge-featuredarticle mw-list-item" title="seçilmiş məqalə"><a href="https://eu.wikipedia.org/wiki/Integral" title="Integral – bask" lang="eu" hreflang="eu" data-title="Integral" data-language-autonym="Euskara" data-language-local-name="bask" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D9%86%D8%AA%DA%AF%D8%B1%D8%A7%D9%84" title="انتگرال – fars" lang="fa" hreflang="fa" data-title="انتگرال" data-language-autonym="فارسی" data-language-local-name="fars" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Integraali" title="Integraali – fin" lang="fi" hreflang="fi" data-title="Integraali" data-language-autonym="Suomi" data-language-local-name="fin" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Int%C3%A9gration_(math%C3%A9matiques)" title="Intégration (mathématiques) – fransız" lang="fr" hreflang="fr" data-title="Intégration (mathématiques)" data-language-autonym="Français" data-language-local-name="fransız" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Integral" title="Integral – qalisiya" lang="gl" hreflang="gl" data-title="Integral" data-language-autonym="Galego" data-language-local-name="qalisiya" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%B8%E0%AA%82%E0%AA%95%E0%AA%B2%E0%AA%A8" title="સંકલન – qucarat" lang="gu" hreflang="gu" data-title="સંકલન" data-language-autonym="ગુજરાતી" data-language-local-name="qucarat" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/Chit-f%C3%BBn-ho%CC%8Dk" title="Chit-fûn-ho̍k – hakka" lang="hak" hreflang="hak" data-title="Chit-fûn-ho̍k" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="hakka" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%99%D7%A0%D7%98%D7%92%D7%A8%D7%9C" title="אינטגרל – ivrit" lang="he" hreflang="he" data-title="אינטגרל" data-language-autonym="עברית" data-language-local-name="ivrit" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%AE%E0%A4%BE%E0%A4%95%E0%A4%B2%E0%A4%A8" title="समाकलन – hind" lang="hi" hreflang="hi" data-title="समाकलन" data-language-autonym="हिन्दी" data-language-local-name="hind" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Integral" title="Integral – xorvat" lang="hr" hreflang="hr" data-title="Integral" data-language-autonym="Hrvatski" data-language-local-name="xorvat" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Entegrasyon_(matematik)" title="Entegrasyon (matematik) – haiti kreol" lang="ht" hreflang="ht" data-title="Entegrasyon (matematik)" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haiti kreol" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Integr%C3%A1l" title="Integrál – macar" lang="hu" hreflang="hu" data-title="Integrál" data-language-autonym="Magyar" data-language-local-name="macar" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BB%D5%B6%D5%BF%D5%A5%D5%A3%D6%80%D5%A1%D5%AC" title="Ինտեգրալ – erməni" lang="hy" hreflang="hy" data-title="Ինտեգրալ" data-language-autonym="Հայերեն" data-language-local-name="erməni" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Integral" title="Integral – indoneziya" lang="id" hreflang="id" data-title="Integral" data-language-autonym="Bahasa Indonesia" data-language-local-name="indoneziya" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Integralo" title="Integralo – ido" lang="io" hreflang="io" data-title="Integralo" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Heildun" title="Heildun – island" lang="is" hreflang="is" data-title="Heildun" data-language-autonym="Íslenska" data-language-local-name="island" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Integrale" title="Integrale – italyan" lang="it" hreflang="it" data-title="Integrale" data-language-autonym="İtaliano" data-language-local-name="italyan" class="interlanguage-link-target"><span>İtaliano</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%98%E1%83%9C%E1%83%A2%E1%83%94%E1%83%92%E1%83%A0%E1%83%90%E1%83%9A%E1%83%98" title="ინტეგრალი – gürcü" lang="ka" hreflang="ka" data-title="ინტეგრალი" data-language-autonym="ქართული" data-language-local-name="gürcü" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Integral" title="Integral – qaraqalpaq" lang="kaa" hreflang="kaa" data-title="Integral" data-language-autonym="Qaraqalpaqsha" data-language-local-name="qaraqalpaq" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Интеграл – qazax" lang="kk" hreflang="kk" data-title="Интеграл" data-language-autonym="Қазақша" data-language-local-name="qazax" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%A2%E1%9E%B6%E1%9F%86%E1%9E%84%E1%9E%8F%E1%9F%81%E1%9E%80%E1%9F%92%E1%9E%9A%E1%9E%B6%E1%9E%9B" title="អាំងតេក្រាល – kxmer" lang="km" hreflang="km" data-title="អាំងតេក្រាល" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="kxmer" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%85%E0%B2%A8%E0%B3%81%E0%B2%95%E0%B2%B2%E0%B2%A8%E0%B2%B6%E0%B2%BE%E0%B2%B8%E0%B3%8D%E0%B2%A4%E0%B3%8D%E0%B2%B0" title="ಅನುಕಲನಶಾಸ್ತ್ರ – kannada" lang="kn" hreflang="kn" data-title="ಅನುಕಲನಶಾಸ್ತ್ರ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%A0%81%EB%B6%84" title="적분 – koreya" lang="ko" hreflang="ko" data-title="적분" data-language-autonym="한국어" data-language-local-name="koreya" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/%C3%8Entegral" title="Întegral – kürd" lang="ku" hreflang="ku" data-title="Întegral" data-language-autonym="Kurdî" data-language-local-name="kürd" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Интеграл – qırğız" lang="ky" hreflang="ky" data-title="Интеграл" data-language-autonym="Кыргызча" data-language-local-name="qırğız" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Integrale" title="Integrale – latın" lang="la" hreflang="la" data-title="Integrale" data-language-autonym="Latina" data-language-local-name="latın" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Integral" title="Integral – Lombard" lang="lmo" hreflang="lmo" data-title="Integral" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Integralas" title="Integralas – litva" lang="lt" hreflang="lt" data-title="Integralas" data-language-autonym="Lietuvių" data-language-local-name="litva" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Integr%C4%81lis" title="Integrālis – latış" lang="lv" hreflang="lv" data-title="Integrālis" data-language-autonym="Latviešu" data-language-local-name="latış" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B8%E0%B4%AE%E0%B4%BE%E0%B4%95%E0%B4%B2%E0%B4%A8%E0%B4%82" title="സമാകലനം – malayalam" lang="ml" hreflang="ml" data-title="സമാകലനം" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Интеграл – monqol" lang="mn" hreflang="mn" data-title="Интеграл" data-language-autonym="Монгол" data-language-local-name="monqol" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%95%E0%A4%B2%E0%A4%A8" title="संकलन – marathi" lang="mr" hreflang="mr" data-title="संकलन" data-language-autonym="मराठी" data-language-local-name="marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kamiran" title="Kamiran – malay" lang="ms" hreflang="ms" data-title="Kamiran" data-language-autonym="Bahasa Melayu" data-language-local-name="malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/L-Integral" title="L-Integral – malta" lang="mt" hreflang="mt" data-title="L-Integral" data-language-autonym="Malti" data-language-local-name="malta" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%84%E1%80%BA%E1%80%90%E1%80%AE%E1%80%82%E1%80%9B%E1%80%B1%E1%80%B8%E1%80%9B%E1%80%BE%E1%80%84%E1%80%BA%E1%80%B8" title="အင်တီဂရေးရှင်း – birman" lang="my" hreflang="my" data-title="အင်တီဂရေးရှင်း" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birman" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl badge-Q70894304 mw-list-item" title=""><a href="https://nl.wikipedia.org/wiki/Integraal" title="Integraal – holland" lang="nl" hreflang="nl" data-title="Integraal" data-language-autonym="Nederlands" data-language-local-name="holland" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Integral" title="Integral – nünorsk norveç" lang="nn" hreflang="nn" data-title="Integral" data-language-autonym="Norsk nynorsk" data-language-local-name="nünorsk norveç" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Integrasjon" title="Integrasjon – bokmal norveç" lang="nb" hreflang="nb" data-title="Integrasjon" data-language-autonym="Norsk bokmål" data-language-local-name="bokmal norveç" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Integracion" title="Integracion – oksitan" lang="oc" hreflang="oc" data-title="Integracion" data-language-autonym="Occitan" data-language-local-name="oksitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Wajjummaa" title="Wajjummaa – oromo" lang="om" hreflang="om" data-title="Wajjummaa" data-language-autonym="Oromoo" data-language-local-name="oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Ca%C5%82ka" title="Całka – polyak" lang="pl" hreflang="pl" data-title="Całka" data-language-autonym="Polski" data-language-local-name="polyak" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A7%D9%86%D9%B9%DB%8C%DA%AF%D8%B1%D9%84" title="انٹیگرل – Western Punjabi" lang="pnb" hreflang="pnb" data-title="انٹیگرل" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Integral" title="Integral – portuqal" lang="pt" hreflang="pt" data-title="Integral" data-language-autonym="Português" data-language-local-name="portuqal" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Integral%C4%83" title="Integrală – rumın" lang="ro" hreflang="ro" data-title="Integrală" data-language-autonym="Română" data-language-local-name="rumın" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Интеграл – rus" lang="ru" hreflang="ru" data-title="Интеграл" data-language-autonym="Русский" data-language-local-name="rus" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Intiggrali" title="Intiggrali – siciliya" lang="scn" hreflang="scn" data-title="Intiggrali" data-language-autonym="Sicilianu" data-language-local-name="siciliya" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Integral" title="Integral – skots" lang="sco" hreflang="sco" data-title="Integral" data-language-autonym="Scots" data-language-local-name="skots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Integral" title="Integral – serb-xorvat" lang="sh" hreflang="sh" data-title="Integral" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serb-xorvat" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Integral" title="Integral – Simple English" lang="en-simple" hreflang="en-simple" data-title="Integral" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Integr%C3%A1l" title="Integrál – slovak" lang="sk" hreflang="sk" data-title="Integrál" data-language-autonym="Slovenčina" data-language-local-name="slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Integral" title="Integral – sloven" lang="sl" hreflang="sl" data-title="Integral" data-language-autonym="Slovenščina" data-language-local-name="sloven" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Integrali" title="Integrali – alban" lang="sq" hreflang="sq" data-title="Integrali" data-language-autonym="Shqip" data-language-local-name="alban" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Интеграл – serb" lang="sr" hreflang="sr" data-title="Интеграл" data-language-autonym="Српски / srpski" data-language-local-name="serb" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Integral" title="Integral – sundan" lang="su" hreflang="su" data-title="Integral" data-language-autonym="Sunda" data-language-local-name="sundan" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Integral" title="Integral – isveç" lang="sv" hreflang="sv" data-title="Integral" data-language-autonym="Svenska" data-language-local-name="isveç" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Ukamilishaji_(hisabati)" title="Ukamilishaji (hisabati) – suahili" lang="sw" hreflang="sw" data-title="Ukamilishaji (hisabati)" data-language-autonym="Kiswahili" data-language-local-name="suahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AF%8A%E0%AE%95%E0%AF%88%E0%AE%AF%E0%AF%80%E0%AE%9F%E0%AF%81" title="தொகையீடு – tamil" lang="ta" hreflang="ta" data-title="தொகையீடு" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9B%E0%B8%A3%E0%B8%B4%E0%B8%9E%E0%B8%B1%E0%B8%99%E0%B8%98%E0%B9%8C" title="ปริพันธ์ – tay" lang="th" hreflang="th" data-title="ปริพันธ์" data-language-autonym="ไทย" data-language-local-name="tay" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C4%B0ntegral" title="İntegral – türk" lang="tr" hreflang="tr" data-title="İntegral" data-language-autonym="Türkçe" data-language-local-name="türk" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Интеграл – tatar" lang="tt" hreflang="tt" data-title="Интеграл" data-language-autonym="Татарча / tatarça" data-language-local-name="tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%86%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB" title="Інтеграл – ukrayna" lang="uk" hreflang="uk" data-title="Інтеграл" data-language-autonym="Українська" data-language-local-name="ukrayna" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%AA%DA%A9%D8%A7%D9%85%D9%84" title="تکامل – urdu" lang="ur" hreflang="ur" data-title="تکامل" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Integral" title="Integral – özbək" lang="uz" hreflang="uz" data-title="Integral" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="özbək" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Integral" title="Integral – Venetian" lang="vec" hreflang="vec" data-title="Integral" data-language-autonym="Vèneto" data-language-local-name="Venetian" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/T%C3%ADch_ph%C3%A2n" title="Tích phân – vyetnam" lang="vi" hreflang="vi" data-title="Tích phân" data-language-autonym="Tiếng Việt" data-language-local-name="vyetnam" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wa mw-list-item"><a href="https://wa.wikipedia.org/wiki/Riveye" title="Riveye – valun" lang="wa" hreflang="wa" data-title="Riveye" data-language-autonym="Walon" data-language-local-name="valun" class="interlanguage-link-target"><span>Walon</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%A7%AF%E5%88%86" title="积分 – çin" lang="zh" hreflang="zh" data-title="积分" data-language-autonym="中文" data-language-local-name="çin" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Chek-hun" title="Chek-hun – Min Nan" lang="nan" hreflang="nan" data-title="Chek-hun" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Min Nan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%A9%8D%E5%88%86" title="積分 – kanton" lang="yue" hreflang="yue" data-title="積分" data-language-autonym="粵語" data-language-local-name="kanton" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a 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İnteqral — Vikipediya