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SEO Keyword summary for en.wikipedia.org/wiki/list_of_integrals_of_trigonometric_functions
Keywords are extracted from the main content of your website and are the primary indicator of the words this page could rank for. By frequenty count we expect your focus keyword to be frac
Focus keyword
Short and long tail
Short Tail Keywords frac sin cos |
long Tail Keywords (2 words) int frac frac sin frac cos integrands involving mboxfor nneq |
long Tail Keywords (3 words) int frac sin int frac cos mboxfor nneq 1mbox integrands involving only integrand involving both involving both sine frac sin axdxcos |
en.wikipedia.org On-Page SEO Scan
Descriptive Elements
The <head> element of a en.wikipedia.org/wiki/list_of_integrals_of_trigonometric_functions page is used to inform the browser and visitors of the page about the general meta information. The head section of the page is where we place the page title, the definition of the HTML version used, the language of in which the page is written. In the head section we can also include JavaScript and CSS (markup) files for the page.
Page title
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list integrals trigonometric functions wikipedia
Meta description
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Meta description SEO
No meta relevance in the description detected !
Content SEO
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Headings
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Emphasis SEO impact
Images
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Images SEO impact
wikipedia free encyclopedia displaystyle sin cos int acos nxdxfrac ansin nxc axdxfrac axc frac asin axcfrac axcos afrac xsin axfrac leftfrac rightsin axa xcos axac xdxfrac sinb cqquad mboxfor neq mbox naxdxfrac axnafrac nint axdxqquad dxsin aln leftcsc axcot axrightc naxfrac nsin axqquad beginalignedint xnsin xnacos naint axdxsum kleq kfrac kcos axsum leq nfrac xnka nnkcos leftaxkfrac rightqquad mboxendaligned axxdxsum infty cdot axxndxfrac axn axxn mathrm bxmathrm cmathrm dxmathrm leftbeginalignedsqrt asqrt mathit arightsleftfrac axmathrm bsqrt amathit rightmathrm sqrt arightcleftfrac righttob acmathrm endalignedrightforadiagup amathrm atan rightc xdx xatan rightfrac leftcos rightrightc xacot leftsin axdx axpm xfrac axsin xncos axafrac ksin lfloor rfloor leftaxfrac rightsum nnksin axxdxln kcdot dxqquad nneq dxcos lefttan axan acot axxfrac sina tan sec xdxtan xxc axint dxqtan axpfrac pxfrac qaln qsin axpcos axcqquad dxtan axdxtan leftsec axtan axrightcfrac rightrightcfrac aoperatorname artanh xtan dxsec xcot xint csc xdxcot xcfrac dxcsc cot leftaxmp xnfrac right axdxcos axdxsin cosa naxcos maxdxfrac axanmfrac nmint maxdxqquad mboxfrac xdxsqrt operatorname arctangant xsqrt rightxqquad infrac mboxsqrt rightoperatorname xrightqquad mboxthis time being any real number naxdxcos maxbegincasesfrac axam axmboxfor mneq axanmcos maxmboxfor nmboxendcases aleftcos axln axasin axrightqquad naxdxsin axanmsin ntan naxcqquad xdxsec xdxcsc bab nxdxint bleftfrac rightbegincasesfrac ncdot cdots textif ntext evenfrac odd more than endcases ccsin cccos ccos cctan npi xadxfrac qquad nxdx nmin mathbb mxcos wikimedia foundation powered mediawiki
Mobile SEO en.wikipedia.org/wiki/list_of_integrals_of_trigonometric_functions
Mobile rendering
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Mobile improvement
Marketing / lead generation for en.wikipedia.org/wiki/list_of_integrals_of_trigonometric_functions
Social Media
Facebook shares | Facebook likes | ||
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SERP Preview
SERP Title
SERP Link
SERP Description
Domain Level SEO
Domain name
16 characters long
Domain name SEO Impact
Path name
functions found in path !
int found in path !
integrals found in path !
trigonometric found in path !
Structured data
Publisher Markup
Other Structured data
Website configuration
Correct processing of non-existing pages?
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Navigation and internal links
Navigation
Url seperator
Human readable urls
Number of links
Link SEO Impact
statistics
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en.m.wikipedia.org |
en.wikipedia.org wikimedia foundation inc
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w httpsenwikipediaorgwindexphptitlelistofintegralsoftrigonometricfunctionsoldid1238143766
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wiki trigonometry
outline
history
usage
trigonometric functions
cos
inverse
generalized trigonometry
identities
exact constants
tables
unit circle
sines
cosines
tangents
cotangents
pythagorean theorem
calculus
trigonometric substitution
inverse trigonometric functions
derivatives
trigonometric series
hipparchus
ptolemy
brahmagupta
alhasib
albattani
regiomontanus
de moivre
euler
fourier
integrals
antiderivative
functions
exponential functions
lists of integrals
trigonometric integral
constant of integration
sine
cosine
integral of the secant function
cosecant
cotangent
bioches rules
tangent
secant
beta function
rational functions
irrational functions
hyperbolic functions
inverse hyperbolic functions
logarithmic functions
gaussian functions
definite integrals
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SEO Advice for en.wikipedia.org
In this section we provide pointers on how you can to optimize your web page so it can be found more easily by search engines and how to make it rank higher by optimizing the content of the page itself. For each of the individual criteria the maximum score is 100%. A score below 70% is considered to be indication that the page is not complying with general SEO standards and should be evaluated and/or fixed. Not every factor is weighted the same and some are not as important as others. Relatively unimportant factors like meta keywords are not included in the overall score.
Item | Factor | Pointers | |
---|---|---|---|
PageTitle | 100% | Far too many sites lack a page title. A page title is the first thing that shows in the search results so always use the title element. | |
Title relevance | 78% | A title should reflect the contents of a site. This site has a 60 % match | |
Title Length | 100% | Limit your title to anywhere between 40 and 70 characters. Your title was 57 characters long | |
Meta Description | 0% | A meta description is the second element that shows in the search results so always use the meta description. | |
Meta description length | 0% | The meta description should be between 145 and 160 characters. This meta description is 1 characters long. | |
Meta description relevance | 0% | Meta Description should reflect the contents of a site. This site has a 0 % match | |
Number of internal links | 85% | Linking to internal pages makes pages easier to find for search engines. Try to keep the number of links on your page roughly below 100. There are 111 internal links on this page. | |
Folder structure | 100% | We found a folder structure in the links on your page. A good folder structure makes a site easier to navigate. We found 3 level 1 folders and 6 folders above or in the first level of navigation. | |
Headings | 100% | Headers should reflect the contents of a site. This site has a 44 % match | |
Links | 16% | Link anchors should to some degree reflect the contents of a site. This site has a 8 % match | |
Image alt tags | 28% | Image alt tags should to some degree reflect the contents of a site. This site has a 10 % match | |
Html ratio | 30% | Try to keep the html / text ratio as low as possible. More html means longer loading times. Layout should be handled in a serpate css file | |
Image descriptions | 97% | 96.521739130435 % of all images have been described via the "alt" attribute. Describing images with relevant text may lead to better results in the search engines. | |
Page errors | 100% | Pages with no errors display significantly faster on most browsers. We detected 0 errors and warnings | |
WordCount | 20% | An ideal page contains between 400 and 600 words.This page contains 4829 words | |
Server response time | 100% | A fast server speeds up a website. This server responds 81.91% faster then average | |
Gzip compression | 30% | This site does not use Gzip compression. Pages may not display as fast as they could | |
Keywords in Domainname | 30% | There are no important keywords in your domain name | |
Keywords in domain path | 100% | There are important keywords in the domain path | |
Structured Data | 100% | Structured data makes it easier for search engines to index your website | |
Inline css | 0% | Do not use inline css declarations. Inline css will slow down the rendering of the website. We detected 249 inline style declarations ( <a style="color:green">) with a size of 8473 bytes | |
Excessive use of the same words | 100% | There is no indication that there are one or more keywords that are used excessively. | |
Frames or iframes | 100% | Perfect, detected not (i)frames on your webpagina | |
Flash | 100% | Perfect, we detected no flash objects on your page | |
Css | 30% | We detected too much (2) CSS files on your page. Css files block the loading of a webpage. | |
Javascript | 100% | Perfect, we did not detect too many blocking JavaScript files | |
Mobile Website | 100% | Perfect, we found a responsive design for mobile users | |
Most important heading | 100% | Perfect, we detected a correct use of the most important (h1) heading! | |
Normalized headings | 40% | We dit not font a normalized heading structure. A heading 2 (h2) for example should be followed by a heading of an equal level (h2), a child heading (h3) or even a aprent heading (h1). |
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en.wikipedia.org images and descriptions
115 images found at en.wikipedia.org Images can improve the user experience for a website by making a pag visually appealing Images can also add extra keyword relevance to a webpage by using alt tags. Images can also slow down a website. If the width and height for a picture is not specified for a browser know in advance how large the image is. A browser must first load the picture and see before it knows how much space should be on the page. Upon reservation In the meantime, the browser can do little but wait. When the height and width for the plate are given in the HTML code, a browser just continues to build for a page while the images load in the background.
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5ccfd65881e83676b003b2d02c50af8e82045282 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}\int x^{n}\sin ax\,dx&=-{\frac {x^{n}}{a}}\cos ax+{\frac {n}{a}}\int x^{n-1}\cos ax\,dx\\&=\sum _{k=0}^{2k\leq n}(-1)^{k+1}{\frac {x^{n-2k}}{a^{1+2k}}}{\frac {n!}{(n-2k)!}}\cos ax+\sum _{k=0}^{2k+1\leq n}(-1)^{k}{\frac {x^{n-1-2k}}{a^{2+2k}}}{\frac {n!}{(n-2k-1)!}}\sin ax\\&=-\sum _{k=0}^{n}{\frac {x^{n-k}}{a^{1+k}}}{\frac {n!}{(n-k)!}}\cos \left(ax+k{\frac {\pi }{2}}\right)\qquad {\mbox{(for }}n>0{\mbox{)}}\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2952871c166663dab259233754344b795ba1e9b3 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}\int x^{n}\cos ax\,dx&={\frac {x^{n}\sin ax}{a}}-{\frac {n}{a}}\int x^{n-1}\sin ax\,dx\\&=\sum _{k=0}^{2k+1\leq n}(-1)^{k}{\frac {x^{n-2k-1}}{a^{2+2k}}}{\frac {n!}{(n-2k-1)!}}\cos ax+\sum _{k=0}^{2k\leq n}(-1)^{k}{\frac {x^{n-2k}}{a^{1+2k}}}{\frac {n!}{(n-2k)!}}\sin ax\\&=\sum _{k=0}^{n}(-1)^{\lfloor k/2\rfloor }{\frac {x^{n-k}}{a^{1+k}}}{\frac {n!}{(n-k)!}}\cos \left(ax-{\frac {(-1)^{k}+1}{2}}{\frac {\pi }{2}}\right)\\&=\sum _{k=0}^{n}{\frac {x^{n-k}}{a^{1+k}}}{\frac {n!}{(n-k)!}}\sin \left(ax+k{\frac {\pi }{2}}\right)\qquad {\mbox{(for }}n>0{\mbox{)}}\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7d39822052ca12c117f7121ef13f59d7fadd8ace height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {x\,dx}{1+\cos ax}}={\frac {x}{a}}\tan {\frac {ax}{2}}+{\frac {2}{a^{2}}}\ln \left|\cos {\frac {ax}{2}}\right|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c0c71e740a637ad718742a884ab0284c19dcf861 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {x\,dx}{1-\cos ax}}=-{\frac {x}{a}}\cot {\frac {ax}{2}}+{\frac {2}{a^{2}}}\ln \left|\sin {\frac {ax}{2}}\right|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/868e1340952b82a678a6ca4c964455ffdb51ec09 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\cos ax\,dx}{1+\cos ax}}=x-{\frac {1}{a}}\tan {\frac {ax}{2}}+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/376acd5ba6dda72e5511ca987900ff39f82c3462 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\cos ax\,dx}{1-\cos ax}}=-x-{\frac {1}{a}}\cot {\frac {ax}{2}}+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/813b2d66a6b5cbd286ad30d71d441aa57081c0e8 height: height attribute not set width: width attribute not set description: {\displaystyle \int (\cos a_{1}x)(\cos a_{2}x)\,dx={\frac {\sin((a_{2}-a_{1})x)}{2(a_{2}-a_{1})}}+{\frac {\sin((a_{2}+a_{1})x)}{2(a_{2}+a_{1})}}+c\qquad {\mbox{(for }}|a_{1}|\neq |a_{2}|{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b34ce80d93081408154a153d81d896074b17aae3 height: height attribute not set width: width attribute not set description: {\displaystyle \int \tan ax\,dx=-{\frac {1}{a}}\ln |\cos ax|+c={\frac {1}{a}}\ln |\sec ax|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/83b8d69c24a94eed938f2e751572e874aff74f7f height: height attribute not set width: width attribute not set description: {\displaystyle \int \tan ^{2}{x}\,dx=\tan {x}-x+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/925e1c6fdb836817a46dedd56d9ad1ba3dfbd3aa height: height attribute not set width: width attribute not set description: {\displaystyle \int \tan ^{n}ax\,dx={\frac {1}{a(n-1)}}\tan ^{n-1}ax-\int \tan ^{n-2}ax\,dx\qquad {\mbox{(for }}n\neq 1{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7c8618438a2fdaff26687b201395b05458f808c0 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {dx}{q\tan ax+p}}={\frac {1}{p^{2}+q^{2}}}(px+{\frac {q}{a}}\ln |q\sin ax+p\cos ax|)+c\qquad {\mbox{(for }}p^{2}+q^{2}\neq 0{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b9a9103841527de43578c2e7776aeb81f0fb114a height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {dx}{\tan ax\pm 1}}=\pm {\frac {x}{2}}+{\frac {1}{2a}}\ln |\sin ax\pm \cos ax|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/eea65135188c69d920b9f24937a482993fed82a9 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\tan ax\,dx}{\tan ax\pm 1}}={\frac {x}{2}}\mp {\frac {1}{2a}}\ln |\sin ax\pm \cos ax|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/747d013893285558422153b2fd7e1aa9784071eb height: height attribute not set width: width attribute not set description: {\displaystyle \int \sec {ax}\,dx={\frac {1}{a}}\ln {\left|\sec {ax}+\tan {ax}\right|}+c={\frac {1}{a}}\ln {\left|\tan {\left({\frac {ax}{2}}+{\frac {\pi }{4}}\right)}\right|}+c={\frac {1}{a}}\operatorname {artanh} {\left(\sin {ax}\right)}+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/62448efb9e0512c1014643b2efa34928c397f1b0 height: height attribute not set width: width attribute not set description: {\displaystyle \int \sec ^{2}{x}\,dx=\tan {x}+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5caad7043f7aa20013456e428c64b7fba0df359f height: height attribute not set width: width attribute not set description: {\displaystyle \int \sec ^{3}{x}\,dx={\frac {1}{2}}\sec x\tan x+{\frac {1}{2}}\ln |\sec x+\tan x|+c.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/bfb83a90e69050a71b631b159f1b641738f85054 height: height attribute not set width: width attribute not set description: {\displaystyle \int \sec ^{n}{ax}\,dx={\frac {\sec ^{n-2}{ax}\tan {ax}}{a(n-1)}}\,+\,{\frac {n-2}{n-1}}\int \sec ^{n-2}{ax}\,dx\qquad {\mbox{ (for }}n\neq 1{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9acabbd90de19b0d361d572dce3398a57c9d653f height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {dx}{\sec {x}+1}}=x-\tan {\frac {x}{2}}+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2845a0bb3c940ca6f9d98303dd5944618ad6a93c height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {dx}{\sec {x}-1}}=-x-\cot {\frac {x}{2}}+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e390b3943ca5bc6cf15a39dead513aafa7973e3a height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\sin {x}}{\cos {x}}}=\int \tan {x}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cc95cac097eea7e31fbb0a49f428dd903d68a25e height: height attribute not set width: width attribute not set description: {\displaystyle \int \csc {ax}\,dx=-{\frac {1}{a}}\ln {\left|\csc {ax}+\cot {ax}\right|}+c={\frac {1}{a}}\ln {\left|\csc {ax}-\cot {ax}\right|}+c={\frac {1}{a}}\ln {\left|\tan {\left({\frac {ax}{2}}\right)}\right|}+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/417803af6cef8535c9b9ee74f75a20ab4180fac0 height: height attribute not set width: width attribute not set description: {\displaystyle \int \csc ^{2}{x}\,dx=-\cot {x}+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c793315af1ab2724bbd7277cf24812703d8023a9 height: height attribute not set width: width attribute not set description: {\displaystyle \int \csc ^{3}{x}\,dx=-{\frac {1}{2}}\csc x\cot x-{\frac {1}{2}}\ln |\csc x+\cot x|+c=-{\frac {1}{2}}\csc x\cot x+{\frac {1}{2}}\ln |\csc x-\cot x|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fb9e86eda7e5b586050afa0bb690b5e1794af6d7 height: height attribute not set width: width attribute not set description: {\displaystyle \int \csc ^{n}{ax}\,dx=-{\frac {\csc ^{n-2}{ax}\cot {ax}}{a(n-1)}}\,+\,{\frac {n-2}{n-1}}\int \csc ^{n-2}{ax}\,dx\qquad {\mbox{ (for }}n\neq 1{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4d3116bd8d583f72077e90f06cf8e867997fdd14 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {dx}{\csc {x}+1}}=x-{\frac {2}{\cot {\frac {x}{2}}+1}}+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f12f1dc04dd4f01c7df46f36cba6653112da4418 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {dx}{\csc {x}-1}}=-x+{\frac {2}{\cot {\frac {x}{2}}-1}}+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8fd8d33638f05fb0f16334bb90a8aa016dc05bca height: height attribute not set width: width attribute not set description: {\displaystyle \int \cot ax\,dx={\frac {1}{a}}\ln |\sin ax|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/36979324717e61101b7119e6b3e995d5ec509d69 height: height attribute not set width: width attribute not set description: {\displaystyle \int \cot ^{2}{x}\,dx=-\cot {x}-x+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c0aef6b771a3ad83d5d62e6df67887774d6de8ed height: height attribute not set width: width attribute not set description: {\displaystyle \int \cot ^{n}ax\,dx=-{\frac {1}{a(n-1)}}\cot ^{n-1}ax-\int \cot ^{n-2}ax\,dx\qquad {\mbox{(for }}n\neq 1{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f957b8e698c1a8b55ba500a962f1b183b557889e height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {dx}{1+\cot ax}}=\int {\frac {\tan ax\,dx}{\tan ax+1}}={\frac {x}{2}}-{\frac {1}{2a}}\ln |\sin ax+\cos ax|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6e697e83f4089e2905dd245cb432fd219dcc493d height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {dx}{1-\cot ax}}=\int {\frac {\tan ax\,dx}{\tan ax-1}}={\frac {x}{2}}+{\frac {1}{2a}}\ln |\sin ax-\cos ax|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f99f9f4158d86f68a6f22ac0b494b8df2a009d24 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {dx}{\cos ax\pm \sin ax}}={\frac {1}{a{\sqrt {2}}}}\ln \left|\tan \left({\frac {ax}{2}}\pm {\frac {\pi }{8}}\right)\right|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/25e0e3cebd7eac046797eefb5e8be824a6ec6008 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {dx}{(\cos ax\pm \sin ax)^{2}}}={\frac {1}{2a}}\tan \left(ax\mp {\frac {\pi }{4}}\right)+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/fac73d6be8f02747aaba1086a025357e0a8a6d15 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {dx}{(\cos x+\sin x)^{n}}}={\frac {1}{2(n-1)}}\left({\frac {\sin x-\cos x}{(\cos x+\sin x)^{n-1}}}+(n-2)\int {\frac {dx}{(\cos x+\sin x)^{n-2}}}\right)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/064e4fca8dab302c4a14d713ffec2d193c49e5aa height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\cos ax\,dx}{\cos ax+\sin ax}}={\frac {x}{2}}+{\frac {1}{2a}}\ln \left|\sin ax+\cos ax\right|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/31c1c965e0a049e416b48908b9083d822fcd820d height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\cos ax\,dx}{\cos ax-\sin ax}}={\frac {x}{2}}-{\frac {1}{2a}}\ln \left|\sin ax-\cos ax\right|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2f7081fc3083a1df9044e044c70fb6749e39772f height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\sin ax\,dx}{\cos ax+\sin ax}}={\frac {x}{2}}-{\frac {1}{2a}}\ln \left|\sin ax+\cos ax\right|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/885121414a63e1158cce975732a0140443059683 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\sin ax\,dx}{\cos ax-\sin ax}}=-{\frac {x}{2}}-{\frac {1}{2a}}\ln \left|\sin ax-\cos ax\right|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/4be1a480baee112532376953a0e514953aac55e5 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\cos ax\,dx}{(\sin ax)(1+\cos ax)}}=-{\frac {1}{4a}}\tan ^{2}{\frac {ax}{2}}+{\frac {1}{2a}}\ln \left|\tan {\frac {ax}{2}}\right|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/5551ba6b1a17809cd93bad200f96d7bd77c41add height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\cos ax\,dx}{(\sin ax)(1-\cos ax)}}=-{\frac {1}{4a}}\cot ^{2}{\frac {ax}{2}}-{\frac {1}{2a}}\ln \left|\tan {\frac {ax}{2}}\right|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cba9a5f34c6745abfcdfea7906197167c4bf7fc4 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\sin ax\,dx}{(\cos ax)(1+\sin ax)}}={\frac {1}{4a}}\cot ^{2}\left({\frac {ax}{2}}+{\frac {\pi }{4}}\right)+{\frac {1}{2a}}\ln \left|\tan \left({\frac {ax}{2}}+{\frac {\pi }{4}}\right)\right|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/89bd9ffed0a439702f128c452dd2e9d363175ef4 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\sin ax\,dx}{(\cos ax)(1-\sin ax)}}={\frac {1}{4a}}\tan ^{2}\left({\frac {ax}{2}}+{\frac {\pi }{4}}\right)-{\frac {1}{2a}}\ln \left|\tan \left({\frac {ax}{2}}+{\frac {\pi }{4}}\right)\right|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0bd704958c5a62ac35486a94c701c4d4d4d89ae1 height: height attribute not set width: width attribute not set description: {\displaystyle \int (\sin ax)(\cos ax)\,dx={\frac {1}{2a}}\sin ^{2}ax+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/92f3a79d9fc7cc05ff77c79d0f9dc0a0c3506c91 height: height attribute not set width: width attribute not set description: {\displaystyle \int (\sin a_{1}x)(\cos a_{2}x)\,dx=-{\frac {\cos((a_{1}-a_{2})x)}{2(a_{1}-a_{2})}}-{\frac {\cos((a_{1}+a_{2})x)}{2(a_{1}+a_{2})}}+c\qquad {\mbox{(for }}|a_{1}|\neq |a_{2}|{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3d738258cd0ad64e8916b1afcdd40bca57eb6a86 height: height attribute not set width: width attribute not set description: {\displaystyle \int (\sin ^{n}ax)(\cos ax)\,dx={\frac {1}{a(n+1)}}\sin ^{n+1}ax+c\qquad {\mbox{(for }}n\neq -1{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/95a29ec1949b61595a138149da7af1fe9b056c1e height: height attribute not set width: width attribute not set description: {\displaystyle \int (\sin ax)(\cos ^{n}ax)\,dx=-{\frac {1}{a(n+1)}}\cos ^{n+1}ax+c\qquad {\mbox{(for }}n\neq -1{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8cc587066f531ba750784dbd9f5b03aeccc67d7f height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}\int (\sin ^{n}ax)(\cos ^{m}ax)\,dx&=-{\frac {(\sin ^{n-1}ax)(\cos ^{m+1}ax)}{a(n+m)}}+{\frac {n-1}{n+m}}\int (\sin ^{n-2}ax)(\cos ^{m}ax)\,dx\qquad {\mbox{(for }}m,n>0{\mbox{)}}\\&={\frac {(\sin ^{n+1}ax)(\cos ^{m-1}ax)}{a(n+m)}}+{\frac {m-1}{n+m}}\int (\sin ^{n}ax)(\cos ^{m-2}ax)\,dx\qquad {\mbox{(for }}m,n>0{\mbox{)}}\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e03f904edd8835bf1f3b47bce34e30cf3e2fbf32 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {dx}{(\sin ax)(\cos ax)}}={\frac {1}{a}}\ln \left|\tan ax\right|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6519ac56d6d1811592f964786eb42751d19b6f8f height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {dx}{(\sin ax)(\cos ^{n}ax)}}={\frac {1}{a(n-1)\cos ^{n-1}ax}}+\int {\frac {dx}{(\sin ax)(\cos ^{n-2}ax)}}\qquad {\mbox{(for }}n\neq 1{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/de84da3e83860aa7dd53d3af5679289da711a241 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {dx}{(\sin ^{n}ax)(\cos ax)}}=-{\frac {1}{a(n-1)\sin ^{n-1}ax}}+\int {\frac {dx}{(\sin ^{n-2}ax)(\cos ax)}}\qquad {\mbox{(for }}n\neq 1{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9b8dded2ee242701ff20afdc86d891f9070f90fd height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\sin ax\,dx}{\cos ^{n}ax}}={\frac {1}{a(n-1)\cos ^{n-1}ax}}+c\qquad {\mbox{(for }}n\neq 1{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0901ab7048597a2d942a8d9ec9251ab116891ac8 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\sin ^{2}ax\,dx}{\cos ax}}=-{\frac {1}{a}}\sin ax+{\frac {1}{a}}\ln \left|\tan \left({\frac {\pi }{4}}+{\frac {ax}{2}}\right)\right|+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9a181636833d2d500b4be5c97a0fc58ab37f96fa height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\sin ^{2}ax\,dx}{\cos ^{n}ax}}={\frac {\sin ax}{a(n-1)\cos ^{n-1}ax}}-{\frac {1}{n-1}}\int {\frac {dx}{\cos ^{n-2}ax}}\qquad {\mbox{(for }}n\neq 1{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/99bc35b310db277a8b20f736913c8178097758b6 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}\int {\frac {\sin ^{2}x}{1+\cos ^{2}x}}\,dx&={\sqrt {2}}\operatorname {arctangant} \left({\frac {\tan x}{\sqrt {2}}}\right)-x\qquad {\mbox{(for x in}}]-{\frac {\pi }{2}};+{\frac {\pi }{2}}[{\mbox{)}}\\&={\sqrt {2}}\operatorname {arctangant} \left({\frac {\tan x}{\sqrt {2}}}\right)-\operatorname {arctangant} \left(\tan x\right)\qquad {\mbox{(this time x being any real number }}{\mbox{)}}\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/872384bfd083802c7e5f81edcc55460dde40addf height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\sin ^{n}ax\,dx}{\cos ax}}=-{\frac {\sin ^{n-1}ax}{a(n-1)}}+\int {\frac {\sin ^{n-2}ax\,dx}{\cos ax}}\qquad {\mbox{(for }}n\neq 1{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/58bdd410008a1b627ede0f2b7104ea01b90192f8 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\sin ^{n}ax\,dx}{\cos ^{m}ax}}={\begin{cases}{\frac {\sin ^{n+1}ax}{a(m-1)\cos ^{m-1}ax}}-{\frac {n-m+2}{m-1}}\int {\frac {\sin ^{n}ax\,dx}{\cos ^{m-2}ax}}&{\mbox{(for }}m\neq 1{\mbox{)}}\\{\frac {\sin ^{n-1}ax}{a(m-1)\cos ^{m-1}ax}}-{\frac {n-1}{m-1}}\int {\frac {\sin ^{n-2}ax\,dx}{\cos ^{m-2}ax}}&{\mbox{(for }}m\neq 1{\mbox{)}}\\-{\frac {\sin ^{n-1}ax}{a(n-m)\cos ^{m-1}ax}}+{\frac {n-1}{n-m}}\int {\frac {\sin ^{n-2}ax\,dx}{\cos ^{m}ax}}&{\mbox{(for }}m\neq n{\mbox{)}}\end{cases}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/32b3ed71c00b7fc752cab0ee21b6b106ccaeed96 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\cos ax\,dx}{\sin ^{n}ax}}=-{\frac {1}{a(n-1)\sin ^{n-1}ax}}+c\qquad {\mbox{(for }}n\neq 1{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/af8d5900b25ed3cda6de1b98479c1fc0d1c30cd9 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\cos ^{2}ax\,dx}{\sin ax}}={\frac {1}{a}}\left(\cos ax+\ln \left|\tan {\frac {ax}{2}}\right|\right)+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/45036dea1d3b23c1be01e446c207f8a2ecfa1bbb height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\cos ^{2}ax\,dx}{\sin ^{n}ax}}=-{\frac {1}{n-1}}\left({\frac {\cos ax}{a\sin ^{n-1}ax}}+\int {\frac {dx}{\sin ^{n-2}ax}}\right)\qquad {\mbox{(for }}n\neq 1{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6d7373dae8faf0f3bcb7f7ddbd6465b952c9d8dc height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\cos ^{n}ax\,dx}{\sin ^{m}ax}}={\begin{cases}-{\frac {\cos ^{n+1}ax}{a(m-1)\sin ^{m-1}ax}}-{\frac {n-m+2}{m-1}}\int {\frac {\cos ^{n}ax\,dx}{\sin ^{m-2}ax}}&{\mbox{(for }}n\neq 1{\mbox{)}}\\-{\frac {\cos ^{n-1}ax}{a(m-1)\sin ^{m-1}ax}}-{\frac {n-1}{m-1}}\int {\frac {\cos ^{n-2}ax\,dx}{\sin ^{m-2}ax}}&{\mbox{(for }}m\neq 1{\mbox{)}}\\{\frac {\cos ^{n-1}ax}{a(n-m)\sin ^{m-1}ax}}+{\frac {n-1}{n-m}}\int {\frac {\cos ^{n-2}ax\,dx}{\sin ^{m}ax}}&{\mbox{(for }}m\neq n{\mbox{)}}\end{cases}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d503c75c8dcbb712f88809162a2e3e20f1ff7b88 height: height attribute not set width: width attribute not set description: {\displaystyle \int (\sin ax)(\tan ax)\,dx={\frac {1}{a}}(\ln |\sec ax+\tan ax|-\sin ax)+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/152292322de9851a1100065e0efe54701f01578b height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\tan ^{n}ax\,dx}{\sin ^{2}ax}}={\frac {1}{a(n-1)}}\tan ^{n-1}(ax)+c\qquad {\mbox{(for }}n\neq 1{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/e73c5092aac709c9971bb933c438ebc917344a22 height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\tan ^{n}ax\,dx}{\cos ^{2}ax}}={\frac {1}{a(n+1)}}\tan ^{n+1}ax+c\qquad {\mbox{(for }}n\neq -1{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/309b37abeb46abc52b16f4643f6f367beaba5cae height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\cot ^{n}ax\,dx}{\sin ^{2}ax}}=-{\frac {1}{a(n+1)}}\cot ^{n+1}ax+c\qquad {\mbox{(for }}n\neq -1{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8addfded4cf47e0543b3217b3415e08576a74e2d height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {\cot ^{n}ax\,dx}{\cos ^{2}ax}}={\frac {1}{a(1-n)}}\tan ^{1-n}ax+c\qquad {\mbox{(for }}n\neq 1{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d3426300c895f6ff40c28455d36d29417d683dee height: height attribute not set width: width attribute not set description: {\displaystyle \int (\sec x)(\tan x)\,dx=\sec x+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/abd49ac7e4242cab5000f8180c53adcd584240f4 height: height attribute not set width: width attribute not set description: {\displaystyle \int (\csc x)(\cot x)\,dx=-\csc x+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/374a70e181eb94295f799038c2d3b81fbbef12ea height: height attribute not set width: width attribute not set description: {\displaystyle b(a,b)} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cbd25f478650fdc0b035db3c07583bf45d1098be height: height attribute not set width: width attribute not set description: {\displaystyle \int _{0}^{\frac {\pi }{2}}\sin ^{n}x\,dx=\int _{0}^{\frac {\pi }{2}}\cos ^{n}x\,dx={\frac {1}{2}}b\left({\frac {n+1}{2}},{\frac {1}{2}}\right)={\begin{cases}{\frac {n-1}{n}}\cdot {\frac {n-3}{n-2}}\cdots {\frac {3}{4}}\cdot {\frac {1}{2}}\cdot {\frac {\pi }{2}},&{\text{if }}n{\text{ is even}}\\{\frac {n-1}{n}}\cdot {\frac {n-3}{n-2}}\cdots {\frac {4}{5}}\cdot {\frac {2}{3}},&{\text{if }}n{\text{ is odd and more than 1}}\\1,&{\text{if }}n=1\end{cases}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6976aecf1b8b7d692492e777f59de99b7b9b8ac1 height: height attribute not set width: width attribute not set description: {\displaystyle \int _{-c}^{c}\sin {x}\,dx=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d17e7b3ec2a19c12316f01d5b4f639bdaee1cce7 height: height attribute not set width: width attribute not set description: {\displaystyle \int _{-c}^{c}\cos {x}\,dx=2\int _{0}^{c}\cos {x}\,dx=2\int _{-c}^{0}\cos {x}\,dx=2\sin {c}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/c1e0a8bab0e106ca691271ae26382c544c64c073 height: height attribute not set width: width attribute not set description: {\displaystyle \int _{-c}^{c}\tan {x}\,dx=0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/23ee4414783a0d33f9ae707bbfdccd206e6ec935 height: height attribute not set width: width attribute not set description: {\displaystyle \int _{-{\frac {a}{2}}}^{\frac {a}{2}}x^{2}\cos ^{2}{\frac {n\pi x}{a}}\,dx={\frac {a^{3}(n^{2}\pi ^{2}-6)}{24n^{2}\pi ^{2}}}\qquad {\mbox{(for }}n=1,3,5...{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/3306ec56ff1a4ef7ab31b0626adefba80fcdc83e height: height attribute not set width: width attribute not set description: {\displaystyle \int _{\frac {-a}{2}}^{\frac {a}{2}}x^{2}\sin ^{2}{\frac {n\pi x}{a}}\,dx={\frac {a^{3}(n^{2}\pi ^{2}-6(-1)^{n})}{24n^{2}\pi ^{2}}}={\frac {a^{3}}{24}}(1-6{\frac {(-1)^{n}}{n^{2}\pi ^{2}}})\qquad {\mbox{(for }}n=1,2,3,...{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1448bcac538b7d3f79cd35ba7a9d4dd4e209f281 height: height attribute not set width: width attribute not set description: {\displaystyle \int _{0}^{2\pi }\sin ^{2m+1}{x}\cos ^{n}{x}\,dx=0\!\qquad n,m\in \mathbb {z} } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1fd076477398fbae83558bce65d5a78edef13200 height: height attribute not set width: width attribute not set description: {\displaystyle \int _{0}^{2\pi }\sin ^{m}{x}\cos ^{2n+1}{x}\,dx=0\!\qquad n,m\in \mathbb {z} } |
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https://login.wikimedia.org/wiki/special:centralautologin/start?type=1x1 height: 1 width: 1 description: no alt description found |
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http://en.wikipedia.org/static/images/footer/wikimedia-button.svg height: 29 width: 84 description: wikimedia foundation |
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http://en.wikipedia.org/w/resources/assets/poweredby_mediawiki.svg height: 31 width: 88 description: powered by mediawiki |
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