en.wikipedia.org website review
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SEO Keyword summary for en.wikipedia.org/wiki/list_of_integrals_of_hyperbolic_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 sinh
Focus keyword
Short and long tail
Short Tail Keywords sinh cosh frac |
long Tail Keywords (2 words) integrals involving sidebar hide involving only hyperbolic functions int sinh |
long Tail Keywords (3 words) move to sidebar list of integrals integrals involving only involving only hyperbolic integrals of hyperbolic integrals involving hyperbolic hyperbolic sine functions |
en.wikipedia.org On-Page SEO Scan
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list integrals hyperbolic functions wikipedia
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Images
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wikipedia free encyclopedia displaystyle int sinh axdxfrac acosh axc asinh axfrac naxdxbegincasesfrac ansinh axcosh ndisplaystyle axdxn frac nneq endcases beginalignedint dxsinh aln lefttanh rightcfrac leftfrac cosh axrightcfrac rightcendaligned naxfrac axan axqquad mboxfor mbox xsinh axsinh bxdxfrac big bxcosh axbcosh bxsinh axbig cqquad neq dxcosh aarctan eaxcfrac aarctansinh axcendaligned xcosh axa afrac rightsinh bxbsinh coshaxfrac eaxcquad tanh xdxln axdxxfrac axac naxdxfrac axint axdxqquad coth xctext xneq operatorname sech xdxarctan csch over rightcln leftcoth xoperatorname xrightctext bxbcosh bxbig naxsinh maxdxfrac axanmsinh nmint maxdxqquad mneq nmboxfrac axam mboxfrac mboxendaligned maxcosh axamncosh naxdxqquad sinhaxbsincxddxfrac coshaxbsincxdfrac sinhaxbcoscxdc sinhaxbcoscxddxfrac coshaxbcoscxdfrac sinhaxbsincxdc coshaxbsincxddxfrac sinhaxbsincxdfrac coshaxbcoscxdc coshaxbcoscxddxfrac sinhaxbcoscxdfrac coshaxbsincxdc wikimedia foundation powered mediawiki
Mobile SEO en.wikipedia.org/wiki/list_of_integrals_of_hyperbolic_functions
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SERP Preview
SERP Title
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Domain Level SEO
Domain name
16 characters long
Domain name SEO Impact
Path name
functions found in path !
hyperbolic found in path !
int found in path !
integrals found in path !
list found in path !
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Correct processing of non-existing pages?
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statistics
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en.m.wikipedia.org |
en.wikipedia.org wikimedia foundation inc
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w httpsenwikipediaorgwindexphptitlelistofintegralsofhyperbolicfunctionsoldid1190568875
printable version
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wiki integrals
antiderivative
hyperbolic functions
list of integrals
constant of integration
the logistic function
lists of integrals
rational functions
irrational functions
trigonometric functions
inverse trigonometric functions
inverse hyperbolic functions
exponential 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 | 100% | A title should reflect the contents of a site. This site has a 100 % match | |
Title Length | 100% | Limit your title to anywhere between 40 and 70 characters. Your title was 54 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 | 100% | 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 38 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 67 % match | |
Links | 20% | Link anchors should to some degree reflect the contents of a site. This site has a 10 % match | |
Image alt tags | 31% | Image alt tags should to some degree reflect the contents of a site. This site has a 11 % 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 | 95% | 94.594594594595 % 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 1730 words | |
Server response time | 30% | A slow server slows down a website. This server responds 16.14% slower the average | |
Gzip compression | 30% | This site does not use Gzip compression. Pages may not display as fast as they could | |
Keywords in Domainname | 100% | There are 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 76 inline style declarations ( <a style="color:green">) with a size of 2642 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
37 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/73afd2753503c736e59bf4dd68a6ef869e8090fa height: height attribute not set width: width attribute not set description: {\displaystyle \int \sinh ax\,dx={\frac {1}{a}}\cosh ax+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/878f791c56c73d432dc08058b0f3bd33c1a642ef height: height attribute not set width: width attribute not set description: {\displaystyle \int \sinh ^{n}ax\,dx={\begin{cases}{\frac {1}{an}}(\sinh ^{n-1}ax)(\cosh ax)-{\frac {n-1}{n}}\displaystyle \int \sinh ^{n-2}ax\,dx,&n>0\\{\frac {1}{a(n+1)}}(\sinh ^{n+1}ax)(\cosh ax)-{\frac {n+2}{n+1}}\displaystyle \int \sinh ^{n+2}ax\,dx,&n<0,n\neq -1\end{cases}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/404e71b18ef9e8e604970e7cf0b3e35735563ae1 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}\int {\frac {dx}{\sinh ax}}&={\frac {1}{a}}\ln \left|\tanh {\frac {ax}{2}}\right|+c\\&={\frac {1}{a}}\ln \left|{\frac {\cosh ax+1}{\sinh ax}}\right|+c\\&={\frac {1}{a}}\ln \left|{\frac {\sinh ax}{\cosh ax+1}}\right|+c\\&={\frac {1}{2a}}\ln \left|{\frac {\cosh ax-1}{\cosh ax+1}}\right|+c\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/24d8780ba8c6da198d7c87a147bc99b2982dec3a height: height attribute not set width: width attribute not set description: {\displaystyle \int x\sinh ax\,dx={\frac {1}{a}}x\cosh ax-{\frac {1}{a^{2}}}\sinh ax+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/66aa553178cbb55a984df7ac955b075551a7f335 height: height attribute not set width: width attribute not set description: {\displaystyle \int (\sinh ax)(\sinh bx)\,dx={\frac {1}{a^{2}-b^{2}}}{\big (}a(\sinh bx)(\cosh ax)-b(\cosh bx)(\sinh ax){\big )}+c\qquad {\mbox{(for }}a^{2}\neq b^{2}{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/8478514124631a7efb7098e4b9c8ce2068ccf050 height: height attribute not set width: width attribute not set description: {\displaystyle \int \cosh ax\,dx={\frac {1}{a}}\sinh ax+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/26745e9ee399f67d44059c3618eee43c0fdfb630 height: height attribute not set width: width attribute not set description: {\displaystyle \int \cosh ^{2}ax\,dx={\frac {1}{4a}}\sinh 2ax+{\frac {x}{2}}+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/7ffb25db1879190b15fc30f2d75aebefce611fce height: height attribute not set width: width attribute not set description: {\displaystyle \int \cosh ^{n}ax\,dx={\begin{cases}{\frac {1}{an}}(\sinh ax)(\cosh ^{n-1}ax)+{\frac {n-1}{n}}\displaystyle \int \cosh ^{n-2}ax\,dx,&n>0\\-{\frac {1}{a(n+1)}}(\sinh ax)(\cosh ^{n+1}ax)+{\frac {n+2}{n+1}}\displaystyle \int \cosh ^{n+2}ax\,dx,&n<0,n\neq -1\end{cases}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/2149f423a0c0272d90a4b571bf4a0086d110774d height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}\int {\frac {dx}{\cosh ax}}&={\frac {2}{a}}\arctan e^{ax}+c\\&={\frac {1}{a}}\arctan(\sinh ax)+c\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cd458e54ed3699ebc1f296c814983668ee3bd34a height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {dx}{\cosh ^{n}ax}}={\frac {\sinh ax}{a(n-1)\cosh ^{n-1}ax}}+{\frac {n-2}{n-1}}\int {\frac {dx}{\cosh ^{n-2}ax}}\qquad {\mbox{(for }}n\neq 1{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/dbf668e6a2fd148b1877031cbce32f46befa35cd height: height attribute not set width: width attribute not set description: {\displaystyle \int x\cosh ax\,dx={\frac {1}{a}}x\sinh ax-{\frac {1}{a^{2}}}\cosh ax+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/225d93801d717e120731343bfa25b123a5388141 height: height attribute not set width: width attribute not set description: {\displaystyle \int x^{2}\cosh ax\,dx=-{\frac {2x\cosh ax}{a^{2}}}+\left({\frac {x^{2}}{a}}+{\frac {2}{a^{3}}}\right)\sinh ax+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/31821ed91dd9384d424e69405c092678351366ab height: height attribute not set width: width attribute not set description: {\displaystyle \int (\cosh ax)(\cosh bx)\,dx={\frac {1}{a^{2}-b^{2}}}{\big (}a(\sinh ax)(\cosh bx)-b(\sinh bx)(\cosh ax){\big )}+c\qquad {\mbox{(for }}a^{2}\neq b^{2}{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/103c2450fda60bc99a198d2366d961f87cb4985e height: height attribute not set width: width attribute not set description: {\displaystyle \int {\frac {dx}{1+\cosh(ax)}}={\frac {2}{a}}{\frac {1}{1+e^{-ax}}}+c\quad } |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/99299a94d3a08b53b54fa0971967e49004f8fb6f height: height attribute not set width: width attribute not set description: {\displaystyle {\frac {2}{a}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d34084777ab4d5122b6fb3a917d140df1caad0dd height: height attribute not set width: width attribute not set description: {\displaystyle \int \tanh x\,dx=\ln \cosh x+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/aa56801fdfacb4eda9dc3fff468d055ceaa8f665 height: height attribute not set width: width attribute not set description: {\displaystyle \int \tanh ^{n}ax\,dx=-{\frac {1}{a(n-1)}}\tanh ^{n-1}ax+\int \tanh ^{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/1fd10aa5030fc327fc1eba419cb87581bd065282 height: height attribute not set width: width attribute not set description: {\displaystyle \int \coth x\,dx=\ln |\sinh x|+c,{\text{ for }}x\neq 0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/69304e9c91b1eefcb7bc218a5080db96369e8e37 height: height attribute not set width: width attribute not set description: {\displaystyle \int \coth ^{n}ax\,dx=-{\frac {1}{a(n-1)}}\coth ^{n-1}ax+\int \coth ^{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/c567185304799602087bcbe1b470a2b9e5b7880b height: height attribute not set width: width attribute not set description: {\displaystyle \int \operatorname {sech} \,x\,dx=\arctan \,(\sinh x)+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/9c5e31944686fc44f7fac3e2e5033a97d005a159 height: height attribute not set width: width attribute not set description: {\displaystyle \int \operatorname {csch} \,x\,dx=\ln \left|\tanh {x \over 2}\right|+c=\ln \left|\coth {x}-\operatorname {csch} {x}\right|+c,{\text{ for }}x\neq 0} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/f8282fbfd2c2d820938cca5be2617f08beee218f height: height attribute not set width: width attribute not set description: {\displaystyle \int (\cosh ax)(\sinh bx)\,dx={\frac {1}{a^{2}-b^{2}}}{\big (}a(\sinh ax)(\sinh bx)-b(\cosh ax)(\cosh bx){\big )}+c\qquad {\mbox{(for }}a^{2}\neq b^{2}{\mbox{)}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/85c496aada1bce9259d2825e8606a87b9582a225 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}\int {\frac {\cosh ^{n}ax}{\sinh ^{m}ax}}\,dx&={\frac {\cosh ^{n-1}ax}{a(n-m)\sinh ^{m-1}ax}}+{\frac {n-1}{n-m}}\int {\frac {\cosh ^{n-2}ax}{\sinh ^{m}ax}}\,dx\qquad {\mbox{(for }}m\neq n{\mbox{)}}\\&=-{\frac {\cosh ^{n+1}ax}{a(m-1)\sinh ^{m-1}ax}}+{\frac {n-m+2}{m-1}}\int {\frac {\cosh ^{n}ax}{\sinh ^{m-2}ax}}\,dx\qquad {\mbox{(for }}m\neq 1{\mbox{)}}\\&=-{\frac {\cosh ^{n-1}ax}{a(m-1)\sinh ^{m-1}ax}}+{\frac {n-1}{m-1}}\int {\frac {\cosh ^{n-2}ax}{\sinh ^{m-2}ax}}\,dx\qquad {\mbox{(for }}m\neq 1{\mbox{)}}\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/09577c7823ece9759ea4ad948902ae27284005a3 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}\int {\frac {\sinh ^{m}ax}{\cosh ^{n}ax}}\,dx&={\frac {\sinh ^{m-1}ax}{a(m-n)\cosh ^{n-1}ax}}+{\frac {m-1}{n-m}}\int {\frac {\sinh ^{m-2}ax}{\cosh ^{n}ax}}\,dx\qquad {\mbox{(for }}m\neq n{\mbox{)}}\\&={\frac {\sinh ^{m+1}ax}{a(n-1)\cosh ^{n-1}ax}}+{\frac {m-n+2}{n-1}}\int {\frac {\sinh ^{m}ax}{\cosh ^{n-2}ax}}\,dx\qquad {\mbox{(for }}n\neq 1{\mbox{)}}\\&=-{\frac {\sinh ^{m-1}ax}{a(n-1)\cosh ^{n-1}ax}}+{\frac {m-1}{n-1}}\int {\frac {\sinh ^{m-2}ax}{\cosh ^{n-2}ax}}\,dx\qquad {\mbox{(for }}n\neq 1{\mbox{)}}\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/0e42067465fc2f9e4aead56de5340c0babeb9434 height: height attribute not set width: width attribute not set description: {\displaystyle \int \sinh(ax+b)\cos(cx+d)\,dx={\frac {a}{a^{2}+c^{2}}}\cosh(ax+b)\cos(cx+d)+{\frac {c}{a^{2}+c^{2}}}\sinh(ax+b)\sin(cx+d)+c} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/01cdc27e035389e4fbb28829c579b7490cd00399 height: height attribute not set width: width attribute not set description: {\displaystyle \int \cosh(ax+b)\sin(cx+d)\,dx={\frac {a}{a^{2}+c^{2}}}\sinh(ax+b)\sin(cx+d)-{\frac {c}{a^{2}+c^{2}}}\cosh(ax+b)\cos(cx+d)+c} |
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