Wikipedia — ирекле энциклопедия проектыннан ([http://tt.chped.com.ttcysuttlart1999.aylandirow.tmf.org.ru/wiki/Интеграл табу latin yazuında])
Интеграл табу — математик анализда дифференциал табу белән нигез операциясе.
![{\displaystyle \int cf(x)\,dx=c\int f(x)\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/afe3300581af3aceb2e44d6e66394934920a82fb)
![{\displaystyle \int [f(x)+g(x)]\,dx=\int f(x)\,dx+\int g(x)\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5dc2c6e2acadf432d22ca42bc6a21af25e48e64d)
![{\displaystyle \int [f(x)-g(x)]\,dx=\int f(x)\,dx-\int g(x)\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b5c5f0ce4c12f5715703d07f46dbd9e067acdd3f)
![{\displaystyle \int f(x)g(x)\,dx=f(x)\int g(x)\,dx-\int \left(d[f(x)]\int g(x)\,dx\right)\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f2da09fdfdcb12ff1a55cb20340291b01e6832c0)
![{\displaystyle \int f(ax+b)\,dx={1 \over a}F(ax+b)\,+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/96e883615da881aa5e2650526bc2d3c845b3bb41)
![{\displaystyle ~\int \!0\,dx=C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f2ee7199067474bf3657b7d1b90d1a707cd56afe)
![{\displaystyle ~\int \!a\,dx=ax+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/33be95cd04af74e8b8f2246f0e256650e9439f1c)
![{\displaystyle ~\int \!x^{n}\,dx={\begin{cases}{\frac {x^{n+1}}{n+1}}+C,&n\neq -1\\\ln \left|x\right|+C,&n=-1\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a55a17b8a5ccc1aa38f90674466f4e99107bf3f7)
![{\displaystyle \int \!{dx \over {a^{2}+x^{2}}}={1 \over a}\,\operatorname {arctg} \,{\frac {x}{a}}+C=-{1 \over a}\,\operatorname {arcctg} \,{\frac {x}{a}}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/08ce4be356f93d2eb8b070919a631358d8bbd562)
Исбатлау
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Уң якта дифференциал табабыз:
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![{\displaystyle \int \!{dx \over {x^{2}-a^{2}}}={1 \over 2a}\ln \left|{x-a \over {x+a}}\right|+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/871476a41dd2f2140caa05fbf7e9226723c04660)
![{\displaystyle \int \!\ln {x}\,dx=x\ln {x}-x+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/45275b4baec7e28918e2df647db3efeb0c522a42)
![{\displaystyle \int {\frac {dx}{x\ln x}}=\ln |\ln x|+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8fd164fe32bc3ec618c186b411292af74282e2c6)
![{\displaystyle \int \!\log _{b}{x}\,dx=x\log _{b}{x}-x\log _{b}{e}+C=x{\frac {\ln {x}-1}{\ln b}}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b7448d564d64f114a126c0c175f3d329f750fd1c)
![{\displaystyle \int \!e^{x}\,dx=e^{x}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/42de79821c1cc0e2dd1cf7a9c35258adba0ab967)
![{\displaystyle \int \!a^{x}\,dx={\frac {a^{x}}{\ln {a}}}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2f40f9f1940b1a23cd3ff4c7cad1c7e8330d3346)
![{\displaystyle \int \!{dx \over {\sqrt {a^{2}-x^{2}}}}=\arcsin {x \over a}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/806a4e8d2ac6559c867772846fe86e2a9dc423a3)
![{\displaystyle \int \!{-dx \over {\sqrt {a^{2}-x^{2}}}}=\arccos {x \over a}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/35932a8e75e457b4f09f9db05ef54543f0722058)
![{\displaystyle \int \!{dx \over x{\sqrt {x^{2}-a^{2}}}}={1 \over a}\,\operatorname {arcsec} \,{|x| \over a}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/53d916ce55ccded26bda7047c80a73fc8f082034)
![{\displaystyle \int \!{dx \over {\sqrt {x^{2}\pm a^{2}}}}=\ln \left|{x+{\sqrt {x^{2}\pm a^{2}}}}\right|+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5f6ef96f46ee3d18224c6bfd8dd310f085561b82)
![{\displaystyle \int \!\sin {x}\,dx=-\cos {x}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d20e0823bcd355411954bca7befbfe8110e5c083)
![{\displaystyle \int \!\cos {x}\,dx=\sin {x}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ec47fbf049078444d1f7e5404d2f449dcc30b7ec)
![{\displaystyle \int \!\operatorname {tg} \,{x}\,dx=-\ln {\left|\cos {x}\right|}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9b508ea79951d8ad0ad2567e1cf60b6c054aa520)
Исбатлау
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![{\displaystyle \int \!\operatorname {ctg} \,{x}\,dx=\ln {\left|\sin {x}\right|}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/36d48a099c4f45add68de628c17b2e26f2b4a2fa)
Исбатлау
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![{\displaystyle \int \!\sec {x}\,dx=\ln {\left|\sec {x}+\operatorname {tg} \,{x}\right|}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/136d63bcaefdaf3bb951de4a4080fb0a769354b3)
![{\displaystyle \int \!\csc {x}\,dx=-\ln {\left|\csc {x}+\operatorname {ctg} \,{x}\right|}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/73272e3de59c9879bc807351009b523006b3cb17)
![{\displaystyle \int \!\sec ^{2}x\,dx=\int \!{dx \over \cos ^{2}x}=\operatorname {tg} \,x+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/05fe6b826b2649edb6638e24646d76fe752c8d8c)
![{\displaystyle \int \!\csc ^{2}x\,dx=\int \!{dx \over \sin ^{2}x}=-\operatorname {ctg} \,x+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4df77edc39e3f8aeee83ace3380ec13729f4e69b)
![{\displaystyle \int \!\sec {x}\,\operatorname {tg} \,{x}\,dx=\sec {x}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ec1aa438db63da8be74d33e976887dd8d01f1f69)
![{\displaystyle \int \!\csc {x}\,\operatorname {ctg} \,{x}\,dx=-\csc {x}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f0193351945a255379566f45c05714ea9f4f3c81)
![{\displaystyle \int \!\sin ^{2}x\,dx={\frac {1}{2}}(x-\sin x\cos x)+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/78fb0258b1b79577e39130bc6e26f3bf014af796)
![{\displaystyle \int \!\cos ^{2}x\,dx={\frac {1}{2}}(x+\sin x\cos x)+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c826aebd5cb185632de6afe3376df8607d50773c)
![{\displaystyle \int \!\sin ^{n}x\,dx=-{\frac {\sin ^{n-1}{x}\cos {x}}{n}}+{\frac {n-1}{n}}\int \!\sin ^{n-2}{x}\,dx,n\in \mathbb {N} ,n\geqslant 2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8c2cbaee4bf8114c25b49ed9483c3d3ce445d167)
![{\displaystyle \int \!\cos ^{n}x\,dx={\frac {\cos ^{n-1}{x}\sin {x}}{n}}+{\frac {n-1}{n}}\int \!\cos ^{n-2}{x}\,dx,n\in \mathbb {N} ,n\geqslant 2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7200af71fcd424138290e58e53078c004715410d)
![{\displaystyle \int \!\operatorname {arctg} \,{x}\,dx=x\,\operatorname {arctg} \,{x}-{\frac {1}{2}}\ln {\left(1+x^{2}\right)}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c61deb03a393c4b663493ed69bdf26e49b38ac9e)
![{\displaystyle \int \operatorname {sh} \,x\,dx=\operatorname {ch} \,x+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4a5a5600eb5d23ced95946cbe2c40759f109f39c)
![{\displaystyle \int \operatorname {ch} \,x\,dx=\operatorname {sh} \,x+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7d34032b883a68b3ed699c005773e071ad02e4df)
![{\displaystyle \int {\frac {dx}{\operatorname {ch} ^{2}\,x}}=\operatorname {th} \,x+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/04f930f9e20247f20aac61f67a60e67075b20497)
![{\displaystyle \int {\frac {dx}{\operatorname {sh} ^{2}\,x}}=-\operatorname {cth} \,x+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b5bca459556d1fdff0078919b7a343519cf01da5)
![{\displaystyle \int \operatorname {th} \,x\,dx=\ln |\operatorname {ch} \,x|+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2c51d4c5275e392b5cc0dc8ab2a94b42dacb841a)
![{\displaystyle \int \operatorname {csch} \,x\,dx=\ln \left|\operatorname {th} \,{x \over 2}\right|+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/56bcf36240b631b52072ad01bc0cfde934eb7afc)
- также
![{\displaystyle \int \operatorname {sech} \,x\,dx=2\,\operatorname {arctg} \,(e^{x})+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d9d8e76200f0d3f44cc78c5755c9e4fbad05e9b)
- также
![{\displaystyle \int \operatorname {sech} \,x\,dx=2\,\operatorname {arctg} \,\left(\operatorname {th} \,{\frac {x}{2}}\right)+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/44f5e16665c1481421f780f89887c90768e8727b)
![{\displaystyle \int \operatorname {cth} \,x\,dx=\ln |\operatorname {sh} \,x|+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/818c9cae4cfd9ba8c210ee94be31700e080d67f3)
Исбатлау
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Исбатлау тикшерү белән башкарыйк:
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Исбатлау тикшерү белән башкарыйк:
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Исбатлау тикшерәбез:
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