ខាងក្រោមនេះជាតារាងអាំងតេក្រាល (ព្រីមីទីវ) នៃអនុគមន៍សនិទាន។ សូមមើល តារាងអាំងតេក្រាល សំរាប់បញ្ជីពេញលេញនៃគ្រប់អាំងតេក្រាល។
![{\displaystyle \int (ax+b)^{n}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/de3a5696d6a0706c62c9fecfd55b741f8d75fa09) |
(ចំពោះ )
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![{\displaystyle \int {\frac {c}{ax+b}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ae40052620dea901ed307eb68b15f2894c9232dd) |
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![{\displaystyle \int x(ax+b)^{n}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/333036d5f19b0939533abfa39bd786fa4dd52b14) |
(ចំពោះ )
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![{\displaystyle \int {\frac {x}{ax+b}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/763c8785f54e41620a4ce5b4b95939368445c2b9) |
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![{\displaystyle \int {\frac {x}{(ax+b)^{2}}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9e40d53171234271b395c0272cd9d81a7be853bb) |
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![{\displaystyle \int {\frac {x}{(ax+b)^{n}}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5e30da5fc40dd25ca71beddbdf2885f5fe04971b) |
(ចំពោះ )
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![{\displaystyle \int {\frac {x^{2}}{ax+b}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dc4c4adc806276f8ff7f4bc0c10c0a87b9d2fdd8) |
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![{\displaystyle \int {\frac {x^{2}}{(ax+b)^{2}}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a4e06ce4a5c063457ad2a3719e3f297312d86585) |
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![{\displaystyle \int {\frac {x^{2}}{(ax+b)^{3}}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/566d32e0b7dc57f9fa4b7024e88c2c869a4c879f) |
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![{\displaystyle \int {\frac {x^{2}}{(ax+b)^{n}}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a33bd0aa22747ecc0b8941d350b227340b743823) |
(ចំពោះ )
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ចំពោះ
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![{\displaystyle \int {\frac {1}{(ax^{2}+bx+c)^{n}}}dx={\frac {2ax+b}{(n-1)(4ac-b^{2})(ax^{2}+bx+c)^{n-1}}}+{\frac {(2n-3)2a}{(n-1)(4ac-b^{2})}}\int {\frac {1}{(ax^{2}+bx+c)^{n-1}}}dx\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e9a2659d0200da3cbebeff9bd68045443500142b)
![{\displaystyle \int {\frac {x}{(ax^{2}+bx+c)^{n}}}dx={\frac {bx+2c}{(n-1)(4ac-b^{2})(ax^{2}+bx+c)^{n-1}}}-{\frac {b(2n-3)}{(n-1)(4ac-b^{2})}}\int {\frac {1}{(ax^{2}+bx+c)^{n-1}}}dx\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fd82710f0ce0729e1f115f1b52e06540672946b9)
![{\displaystyle \int {\frac {1}{x(ax^{2}+bx+c)}}dx={\frac {1}{2c}}\ln \left|{\frac {x^{2}}{ax^{2}+bx+c}}\right|-{\frac {b}{2c}}\int {\frac {1}{ax^{2}+bx+c}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/505fd268d136f336322d8635315c3983c3c8aba6)
![{\displaystyle \int {\frac {dx}{x^{2^{n}}+1}}=\sum _{k=1}^{2^{n-1}}\left\{{\frac {1}{2^{n-1}}}\left[\sin({\frac {(2k-1)\pi }{2^{n}}})\arctan[\left(x-\cos({\frac {(2k-1)\pi }{2^{n}}})\right)\csc({\frac {(2k-1)\pi }{2^{n}}})]\right]-{\frac {1}{2^{n}}}\left[\cos({\frac {(2k-1)\pi }{2^{n}}})\ln \left|x^{2}-2x\cos({\frac {(2k-1)\pi }{2^{n}}})+1\right|\right]\right\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d961dbbe0264f48b1ec1e3ddeb69e9e8d0d83097)
គ្រប់អនុគមន៍សនិទានទាំងអស់អាចធ្វើអាំងតេក្រាលបានដោយប្រើសមីការនិងអាំងតេក្រាលដោយផ្នែក ដោយបំបែកអនុគមន៍សនិទានជាផលបូកនៃអនុគមន៍ដែលមានទំរង់៖
![{\displaystyle {\frac {ex+f}{\left(ax^{2}+bx+c\right)^{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/785692bdf4082452ab13d9424805cbcab7381cc6)