Slijedi popis integrala (antiderivacija funkcija) racionalnih funkcija. Za potpun popis integrala funkcija, pogledati tablica integrala i popis integrala.
![{\displaystyle \int (ax+b)^{n}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/de3a5696d6a0706c62c9fecfd55b741f8d75fa09) |
|
![{\displaystyle \int {\frac {1}{ax+b}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/df66efb02b8568f481de153fb2988a0b515a0242) |
|
![{\displaystyle \int x(ax+b)^{n}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/333036d5f19b0939533abfa39bd786fa4dd52b14) |
|
![{\displaystyle \int {\frac {x}{ax+b}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/763c8785f54e41620a4ce5b4b95939368445c2b9) |
|
![{\displaystyle \int {\frac {x}{(ax+b)^{2}}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9e40d53171234271b395c0272cd9d81a7be853bb) |
|
![{\displaystyle \int {\frac {x}{(ax+b)^{n}}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5e30da5fc40dd25ca71beddbdf2885f5fe04971b) |
|
![{\displaystyle \int {\frac {x^{2}}{ax+b}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dc4c4adc806276f8ff7f4bc0c10c0a87b9d2fdd8) |
|
![{\displaystyle \int {\frac {x^{2}}{(ax+b)^{2}}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a4e06ce4a5c063457ad2a3719e3f297312d86585) |
|
![{\displaystyle \int {\frac {x^{2}}{(ax+b)^{3}}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/566d32e0b7dc57f9fa4b7024e88c2c869a4c879f) |
|
![{\displaystyle \int {\frac {x^{2}}{(ax+b)^{n}}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a33bd0aa22747ecc0b8941d350b227340b743823) |
|
![{\displaystyle \int {\frac {mx+n}{ax^{2}+bx+c}}dx=}](https://wikimedia.org/api/rest_v1/media/math/render/svg/37eabaf91b1d7cb37d8ff5bd1a5c6f845269a66a) |
|
![{\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\,\!+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/24c3043e17c73f3cd2e6017569599d8daa62fa98)
![{\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\,\!+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/151ec39cac59b636fb58d052f0893a7e5e3aba80)
![{\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+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/219642ab4cb4f9772c75de0656ada1e4ef681fc4)
Bilo koja racionalna funkcija se može integrirati rabeći gornje jednadžbe i parcijalne razlomke u integriranju, dekompozicijom racionalne funkcije u zbroj funkcija oblika:
.