tabel integral.
![{\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 {1}{x(ax+b)}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3d4ddae3c001768c3585f11a2ab79a33948ff10d) |
|
![{\displaystyle \int {\frac {1}{x^{2}(ax+b)}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/de4c46f343b53213bdd247524fedfe1fe83adfce) |
|
![{\displaystyle \int {\frac {1}{x^{2}(ax+b)^{2}}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0a001bbd435ece2d331003b2ee9e583f1365fa3a) |
|
![{\displaystyle \int {\frac {1}{x^{2}+a^{2}}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/56929c9957fae8101b3a8976aafc2f036eb6ba0c) |
|
![{\displaystyle \int {\frac {1}{x^{2}-a^{2}}}dx=}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d28ca7746e7b62fbd37aeaa5b796274bfd19c9b2) |
![{\displaystyle -{\frac {1}{a}}\,\mathrm {arctanh} {\frac {x}{a}}={\frac {1}{2a}}\ln {\frac {a-x}{a+x}}\qquad {\mbox{(untuk }}|x|<|a|{\mbox{)}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b2134d311fcb0ef9c531494d9cdd54b800ca2f31)
|
|
![{\displaystyle -{\frac {1}{a}}\,\mathrm {arccoth} {\frac {x}{a}}={\frac {1}{2a}}\ln {\frac {x-a}{x+a}}\qquad {\mbox{(untuk }}|x|>|a|{\mbox{)}}\,\!}](https://wikimedia.org/api/rest_v1/media/math/render/svg/87ac2abedb9c606a269a64303a20723c4f3db9fc)
|
![{\displaystyle \int {\frac {1}{ax^{2}+bx+c}}dx=}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d868069007e10dcb0b43e752b782d24ca9103b75) |
![{\displaystyle {\frac {2}{\sqrt {4ac-b^{2}}}}\arctan {\frac {2ax+b}{\sqrt {4ac-b^{2}}}}\qquad {\mbox{(untuk }}4ac-b^{2}>0{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/943d8c686fc3662209817ba6a5bce1f2df83adb9)
|
|
![{\displaystyle -{\frac {2}{\sqrt {b^{2}-4ac}}}\,\mathrm {arctanh} {\frac {2ax+b}{\sqrt {b^{2}-4ac}}}={\frac {1}{\sqrt {b^{2}-4ac}}}\ln \left|{\frac {2ax+b-{\sqrt {b^{2}-4ac}}}{2ax+b+{\sqrt {b^{2}-4ac}}}}\right|\qquad {\mbox{(untuk }}4ac-b^{2}<0{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0896c4a1fc2a9a40092ec26ab0231e2119bcc00c)
|
|
![{\displaystyle -{\frac {2}{2ax+b}}\qquad {\mbox{(untuk }}4ac-b^{2}=0{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/03ceba1be57c1fc093c20fc9ef213b9536f5c9b8)
|
![{\displaystyle \int {\frac {x}{ax^{2}+bx+c}}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/55d371537c3e658647749a2648b98d142e519092) |
|
![{\displaystyle \int {\frac {mx+n}{ax^{2}+bx+c}}dx=}](https://wikimedia.org/api/rest_v1/media/math/render/svg/37eabaf91b1d7cb37d8ff5bd1a5c6f845269a66a) |
![{\displaystyle {\frac {m}{2a}}\ln \left|ax^{2}+bx+c\right|+{\frac {2an-bm}{a{\sqrt {4ac-b^{2}}}}}\arctan {\frac {2ax+b}{\sqrt {4ac-b^{2}}}}\qquad {\mbox{(untuk }}4ac-b^{2}>0{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e110a48fba8dd41b7c1fdd63786901984d5678a6)
|
|
![{\displaystyle {\frac {m}{2a}}\ln \left|ax^{2}+bx+c\right|+{\frac {2an-bm}{a{\sqrt {b^{2}-4ac}}}}\,\mathrm {artanh} {\frac {2ax+b}{\sqrt {b^{2}-4ac}}}\qquad {\mbox{(untuk }}4ac-b^{2}<0{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7d93c584e27aedfb1e761fa9369be359dac8f140)
|
|
![{\displaystyle {\frac {m}{2a}}\ln \left|ax^{2}+bx+c\right|-{\frac {2an-bm}{a(2ax+b)}}\,\,\,\,\,\,\,\,\,\,\qquad {\mbox{(untuk }}4ac-b^{2}=0{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bf00201004b54c08084bd390caf9bbb73c95e870)
|
![{\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)
Fungsi rasional apapun dapat diintegrasikan melalui persamaan-persamaan di atas dengan memanfaatkan integrasi parsial, dengan menguraikan fungsi rasional menjadi penjumlahan fungsi-fungsi dalam bentuk
.
- Kurnianingsih, Sri (2007). Matematika SMA dan MA 3A Untuk Kelas XII Semester 1 Program IPA. Jakarta: Esis/Erlangga. ISBN 979-734-504-1. (Indonesia)
- Kurnianingsih, Sri (2007). Matematika SMA dan MA 3A Untuk Kelas XII Semester 1 Program IPS. Jakarta: Esis/Erlangga. ISBN 979-734-567-X. (Indonesia)