求导公式与积分公式

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  • https://baike.baidu.com/item/%E7%A7%AF%E5%88%86%E8%A1%A8
  • https://baike.baidu.com/item/%E7%A7%AF%E5%88%86%E5%85%AC%E5%BC%8F
  • https://baike.baidu.com/item/%E5%AF%BC%E6%95%B0%E8%A1%A8
  • https://blog.csdn.net/qq_36460397/article/details/78799816

导数公式

求导公式与积分公式_第1张图片

不定积分

1)含a+bx的积分

https://gss1.bdstatic.com/9vo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D244/sign=0ff96c3caeaf2eddd0f14eedb9110102/ca1349540923dd542fbeb552d309b3de9c82483e.jpg

https://gss3.bdstatic.com/7Po3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D285/sign=a4583d46530fd9f9a4175261102cd42b/4a36acaf2edda3cc3379aa1a03e93901213f926e.jpg

2)含有 https://gss3.bdstatic.com/-Po3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D53/sign=77e63843f0edab6470724dc3f53656d1/d8f9d72a6059252d07c35b8c3f9b033b5ab5b966.jpg 的积分:

https://gss1.bdstatic.com/-vo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D425/sign=17144dfe08d162d981ee631e24dfa950/8644ebf81a4c510fcce5e1206259252dd42aa5e2.jpg

https://gss3.bdstatic.com/-Po3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D480/sign=608d3cdb60d9f2d3241125e799ec8a53/6159252dd42a28342fe2353159b5c9ea15cebf47.jpg

https://gss3.bdstatic.com/7Po3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D306/sign=e676a100324e251fe6f7e2f89186c9c2/5366d0160924ab183069e20d37fae6cd7b890b88.jpg

https://gss0.bdstatic.com/-4o3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D456/sign=491160449058d109c0e3a8b7e758ccd0/c9fcc3cec3fdfc030600e082d63f8794a4c2268b.jpg

3)含有x^2±α^2的积分

 

4)含有https://gss2.bdstatic.com/-fo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D48/sign=a49c35ae66224f4a5399721b08f79156/95eef01f3a292df5f699ef9db7315c6035a873db.jpg a>0)的积分

5)含有 https://gss1.bdstatic.com/-vo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D160/sign=14035687b30e7bec27da07e71f2fb9fa/18d8bc3eb13533faaf89d1a6a3d3fd1f41345b7e.jpg 的积分:

https://gss2.bdstatic.com/9fo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D273/sign=9d00b8a39616fdfadc6cc1e9878d8cea/94cad1c8a786c91745d111b1c23d70cf3ac75763.jpg

6)含有 https://gss3.bdstatic.com/-Po3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D138/sign=f3d88aa74a34970a4373142cadcbd1c0/38dbb6fd5266d016522fdca09c2bd40735fa3507.jpg的积分

https://gss2.bdstatic.com/9fo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D383/sign=916fbb81a41ea8d38e22720ca40b30cf/38dbb6fd5266d016abb19212952bd40735fa355b.jpg

https://gss0.bdstatic.com/-4o3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D469/sign=3b4b9dc87f1ed21b7dc92fe3946fddae/aa64034f78f0f736131c403b0855b319ebc4132d.jpg

https://gss3.bdstatic.com/-Po3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D338/sign=cdd4e3be48ed2e73f8e9802fbf00a16d/58ee3d6d55fbb2fbb8b854284d4a20a44623dc7d.jpg

https://gss1.bdstatic.com/9vo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D387/sign=93e35a2d60d0f703e2b293d43ffb5148/242dd42a2834349b1acb62bfcbea15ce36d3be3e.jpg

https://gss0.bdstatic.com/94o3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D238/sign=121241fe08d162d981ee651f29dfa950/0d338744ebf81a4c4115e3f3d52a6059252da6e0.jpg

7)含有 https://gss3.bdstatic.com/-Po3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D153/sign=1cdb34118926cffc6d2abbb78a004a7d/8b13632762d0f7033a11d75403fa513d2797c593.jpg 的积分 

8)含有  的积分

https://gss3.bdstatic.com/-Po3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D325/sign=d7a30ea25cdf8db1b82e7a663c22dddb/bba1cd11728b471032d1f2f6c1cec3fdfc032309.jpg

https://gss3.bdstatic.com/7Po3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D321/sign=73bd383159b5c9ea66f305e1e439b622/37d12f2eb9389b5008e4ee688735e5dde7116ef4.jpg

https://gss0.bdstatic.com/94o3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D415/sign=7aa3820b4890f60300b09d460c12b370/8b13632762d0f70361ae9be60afa513d2697c5e8.jpg

https://gss1.bdstatic.com/-vo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D347/sign=22a6251d8882b90139adc537448da97e/562c11dfa9ec8a138e7d59daf503918fa0ecc0a1.jpg

https://gss0.bdstatic.com/94o3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D345/sign=54d1578b820a19d8cf03820106fa82c9/7c1ed21b0ef41bd53500e6ce53da81cb39db3dbc.jpg

9)含有  的积分

https://gss0.bdstatic.com/-4o3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D323/sign=6cc00f91013b5bb5bad726fc05d2d523/b90e7bec54e736d16bda823299504fc2d562693a.jpg

https://gss0.bdstatic.com/-4o3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D403/sign=eb4fad85a2ec08fa220012a76aee3d4d/c8ea15ce36d3d539aa4c06f93887e950352ab092.jpg 

https://gss2.bdstatic.com/9fo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D571/sign=e756dac779899e517c8e3a1373a6d990/377adab44aed2e7359788f168501a18b87d6fa73.jpg

https://gss2.bdstatic.com/-fo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D140/sign=4d818c5bfa1986184547eb807aec2e69/4e4a20a4462309f76ec8a428700e0cf3d7cad661.jpg

https://gss0.bdstatic.com/94o3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D266/sign=e565dac779899e517c8e3d1274a6d990/f9198618367adab49a72127989d4b31c8701e46e.jpg

https://gss0.bdstatic.com/-4o3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D167/sign=a59c0920c45c1038207ecac48510931c/8435e5dde71190ef3a0a9be5cc1b9d16fdfa6012.jpg

https://gss3.bdstatic.com/-Po3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D320/sign=3e8730dd932397ddd2799e066983b216/3b292df5e0fe9925e78e606a36a85edf8db1710d.jpg

https://gss0.bdstatic.com/94o3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D236/sign=f470bc001bd8bc3ec20801c9b48aa6c8/d31b0ef41bd5ad6e45356dd083cb39dbb6fd3c3f.jpg

https://gss0.bdstatic.com/94o3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D246/sign=ab26c7e7a964034f0bcdc50299c27980/e824b899a9014c088edb219f087b02087bf4f42c.jpg

10)含有三角函数的积分

https://gss2.bdstatic.com/9fo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D149/sign=da1106cd9d3df8dca23d8b95f41072bf/0eb30f2442a7d933624bec49af4bd11373f0012c.jpg

https://gss0.bdstatic.com/-4o3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D158/sign=195cea202a34349b70066a80f1ea1521/7dd98d1001e939011d4e860479ec54e736d196bf.jpg

https://gss2.bdstatic.com/-fo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D185/sign=9552a137fadcd100c99cfc29478a47be/d043ad4bd11373f02c9764a5a60f4bfbfbed045b.jpg

https://gss2.bdstatic.com/-fo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D195/sign=9430e739ca95d143de76e02a46f18296/8601a18b87d6277f48b839022a381f30e924fc66.jpg

https://gss0.bdstatic.com/-4o3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D225/sign=688cb99ea6c27d1ea1263cc62ed4adaf/78310a55b319ebc40bf67da38026cffc1e171679.jpg

https://gss2.bdstatic.com/-fo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D393/sign=5dcf32398544ebf869716236eaf8d736/caef76094b36acaf18729dc67ed98d1001e99c7d.jpg

https://gss0.bdstatic.com/94o3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D199/sign=894d9ee60afa513d55aa68d7046c554c/023b5bb5c9ea15ce2e11eb33b4003af33a87b208.jpg

https://gss2.bdstatic.com/-fo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D192/sign=248075e72c738bd4c021b638938b876c/08f790529822720ef2c7e8c079cb0a46f21fabfb.jpg

https://gss3.bdstatic.com/-Po3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D468/sign=9159ef1c0b24ab18e416e0310dfae69a/1f178a82b9014a90353c4c87ab773912b31bee8e.jpg

https://gss2.bdstatic.com/-fo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D476/sign=a5bd9264dfc451daf2f60dec80fd52a5/eac4b74543a982267194211d8882b9014a90ebb7.jpg

11)含有反三角函数的积分

https://gss2.bdstatic.com/9fo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D272/sign=7c116d6cd2160924d825a51ce606359b/3812b31bb051f8194cf40970d8b44aed2e73e733.jpg

https://gss0.bdstatic.com/94o3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D307/sign=ab0fbd81a41ea8d38e227204a00b30cf/ac6eddc451da81cba12e89f75066d0160924313b.jpg

https://gss2.bdstatic.com/-fo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D324/sign=065979290bf79052eb1f413c38f2d738/b3119313b07eca8043c533dd932397dda04483c3.jpg

12)含有指数函数的积分

https://gss3.bdstatic.com/7Po3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D112/sign=eae443e33b01213fcb334add66e636f8/d058ccbf6c81800a7e2cfe34b33533fa828b473a.jpg

https://gss2.bdstatic.com/-fo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D133/sign=d856d152d309b3deefbfe06bffbf6cd3/8694a4c27d1ed21b80ec58dfaf6eddc451da3fe6.jpg

https://gss0.bdstatic.com/94o3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D331/sign=066e3087ab773912c0268362c9198675/279759ee3d6d55fb4296001c6f224f4a20a4ddbc.jpg

13)含有对数函数的积分

14)含有双曲函数的积分

https://gss2.bdstatic.com/-fo3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D168/sign=4febe38ccb177f3e1434f80b48cf3bb9/d50735fae6cd7b8900724bb90d2442a7d9330ee9.jpg

定积分

https://gss0.bdstatic.com/94o3dSag_xI4khGkpoWK1HF6hhy/baike/s%3D545/sign=fbcd34d38f1001e94a3c140b8d0e7b06/ca1349540923dd540e4fda52d309b3de9c8248cf.jpg

积分定理

求导公式与积分公式_第2张图片

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