簡介
積分的計算要比導數的計算靈活、複雜,為了實用的方便,往往把常用的積分公式匯集成表,這種表叫作積分表。求積分時,可根據被積函式的類型,在積分表內查得其結果,有時還要經過簡單變形才能在表內查得所需的結果 。
內容分類
積分表被分為以下幾個部分 :
•有理函式積分表
•無理函式積分表
•三角函式積分表
•指數函式積分表
•對數函式積分表
•反三角函式積分表
•雙曲函式積分表
•反雙曲函式積分表
具體內容
![積分表](/img/2/bc3/wZwpmLwYjMyYDNyczM2EzM1UTM1QDN5MjM5ADMwAjMwUzL3MzLzQzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
(1)含有 的積分 :
![積分表](/img/e/84c/wZwpmL1ITM2QDM0czM2EzM1UTM1QDN5MjM5ADMwAjMwUzL3MzL2AzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![積分表](/img/9/644/wZwpmL2UTM4UjNzADN2EzM1UTM1QDN5MjM5ADMwAjMwUzLwQzL4MzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![積分表](/img/2/b09/wZwpmL4QTN3kTM4IzM2EzM1UTM1QDN5MjM5ADMwAjMwUzLyMzL2gzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![積分表](/img/d/592/wZwpmL1UzM5gTNzQzM2EzM1UTM1QDN5MjM5ADMwAjMwUzL0MzL4czLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![積分表](/img/e/909/wZwpmL2ITMzQzNzQTM2EzM1UTM1QDN5MjM5ADMwAjMwUzL0EzLyMzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![積分表](/img/1/aff/wZwpmLxADNyQjN3IzM2EzM1UTM1QDN5MjM5ADMwAjMwUzLyMzL4AzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
(2)含有 的積分 :
![積分表](/img/7/70e/wZwpmL1ETMzkTN2EDN2EzM1UTM1QDN5MjM5ADMwAjMwUzLxQzLygzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![積分表](/img/f/af2/wZwpmL3MjN0QTM3AjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLwIzL3QzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![積分表](/img/c/42e/wZwpmLyMDNzcjN4MzM2EzM1UTM1QDN5MjM5ADMwAjMwUzLzMzLwczLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![積分表](/img/3/9ef/wZwpmLyUDN1IDO4YzM2EzM1UTM1QDN5MjM5ADMwAjMwUzL2MzL1IzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![積分表](/img/5/77e/wZwpmLzYjM3MTN3gTM2EzM1UTM1QDN5MjM5ADMwAjMwUzL4EzLzQzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![積分表](/img/2/cdf/wZwpmLyczMxczN4QTM2EzM1UTM1QDN5MjM5ADMwAjMwUzL0EzL0YzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![積分表](/img/2/763/wZwpmL3QjNwEDO4IzM2EzM1UTM1QDN5MjM5ADMwAjMwUzLyMzLzUzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![積分表](/img/6/623/wZwpmLxgzN5gjM0YzM2EzM1UTM1QDN5MjM5ADMwAjMwUzL2MzLzMzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
(3)含有 的積分 :
![積分表](/img/b/e9c/wZwpmLxYzNwIDNxQzM2EzM1UTM1QDN5MjM5ADMwAjMwUzL0MzL4QzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![積分表](/img/a/97d/wZwpmLyUDMycjMxIjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLyIzLyAzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![積分表](/img/6/344/wZwpmLyEjM4QjN3QTM2EzM1UTM1QDN5MjM5ADMwAjMwUzL0EzLwUzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
(4)含有 的積分 :
![積分表](/img/c/c98/wZwpmLwEjN5EzM1gTM2EzM1UTM1QDN5MjM5ADMwAjMwUzL4EzL3MzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![積分表](/img/1/0f0/wZwpmL3cjM5kDMwQDN2EzM1UTM1QDN5MjM5ADMwAjMwUzL0QzL4UzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
(5)含有 的積分 :
![積分表](/img/5/765/wZwpmL1czN5kzM2gTM2EzM1UTM1QDN5MjM5ADMwAjMwUzL4EzLzczLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![積分表](/img/0/fcb/wZwpmLzgTM0MzN2EDN2EzM1UTM1QDN5MjM5ADMwAjMwUzLxQzL3czLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
(6)含有 的積分 :
![積分表](/img/1/4d2/wZwpmL0MTO2YTM2QzM2EzM1UTM1QDN5MjM5ADMwAjMwUzL0MzLzAzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![積分表](/img/9/482/wZwpmL0IjN1cjMwQDN2EzM1UTM1QDN5MjM5ADMwAjMwUzL0QzLyUzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![積分表](/img/2/03e/wZwpmL3YjM5gDO4UzM2EzM1UTM1QDN5MjM5ADMwAjMwUzL1MzL1IzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![積分表](/img/2/e93/wZwpmL3IzNxcTO2czM2EzM1UTM1QDN5MjM5ADMwAjMwUzL3MzL0YzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![積分表](/img/f/ef4/wZwpmL2YTM2kzN3IjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLyIzL1IzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![積分表](/img/7/28f/wZwpmLxYzN4IzM3czM2EzM1UTM1QDN5MjM5ADMwAjMwUzL3MzLwIzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![積分表](/img/2/137/wZwpmLzETN2MTN0ADN2EzM1UTM1QDN5MjM5ADMwAjMwUzLwQzL1QzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![積分表](/img/8/ddf/wZwpmLxEDO3kjM3gzM2EzM1UTM1QDN5MjM5ADMwAjMwUzL4MzL4AzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
(7)含有 的積分 :
![積分表](/img/8/067/wZwpmLzQjM2ATOwcTM2EzM1UTM1QDN5MjM5ADMwAjMwUzL3EzLwEzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![積分表](/img/3/eef/wZwpmLzcDM0gjM3gzM2EzM1UTM1QDN5MjM5ADMwAjMwUzL4MzLwAzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
(8)含有 的積分 :
![積分表](/img/2/a5c/wZwpmLzcDOzYzN5EjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLxIzL3AzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![積分表](/img/7/6bc/wZwpmL3IDM2kTM3QzM2EzM1UTM1QDN5MjM5ADMwAjMwUzL0MzL2QzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![積分表](/img/0/dfb/wZwpmLzUjMzkTM3UzM2EzM1UTM1QDN5MjM5ADMwAjMwUzL1MzLwQzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![積分表](/img/8/a51/wZwpmLwEjMxEzM0ADN2EzM1UTM1QDN5MjM5ADMwAjMwUzLwQzLxQzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![積分表](/img/c/6a2/wZwpmLyYDM5cDOxQTM2EzM1UTM1QDN5MjM5ADMwAjMwUzL0EzL1MzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![積分表](/img/3/58b/wZwpmL2cTO4IDO2EzM2EzM1UTM1QDN5MjM5ADMwAjMwUzLxMzLzUzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![積分表](/img/3/2f7/wZwpmL3ETM0QTO4czM2EzM1UTM1QDN5MjM5ADMwAjMwUzL3MzLzIzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![積分表](/img/c/733/wZwpmLwYDN0ADOzgTM2EzM1UTM1QDN5MjM5ADMwAjMwUzL4EzL4EzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
(9)含有 的積分 :
![積分表](/img/d/6f1/wZwpmLygTMwYTNzQTM2EzM1UTM1QDN5MjM5ADMwAjMwUzL0EzL3UzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![積分表](/img/0/011/wZwpmLwQTMzYjN3IjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLyIzL4IzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![積分表](/img/5/2dd/wZwpmL0QTMzcDMwUzM2EzM1UTM1QDN5MjM5ADMwAjMwUzL1MzLwQzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![積分表](/img/c/bbb/wZwpmLxUDNyYTO4AjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLwIzLwgzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![積分表](/img/7/823/wZwpmL4cTMygjMyYjM2EzM1UTM1QDN5MjM5ADMwAjMwUzL2IzLwMzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![積分表](/img/2/c82/wZwpmL3AzM0gTN2IDN2EzM1UTM1QDN5MjM5ADMwAjMwUzLyQzLyYzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![積分表](/img/c/dfa/wZwpmLwczN2YTOyQDN2EzM1UTM1QDN5MjM5ADMwAjMwUzL0QzL0IzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![積分表](/img/5/b42/wZwpmLzgjN1QDO0IDN2EzM1UTM1QDN5MjM5ADMwAjMwUzLyQzL0MzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![積分表](/img/1/c53/wZwpmL4AzNzEDOxEDN2EzM1UTM1QDN5MjM5ADMwAjMwUzLxQzL3AzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![積分表](/img/5/9ce/wZwpmL0MTO3IDOzEDN2EzM1UTM1QDN5MjM5ADMwAjMwUzLxQzL3EzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![積分表](/img/9/44d/wZwpmLxUjNzkzN5czM2EzM1UTM1QDN5MjM5ADMwAjMwUzL3MzLzQzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
(10)含有三角函式的積分 :
![積分表](/img/f/b7d/wZwpmL0AjN3ADO1QTM2EzM1UTM1QDN5MjM5ADMwAjMwUzL0EzLyAzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![積分表](/img/a/0a7/wZwpmL0cTO1gTNyMjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLzIzLyQzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![積分表](/img/6/8e5/wZwpmLyEjNzkDN0YzM2EzM1UTM1QDN5MjM5ADMwAjMwUzL2MzL1UzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![積分表](/img/b/23e/wZwpmLxMjMyYTN3EjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLxIzL3UzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![積分表](/img/1/4c9/wZwpmL2cjN4QTN3AjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLwIzLwYzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![積分表](/img/a/966/wZwpmLwIDN5ADN2UjM2EzM1UTM1QDN5MjM5ADMwAjMwUzL1IzLzUzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![積分表](/img/0/f07/wZwpmL1gDMzkDNzIDN2EzM1UTM1QDN5MjM5ADMwAjMwUzLyQzL0IzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![積分表](/img/f/0f6/wZwpmLyUzN5YTM0EjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLxIzL1IzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![積分表](/img/8/cef/wZwpmL4ETO2gTN3MzM2EzM1UTM1QDN5MjM5ADMwAjMwUzLzMzLzUzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![積分表](/img/a/5de/wZwpmLzUjN1ITN3YTM2EzM1UTM1QDN5MjM5ADMwAjMwUzL2EzL1QzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![積分表](/img/8/c06/wZwpmL4UzM2EDO4UzM2EzM1UTM1QDN5MjM5ADMwAjMwUzL1MzLyczLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![積分表](/img/0/257/wZwpmL0gjM4EDO3EjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLxIzL4YzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![積分表](/img/6/2cb/wZwpmL1QDNwkzM1UzM2EzM1UTM1QDN5MjM5ADMwAjMwUzL1MzLzIzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![積分表](/img/9/aa3/wZwpmL0EjN5ITNwIjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLyIzLwQzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![積分表](/img/f/ede/wZwpmLxADOyQTO0kzM2EzM1UTM1QDN5MjM5ADMwAjMwUzL5MzLwQzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![積分表](/img/2/05f/wZwpmLzMTNwcTN3MzM2EzM1UTM1QDN5MjM5ADMwAjMwUzLzMzLzIzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![積分表](/img/4/3f2/wZwpmL1YTO0ITOzQTM2EzM1UTM1QDN5MjM5ADMwAjMwUzL0EzL4QzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![積分表](/img/9/168/wZwpmLzMTO0MjM4MzM2EzM1UTM1QDN5MjM5ADMwAjMwUzLzMzL3YzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![積分表](/img/4/258/wZwpmL4EzM3MTO5MjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLzIzLygzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
(11)含有反三角函式的積分 :
![積分表](/img/5/6d5/wZwpmL0UzN3ETO1EDN2EzM1UTM1QDN5MjM5ADMwAjMwUzLxQzL4gzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![積分表](/img/7/fc4/wZwpmL3gzNxEDO5kTM2EzM1UTM1QDN5MjM5ADMwAjMwUzL5EzL2AzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![積分表](/img/b/d30/wZwpmL3UjN3UjM1QTM2EzM1UTM1QDN5MjM5ADMwAjMwUzL0EzLwUzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![積分表](/img/4/f03/wZwpmLzYTO3ATO0IjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLyIzLzIzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![積分表](/img/2/286/wZwpmL0QjNzMzNwYjM2EzM1UTM1QDN5MjM5ADMwAjMwUzL2IzL1AzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
(12)含有指數函式的積分 :
![積分表](/img/9/492/wZwpmLyIDN0gzM2YTM2EzM1UTM1QDN5MjM5ADMwAjMwUzL2EzLygzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![積分表](/img/c/c62/wZwpmL1ITN5QDOyEjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLxIzL2YzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![積分表](/img/c/0c6/wZwpmL3gzNzUzN4EjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLxIzLxQzLt92YucmbvRWdo5Cd0FmLwE2LvoDc0RHa.jpg)
![積分表](/img/5/763/wZwpmL0EDO0ATM1kzM2EzM1UTM1QDN5MjM5ADMwAjMwUzL5MzLzAzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![積分表](/img/4/d33/wZwpmL0ETM0ETNxIzM2EzM1UTM1QDN5MjM5ADMwAjMwUzLyMzL4IzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
(13)含有對數函式的積分 :
![積分表](/img/3/db2/wZwpmLyIzN2czNzYTM2EzM1UTM1QDN5MjM5ADMwAjMwUzL2EzLxEzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![積分表](/img/4/1e6/wZwpmL0gTOwADN1IDN2EzM1UTM1QDN5MjM5ADMwAjMwUzLyQzL2IzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)
![積分表](/img/4/a8b/wZwpmLzAjM5kzMwYjM2EzM1UTM1QDN5MjM5ADMwAjMwUzL2IzLzQzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![積分表](/img/d/f64/wZwpmL1YTM2kDM4EjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLxIzLzUzLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
(14)含有雙曲函式的積分 :
![積分表](/img/f/c22/wZwpmLxMDMwMDM0EjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLxIzL0czLt92YucmbvRWdo5Cd0FmLzE2LvoDc0RHa.jpg)
![積分表](/img/f/cac/wZwpmL4gDMyUDO3EjM2EzM1UTM1QDN5MjM5ADMwAjMwUzLxIzL2czLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![積分表](/img/4/ad0/wZwpmL3cDO3gTN2gzM2EzM1UTM1QDN5MjM5ADMwAjMwUzL4MzL4IzLt92YucmbvRWdo5Cd0FmLyE2LvoDc0RHa.jpg)
![積分表](/img/2/667/wZwpmLyQjMyEjMyUzM2EzM1UTM1QDN5MjM5ADMwAjMwUzL1MzL2YzLt92YucmbvRWdo5Cd0FmLxE2LvoDc0RHa.jpg)
![積分表](/img/2/89e/wZwpmLyUDM0gjN4YTM2EzM1UTM1QDN5MjM5ADMwAjMwUzL2EzLxgzLt92YucmbvRWdo5Cd0FmL0E2LvoDc0RHa.jpg)