众所周知,反三角函数的不定积分是比较麻烦的,这是多少年以来的难题,连递推公式都没有,在国内所能看到的国内外数学手册中也没有。这里初步提出四个定理,愿与读者一同来探讨这个问题。定理一:反正弦函数的不定积分(arcsinz)~ndz等于一个变量t的两个相关数式t~0与sint之积,及其连续导数积之和。 As we all know, the indefinite integral of the anti-trigonometric function is rather troublesome. This is a problem that has lasted for many years. There are no formulas for recursion. There are no math manuals that can be seen domestically at home. Here initially proposed four theorems, is willing to work with readers to explore this issue. Theorem 1: The arcsinz ~ ndz of an arcsine function is equal to the sum of the product of two correlated numbers t ~ 0 and sint of a variable t, and its continuous derivatives.