利用反函数求不定积分

Indefinite Integral by Inverse Function

若函数y=f（x）的反函数x=f-1（y）存在且可积，则有此公式将求f（X）的不定积分转化为求其反函数f-1（y）的不定积分．待积出之后，再用直接函数表示．更一般地，若g（X）的一个原函数G（X）易求且y=f（X）的反函数X=f-1（y）好解出来，则进一步可得到积分的法则．

The indefinite integral of a function y=f(x) can be expressed by the following equation, if and only if,the function's inverse function x=f-1 (y) exists and can be integrated Which transforms the indefinite integral of the function f(x) to integrate its inverse function f-1(y).After integrated the inverse function, using equation y = f(x) to express the integral in variable x.In general, if the primitive function G(x) of function g(x) is easy to get and the inverse function x=f-1 (y) of function y=f(x) is easy to solve, then