更号下1减x分之x求积分
发布网友
发布时间：2022-04-22 22:59
共1个回答
热心网友
时间：2023-06-28 07:42
x-x^2 = 1/4 - (x- 1/2)^2
let
x-1/2 = (1/2) sinu
dx = (1/2) cosu
∫√[x/(1-x) ] dx
=∫x/√(x-x^2) dx
=∫ (1/2) ( 1+ sinu)
=(1/2) ( u- cosu ) + C
=(1/2) [ arcsin(2x-1) - 2√(x-x^2) ] + C
