∫(x-1)/√(1-4x^2)dx

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/22 16:05:37
∫(x-1)/√(1-4x^2)dx∫(x-1)/√(1-4x^2)dx∫(x-1)/√(1-4x^2)dx令x=(1/2)sit,则I=∫[(x-1)/√(1-4x^2)]dx=(1/2)∫[(1/

∫(x-1)/√(1-4x^2)dx
∫(x-1)/√(1-4x^2)dx

∫(x-1)/√(1-4x^2)dx
令 x=(1/2)sit, 则
I =∫[(x-1)/√(1-4x^2)]dx = (1/2)∫[(1/2)sint-1]dt = -(1/2)[(1/2)cost+t]+C
= -(1/4)[√(1-4x^2)+2arcsin(2x)]+C