∫(x-1)/√(1-4x^2)dx

Question

如题所述

Answer 1

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