求不定积分∫1/√(9-4x^2)dx=_数学解答

求不定积分∫1/√(9-4x^2)dx=

人气：234 ℃　时间：2020-02-05 17:52:02

解答

换元, 令u = 2x,
∫1/√(9-4x^2)dx = (1/2) ∫1/√(9- u^2) du
= (1/2) * arcsin(u/3) + C
= (1/2) * arcsin( 2x/3) + C