x^2⼀(a^2-x^2)^1⼀2的不定积分是怎么求的?谢谢。

2025-03-06 20:16:34
推荐回答(1个)
回答1:

let
x=asiny
dx=acosy dy

∫x^2/√(a^2-x^2) dx
=a^2∫ (siny)^2 dy
=(a^2/2)∫ (1-cos2y) dy
=(a^2/2) [y-(1/2)sin2y] + C
=(a^2/2) [arcsin(x/a)- x/√(a^2-x^2)] + C