x^3/[根号(1-x^2)]不定积分

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x^3/[根号(1-x^2)]不定积分x^3/[根号(1-x^2)]不定积分x^3/[根号(1-x^2)]不定积分∫x^3/√(1-x^2)dxletx=sinydx=cosydy∫x^3/√(1-x

x^3/[根号(1-x^2)]不定积分
x^3/[根号(1-x^2)]不定积分

x^3/[根号(1-x^2)]不定积分
∫x^3/√(1-x^2) dx
let
x= siny
dx = cosydy
∫x^3/√(1-x^2) dx
= ∫(siny)^3 dy
= -∫(siny)^2 dcosy
= -∫[1-(cosy)^2] dcosy
= (cosy)^3/3 - cosy + C
=(1/3) (1-x^2)^(3/2) -(1-x^2)^(1/2) + C