∫ (1-x)/√(4-9x²) dx,令x = (2/3)sinβ,dx = (2/3)cosβ dβ
√(4-9x²) = √(4-4sin²β) = 2cosβ.sinβ = 3x/2,cosβ = √(4-9x²) / 2
原式= (1/3)∫ (1-2/3sinβ) dβ
= (1/3)∫ dβ - (2/9)∫ sinβ dβ
= (1/3)β - (2/9)(-cosβ) + C
= (1/3)arcsin(3x/2) + (2/9)*√(4-9x²) / 2 + C
= (1/3)arcsin(3x/2) + (1/9)√(4-9x²) + C