5.令x=sinz,dx=cosz dz,cosz=√(1-x²)
∫ x²/√(1-x²) dx = ∫ sin²z*cosz/√(1-sin²z) dz
= ∫ sin²z*cosz/cosz dz
= ∫ sin²z dz
= (1/2)∫ (1-cos2z) dz
= (1/2)(z-1/2*sin2z) + C
= (1/2)z-1/2*sinz*cosz + C
= (1/2)arcsinx - 1/2*x*√(1-x²) + C
= (1/2)[arcsinx - x√(1-x²)] + C
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