解：令x=asint，则dx=acost dt ∫x²/√(a²-x²) dx=∫a²sin²t/(acost)·acost dt=a²∫sin²t dt=a²∫(1-cos2x)/2 dt=a²[t-1/4·sin2x]+C=a²[arcsin(x/a)-1/2·x/a·√(1-x²/x²)]+C
