解：令x=asint，则dx=acost dt∫x²/√(a²-x²) dx=∫a²sin²t/(acost)·acostdt=a²∫sin²t dt=a²∫(1-cos2t)/2 dt=a²∫1/2dt-a²∫cos2tdt=a²t/2-1/2·a²sin2t+C=1/2·a²arcsin(x/a)-x·√(a²-x²)+C
