解：令arcsinx=t，则x=sint∫(arcsinx)²dx=∫t²d(sint)=t²·sint-∫sintd(t²)=t²·sint-2∫tsintdt=t²·sint+2∫td(cost)=t²·sint+2tcost-2∫costdt=t²·sint+2tcost-2sint +C=x·(arcsinx)²+2√(1-x²)·arcsinx-2x +C
