根据原函数的定义,就是求F(x)=∫f(x)dx∫xsin²xdx=∫x(1-cos2x)/2dx=x²-1/2∫xcos2xdx其中∫xcos2xdx=1/2xsin2x-1/2∫sin2xdx=1/2xsin2x+1/4cos2x+C则原式=x²-1/4xsin2x-1/8cos2x+C