原积分=∫[1-3cosx+3(cosx)^2-(cosx)^3]dx
=∫(1-3cosx)dx+3∫(cosx)^2dx-∫(cosx)^3dx
=x-3sinx+3/2∫(1+cos2x)dx-∫(cosx)^2dsinx
=x-3sinx+3/4∫cos2xd2x+3/2∫dx-∫[1-(sinx)^2]dsinx
=5/2×x-4sinx+3/4×sin2x+1/3×(sinx)^3+C.