次数那么高,明显要降次啦
原式=∫[1-(cosx)^2]^2*sinxdx
=-∫[1-(cosx)^2]^2d(cosx)
令t=cosx,则原式=-∫(1-t^2)^2dt
=-∫(t^4-2t^2+1)dt
=-(1/5)t^5+(2/3)t^3-t+C
=-(1/5)(cosx)^5+(2/3)(cosx)^3-cosx+C