=∫(sinx）^2(cosx)^2(sinx)^2dx
=(1/4)∫(sin2x)^2(sinx)^2dx
=(1/4)(1/2)(1/2) ∫(1-cos4x)(1-cos2x)dx
=(1/16) ∫(1-cos4x-cos2x+cos4xcos2x)dx
=x/16-(1/16)(1/4)∫cos4xd(4x)-(1/16)(1/2)∫cos2xd(2x)+(1/16)(1/2) ∫(cos6x+cos2x)dx
=x/16-sin4x/64-sin2x/32+(1/32)(1/6)∫(cos6xd(6x)+(1/32)(1/2) ∫cos2xd(2x)
=x/16-sin4x/64-sin2x/32+sin6x/192+sin2x/64+C
=x/16-sin4x/64-sin2x/64+sin6x/192+C
注意:cos4xcos2x=cos6x/2+cos2x/2为积化和公式,