求下列不定积分：∫sinxcosxdx．

求下列不定积分：∫sinxcosxdx．
【正确答案】：∫xsinxcosxdx=1/2∫xsin2xdx=-(1/4)∫xd(cos2x)=-(1/4)(xcos2x-∫cos2xdx)=-(1/4)(xcos2x-1/2sin2x)+c=1/8(sin2x-2xcos2x)+c．