答：
原积分
=1/2∫x^2sin2x dx
=-1/4∫x^2 d(cos2x)
=-1/4x^2cos2x+1/4∫cos2x d(x^2)
=-1/4x^2cos2x+1/2∫xcos2x dx
=-1/4x^2cos2x+1/4∫x d(sin2x)
=-1/4x^2cos2x+1/4xsin2x-1/4∫sin2x dx
=-1/4x^2cos2x+1/4xsin2x+1/8cos2x + C
疯狂了.癫狂了∫x^2sinxcosxdx千万不要跳步
答：
原积分
=1/2∫x^2sin2x dx
=-1/4∫x^2 d(cos2x)
=-1/4x^2cos2x+1/4∫cos2x d(x^2)
=-1/4x^2cos2x+1/2∫xcos2x dx
=-1/4x^2cos2x+1/4∫x d(sin2x)
=-1/4x^2cos2x+1/4xsin2x-1/4∫sin2x dx
=-1/4x^2cos2x+1/4xsin2x+1/8cos2x + C