求不定积分∫xsin²xdx　在线等

求不定积分∫xsin²xdx　在线等
求不定积分∫xsin²xdx　在线等

求不定积分∫xsin²xdx　在线等
∫xsin²xdx=(1/2)∫x(1-cos2x)dx=(1/2)∫xdx-(1/2)∫ xcos2xdx
=(1/4)x^2-(1/4)∫ xd(sin2x)=(1/4)x^2-(1/4)xsin2x+(1/4)∫ (sin2x)dx
=(1/4)x^2-(1/4)xsin2x-(1/8)cos2x+C