求不定積分∫xsin²;xdx線上等

求不定積分∫xsin²;xdx線上等

∫xsin²;xdx=(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