∫ x²cos²x dx
=(1/2)∫ x²(1+cos2x) dx
=(1/2)∫ x² dx + (1/2)∫ x²cos2x dx
=(1/6)x³ + (1/4)∫ x² d(sin2x)
分部积分
=(1/6)x³ + (1/4)x²sin2x - (1/4)∫ 2xsin2x dx
=(1/6)x³ + (1/4)x²sin2x + (1/4)∫ x d(cos2x)
=(1/6)x³ + (1/4)x²sin2x + (1/4)xcos2x - (1/4)∫ cos2x dx
=(1/6)x³ + (1/4)x²sin2x + (1/4)xcos2x - (1/8)sin2x + C
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