求不定积分∫xcos2xdx 求过程答案!谢谢!
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![求不定积分∫xcos2xdx 求过程答案!谢谢!](/uploads/image/z/13878316-28-6.jpg?t=%E6%B1%82%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86%E2%88%ABxcos2xdx+%E6%B1%82%E8%BF%87%E7%A8%8B%E7%AD%94%E6%A1%88%21%E8%B0%A2%E8%B0%A2%21)
求不定积分∫xcos2xdx 求过程答案!谢谢!
求不定积分∫xcos2xdx 求过程答案!谢谢!
求不定积分∫xcos2xdx 求过程答案!谢谢!
∫ xcos2x dx
= (1/2)∫ xcos2x d2x
= (1/2)∫ x dsin2x
= (1/2)xsin2x - (1/2)∫ sin2x dx
= (1/2)xsin2x - (1/2)(1/2)(-cos2x) + C
= (1/2)xsin2x + (1/4)cos2x + C
∫xcos2xdx =∫x2cos2xdx/2 =(xsin2x-∫sin2xdx)/2=(xsinx-∫2sin2xdx/2)/2=xsinx/2+cos2x/4
4sinx^2-2x^2