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æ±â«e^x*cos2x dx
â«e^x*cos2x dx = (1/2)â«e^x d(sin2x)
= (1/2)(e^x)(sin2x) - (1/2)â«e^x*sin2x dx
= (1/2)(e^x)(sin2x) - (1/2)(-1/2)â«e^x d(cos2x)
= (1/2)(e^x)(sin2x) + (1/4)(e^x)(cos2x) - (1/4)â«e^x*cos2x dxï¼å°æåé£ä¸ªç§¯å移å°å·¦è¾¹å¾
(1+1/4)â«e^x*cos2x dx = (1/4)(e^x)(2sin2x+cos2x)
â«e^x*cos2x dx = (1/5)(e^x)(2sin2x+cos2x) + C
â«e^x*sin²x dx
= â«e^x*(1/2)(1-cos2x) dx
= (1/2)â«e^x dx - (1/2)â«e^x*cos2x dxï¼ä»£å
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= (1/2)(e^x) - (1/2)(1/5)(e^x)(2sin2x+cos2x) + C''
= (1/10)(e^x)(5-2sin2x-cos2x) + C''
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