【sin2xcos3xdx】∫sin2xcos3xdx等于多少
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解决时间 2021-02-06 08:38
- 提问者网友：送舟行
- 2021-02-05 22:04
【sin2xcos3xdx】∫sin2xcos3xdx等于多少
最佳答案
- 五星知识达人网友：第幾種人
- 2021-02-05 22:13
【答案】 先利用积化和差公式：
sin(A)cos(B) = (1/2)[sin(A+B) + sin(A-B)]
∴sin(2x)cos(3x) = (1/2)[sin(2x+3x) + sin(2x-3x)]
= (1/2)[sin5x + sin(-x)]
= (1/2)(sin5x - sinx)
∴∫ sin(2x)cos(3x) dx
= (1/2)∫ sin(5x) dx - (1/2)∫ sinx dx
= (1/2)(1/5)∫ sin(5x) d(5x) - (1/2)∫ sinx dx
= (1/10)(-cos(5x)] + (1/2)cosx + C
= (1/10)[5cosx - cos(5x)] + C
sin(A)cos(B) = (1/2)[sin(A+B) + sin(A-B)]
∴sin(2x)cos(3x) = (1/2)[sin(2x+3x) + sin(2x-3x)]
= (1/2)[sin5x + sin(-x)]
= (1/2)(sin5x - sinx)
∴∫ sin(2x)cos(3x) dx
= (1/2)∫ sin(5x) dx - (1/2)∫ sinx dx
= (1/2)(1/5)∫ sin(5x) d(5x) - (1/2)∫ sinx dx
= (1/10)(-cos(5x)] + (1/2)cosx + C
= (1/10)[5cosx - cos(5x)] + C
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- 1楼网友：深街酒徒
- 2021-02-05 23:53
回答的不错
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