∫dx/(sin²2x)=¼∫dx/(sin²x·cos²x)是如何推导的?为什么不是等于½∫dx/(sin²x·cos²x)?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/12 05:15:56
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∫dx/(sin²2x)=¼∫dx/(sin²x·cos²x)是如何推导的?为什么不是等于½∫dx/(sin²x·cos²x)?
∫dx/(sin²2x)=¼∫dx/(sin²x·cos²x)是如何推导的?
为什么不是等于½∫dx/(sin²x·cos²x)?
∫dx/(sin²2x)=¼∫dx/(sin²x·cos²x)是如何推导的?为什么不是等于½∫dx/(sin²x·cos²x)?
∵sin(2x)=2sinx*cosx (这是倍角公式)
∴sin²(2x)=(2sinx*cosx)²=4sin²x*cos²x
故∫dx/sin²(2x)=∫dx/(4sin²x*cos²x)=(1/4)∫dx/(sin²x*cos²x).