tanx/2求不定积分
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tanx/2求不定积分
![tanx/2求不定积分](/uploads/image/z/17285676-60-6.jpg?t=tanx%2F2%E6%B1%82%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86)
∫tan(x/2) dx
= 2∫sin(x/2)/cos(x/2) d(x/2)
= -2∫1/cos(x/2) d[cos(x/2)]
= -2ln|cos(x/2)| + C
= 2ln|sec(x/2)| + C
= 2∫sin(x/2)/cos(x/2) d(x/2)
= -2∫1/cos(x/2) d[cos(x/2)]
= -2ln|cos(x/2)| + C
= 2ln|sec(x/2)| + C
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