∫1/sin(x/2)dx

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/11 00:23:52

∫1/sin(x/2)dx

∫1/sin(x/2)dx
=2∫csc(x/2)d(x/2)
=2∫sin(x/2)/(sin(x/2)^2)d(x/2)
=-2∫dcos(x/2)/(1-(cos(x/2))^2)
=ln|(1-cos(x/2))/(1+cos(x/2))|
=2ln|csc(x/2)-cot(x/2)|+C

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