∫1/(1+cos^2(x)) dx

来源：学生作业帮助网编辑：作业帮时间：2024/11/06 08:54:41

∫1/(1+cos^2(x)) dx
∫1/(1+cos^2(x)) dx

∫1/(1+cos^2(x)) dx
∫dx/{1+[cos(x)]^2}
= ∫[sec(x)]^2dx/{1+[sec(x)]^2}
= ∫[sec(x)]^2dx/{2+ [tan(x)]^2}
= ∫2^(-1/2)d[tan(x)/2^(1/2)]/{1+ [tan(x)/2^(1/2)]^2}
= 2^(-1/2)arctan[tan(x)/2^(1/2)] + C
C 为任意常数.

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