不定积分：∫dx/(3+sin^2x)=

来源：学生作业帮编辑：搜搜考试网作业帮分类：数学作业时间：2024/08/09 00:18:56

∫dx/(3+sin^2x)=∫dx/(4-cos^2x)
∫dx/[2+cosx)][2-cosx]=
∫(1/4)/[2-cosx]+(1/4)/[2+cosx]dx=
(1/4)∫1/[2-cosx]+1/[2+cosx]dx=
(1/4){{2/3^(1/2)arctan{[(2+1)/(2-1)]^(1/2)tan(x/2)}}+{2/3^(1/2)arctan{[(2-1)/(2+1)]^(1/2)tan(x/2)}}}

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