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∫(下限π/4,上限π/3)x/sinx^2dx用分部几分法

题目详情
∫(下限π/4,上限π/3)x/sinx^2 dx 用分部几分法
▼优质解答
答案和解析
∫(下限π/4,上限π/3)x/sinx^2 dx =-∫(下限π/4,上限π/3)xdcotx =-xcotx (下限π/4,上限π/3)+∫(下限π/4,上限π/3)cotxdx=(根号3/9-1/4)π+ln|sinx|(下限π/4,上限π/3)=(根号3/9-1/4)π+1/2ln(2/3)
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