用分部积分法求∫(xcosx）/[(sinx)^3]dx

题目详情

用分部积分法求∫(xcosx）/[(sinx)^3] dx

▼优质解答

答案和解析

∫(xcosx）/[(sinx)^3] dx
=∫x/[(sinx)^3] dsinx
=-1/2∫x d(1/sin^2x)
=-1/2x/sin^2x+1/2∫(1/sin^2x)dx
=-1/2x/sin^2x+1/2∫csc^2xdx
=-1/2x/sin^2x-1/2cotx+C

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