∫xdx/(1-x)^3

题目详情

∫xdx/(1-x)^3

▼优质解答

答案和解析

∫xdx/(1-x)^3
=-∫xdx/(x-1)^3
=-∫xd(x-1)/(x-1)^3
=1/2∫xd[1/(x-1)^2 ]
=x/[2(x-1)^2] -1/2∫1/(x-1)^2dx
=x/[2(x-1)^2] -1/2∫1/(x-1)^2d(x-1)
=x/[2(x-1)^2] +1/[2(x-1)] +C

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