积分(1-lnx)d(x)/(x-lnx)^2

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积分(1-lnx)d(x)/(x-lnx)^2积分(1-lnx)d(x)/(x-lnx)^2积分(1-lnx)d(x)/(x-lnx)^2(x-lnx)''=1-1/x,∫[(1-lnx)/(x-lnx

积分(1-lnx)d(x)/(x-lnx)^2
积分(1-lnx)d(x)/(x-lnx)^2

积分(1-lnx)d(x)/(x-lnx)^2
(x-lnx) ' = 1 - 1/x,
∫ [(1- lnx) / (x-lnx)^2 ] dx = ∫ [(x- lnx) - x * (1 - 1/x) ] /(x-lnx)^2 ] dx
= ∫ (-x) * (1 - 1/x) / (x-lnx)^2 ] dx + ∫ 1/(x- lnx) dx
= ∫ x d [1/(x-lnx)] + ∫ 1/(x- lnx) dx
= x / (x-lnx) - ∫ 1/(x- lnx) dx + ∫ 1/(x- lnx) dx
= x / (x-lnx) + C