∫x* ln (x-1) dx

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∫x* ln (x-1) dx
∫x* ln (x-1) dx

∫x* ln (x-1) dx
用分部积分法：
∫x*ln(x-1)dx
=1/2∫xln(x-1)dx^2
=1/2x^2ln(x-1)-1/2∫x^2dln(x-1)
=1/2x^2ln(x-1)-1/2∫x^2/(x-1)dx
=1/2x^2ln(x-1)-1/2∫(x^2-1+1)/(x-1)dx
=1/2x^2ln(x-1)-1/2∫[x+1+1/(x-1)]dx
=1/2x^2ln(x-1)-1/4x^2-x/2-1/2ln(x-1)+C

∫(ln ln x + 1/ln x)dx ∫x*ln(x²+1)dx ∫x*ln(x-1)dx ∫x* ln (x-1) dx 求不定积分?∫ ln(x+1) dx 求积分：∫-ln(1-x)dx ∫ln(1+x²)dx ∫ln(1+x^2)dx ∫ln(1+√x)dx ∫ ln(x^2 -1)dx 步骤 ∫ln(x+1)dx怎么解 ∫[ln(lnx)]dx／x ∫[ln(lnx)]dx／x {∫[ln(lnx)／x]}dx ∫ln(x/2)dx ∫[ln(1+x)-lnx]/x(1+x)dx ∫[ln(x+1)-lnx]/x(x+1) dx ∫1+x^2 ln^2x / x lnx dx