用分步积分
∫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
用分步积分
∫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