OK
∫udv=uv-∫vdu知道吧
这里：udv=xdx,v=(1/2)x^2
所以：原式=[(1/2)x^2]ln(x-1)-(1/2)∫(x^2dln(x-1)
=[(1/2)x^2]ln(x-1)-(1/2)∫(x^2)/(x-1)dx
=[(1/2)x^2]ln(x-1)-(1/2)∫[(x+1)(x-1)+1]/(x-1)dx
=[(1/2)x^2]ln(x-1)-(1/2)∫[(x+1)dx+∫1/(x-1)dx
=[(1/2)x^2]ln(x-1)-(1/4)(x+1)^2+ln(x-1)
敲了半天,能采纳?