∫1/[x*(x-1)^2]dx=∫(x-(x-1))/[x*(x-1)^2]dx=∫1/(x-1)^2dx-∫1/[x*(x-1)]dx=∫1/(x-1)^2dx-(∫1/(x-1)-1/xdx)=∫1/(x-1)^2dx-∫dx/(x-1)+∫1/xdx=-1/(x-1)-ln(x-1)+lnx+C
