∫lnxdx/x^3
=-1/2∫lnxd(1/x^2)
=-1/2lnx/x^2+1/2∫1/x^2dlnx
=-1/2lnx/x^2+1/2∫1/x^3dx
=-1/2lnx/x^2-1/4*1/x^2+C