求limx→1{[∫1x(1-t+lnt)dt]/(x-3)3}

求limx→1{[∫1x(1-t+lnt)dt]/(x-3)3}
【正确答案】：limx→1∫0x{[(1-t+lnt)]dt/(x-1)3}=limx→1{(1-x+lnx)/[3(x-1)2} =limx→1{[-1+(1/x)]/[6(x-1)]}