企源知识库

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