令 x-t = u， 则 t = x-u， dt = -dulim∫(上x, 下0) (x-t)^a e^(-t)dt/x^(a+1)= lim∫(上0, 下x) u^a e^(u-x)(-du)/x^(a+1)= lim∫(上x, 下0) u^a e^udu/[(e^x)x^(a+1)] = lim∫(上x, 下0) u^a e^udu/x^(a+1) (0/0)= limx^a e^x/[(a+1)x^a] = lime^x/(a+1) = 1/(a+1)
希望有所帮助，望采纳哦
