将x换成a-x
0≤x≤1
-1≤-x≤0
a-1≤a-x≤a
∫(0 1)[e^x /(1+x)]dx
=∫(a-1 a)[e^(a-x)/[1+(a-x)]]dx
=∫(a-1 a)[(e^a)·e^(-x)/(-x+a+1)]dx
=(-e^a)∫(a-1 a) [e^(-x)/(x-a-1)]dx
∫(0 1)[e^x /(1+x)]dx=A
(-e^a)∫(a-1) a) [e^(-x)/(x-a-1)]dx=A
∫(a-1 a) [e^(-x)/(x-a-1)]dx=A/(-e^a)=-A/e^a
提示：本题的用意是用A表示后面的定积分,只要想办法构造后面的积分项就可以了.将x换成a-x后,原来的积分区间(0 1)变成了(a-1 a),后面的积分项也比较容易推出来.