試題詳解

18. Let g( x ) be the inverse function of the function f ( x )= xe^x , where x ≥ 0, i.e., g(f(x)) = x, and f(g(x)) = x for x ≥ 0. Which of the following items is the value of the integral ?
(A) e – 1
(B) 1
(C) e
(D) 1 + ln 2
(E) e ² – 1