1.

Let f:R^(+)to R be a differentiable function satisfyingf(x) f(x)=e+(1-x)ln((x)/(e ))+int_(1)^(x)f(t)dt AA x in R^(+). If the area enclosed by the curve g(x)=x[f(x)-e^(x)] lying in the fourth quadrant is A, then find the value ofA^(-2).

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