Let f:[1,∞)→Rf:[1,\infty) \to Rf:[1,∞)→R be a differentiable function defined as f(x)=∫1xf(t)dt+(1−x)(logex−1)+ef(x)=\int\limits_{1}^{x} f(t) dt+(1-x)(\log_e x-1)+ef(x)=1∫xf(t)dt+(1−x)(logex−1)+e. Then the value fo f(f(1))f(f(1))f(f(1)) is :
(1+ee)(1+e^e)(1+ee)
(1+e)(1+e)(1+e)
(1+e+ee)(1+e+e^e)(1+e+ee)
1+2e1+2e1+2e