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Let f:[1,oo) to RR be a differentiable f...

Let `f:[1,oo) to RR` be a differentiable function such that `f(1)=1/3` and `3 int_1 ^x f(t) dt = x f(x) -x^3/3 , x in [1,oo)`. Let `e` denote the base of the natural logarithm. Then the value of `f(e)` is

A

`(e^2+4)/3`

B

`(log_e 4 +e) /3`

C

`(4e^2)/3`

D

`(e^2-4)/3`

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