Evaluating function with integral

Calculus Level 3

If f(x)f(x) is a function defined for all positive real numbers such that xf(x)= x+1xf(t)dt,xf(x)=\ x+\int_{1}^{x} f(t)dt, what is k=110f(ek)?\sum_{k=1}^{10} f(e^k)?

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