Deducing From The Integral

Calculus Level 5

A differentiable function $$f$$ is defined on the positive real numbers such that

$\int_{1}^{xy} f(t) \, dt = y\int_{1}^{x} f(t) \, dt + x\int_{1}^{y} f(t) \, dt.$

If $$f(1) = 3$$, what is $$f(e)$$?

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