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Calculus Level 4

Let \(f: \mathbb {R^+\to R}\) be a differential function with \(f(1) = 3\) and satisfying

\[\large \int _{ 1 }^{ xy }f(t) \ dt = y\int _{ 1 }^{ x } f( t) \ dt + x\int _{ 1 }^{ y } f( t) \ dt\]

Find \(f(e)\).

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