Let \(f: \mathbb {R^+\to R}\) be an infinitely differentiable 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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by
abdulmuttalib lokhandwala
