Let \(f(x+y) = f(x) f(y)\), \(f(0) \neq 0\). If \(x^2 g(x) = \int_0^x (t^2 f(t) + t g(t)) \, dt\), then \(g(2)\) is equal to
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The functional equation \(f(x+y) = f(x)f(y)\) implies \(f(x) = a^x\). If no other information is given, check if \(f(x)=1\) (where $a=1$) simplifies the integral equation effectively.