Let \(\mathrm{f}:[1,\infty )\to [2,\infty )\) be a differentiable function, If \(10{\int }_{1}^{x}f(\mathrm{t})\mathrm{d…

Let \(\mathrm{f}:[1,\infty )\to [2,\infty )\) be a differentiable function, If \(10{\int }_{1}^{x}f(\mathrm{t})\mathrm{dt}=5\mathrm{x}f(\mathrm{x})-{\mathrm{x}}^{5}-9\) for all \(\mathrm{x}\geq 1\), then the value of \(f(3)\) is :

[JEE Main 2025, 2 Apr (Shift 2)]