Let \(f\left(x\right)=\int \left(\frac{16x+24}{{x}^{2}+2x-15}\right)dx\). If \(f(4)=14{\log }_{e}(3)\) and \(f(7)={\log …

Let \(f\left(x\right)=\int \left(\frac{16x+24}{{x}^{2}+2x-15}\right)dx\). If \(f(4)=14{\log }_{e}(3)\) and \(f(7)={\log }_{e}\left({2}^{\alpha }{3}^{\beta }\right)\), \(\alpha ,\beta \in N\), then \(\alpha +\beta\) is equal to:

[JEE Main 2026, 2 Apr (Shift 2)]