Let \(f\left(x\right)=\int \frac{dx}{{x}^{\left(\frac{2}{3}\right)}+2{x}^{\left(\frac{1}{2}\right)}}\) be such that \(f\…

Let \(f\left(x\right)=\int \frac{dx}{{x}^{\left(\frac{2}{3}\right)}+2{x}^{\left(\frac{1}{2}\right)}}\) be such that \(f\left(0\right)=−26+24\text{ }{\log }_{e}\left(2\right).\)If \(f\left(1\right)=a+b\text{ }{\log }_{e}\left(3\right),\) where \(a,b\in Z,\) then \(a+b\) is equal to:

[JEE Main 2026, 28 Jan (Shift 2)]