Indefinite Integrals

Let \(I(x)=\int \sqrt{\frac{x+7}{x}} \mathrm{~d} x\) and \(I(9)=12+7 \log _{e} 7\). If \(I(1)=\alpha+7 \log _{e}(1+2 \sqrt{2})\), then \(\alpha^{4}\) is equal to _________.