Question
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 _________.
Correct Answer
64
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 _________.