Let I(x)=∫ √((x+7)/x) ~d x and I(9)=12+7 log e 7. If I(1)=α+7 log e (1+2 √(2)), then α⁴ is equal to _ _ _ _ _.

Integral Calculus: JEE Main 2023 Mathematics question

JEE Main 2023 · 12 Apr, Morning shift · Q34

JEE Main 202312 Apr, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

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 _________.

Your answerType your answer. Integers and decimals are accepted.