NVAMediumJEE Main 2023 · 12 April, Shift 1Indefinite Integrals

Mathematics Question from JEE Main 2023 · 12 April, Shift 1

Let I(x)I(x) = x+7xdx\int \sqrt{\frac{x+7}{x}} \, dx and I(9)=12+7loge7I(9) = 12 + 7 \log_e 7. If I(1)=α+7loge(1+22)I(1) = \alpha + 7 \log_e (1+2\sqrt{2}), then α4\alpha^4 is equal to:

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