Consider the function $f(x) = x^{-\ln x}$. Let $U(x)$ be a function such that $U'(x) > 0$ and $U(x) < x$. Suppose that $\int_0^\infty U(f(x)) = T$. What function $U$ maximizes the quantity $\int_0^\infty \ln(U(f(x)))$?
2026-05-05 20:30:56.1778013056
Maximizing an Integral Quantity
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