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Let $f,g: R \rightarrow R$ be two positive increasing functions. Under what (non-trivial) conditions one can guarantee that $\int_{0}^{\infty}f'g dx\geq \int_{0}^{\infty}g'fdx$.

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Say, if $f/g$ is nondecreasing (plus something to take care of convergence), but that's way too strong.

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