Convex? (Solved)

Summary: For each $N \in \NN$ define the function $f_N: \RR_+^N \to \RR_+$ by $f_N(x_1, \ldots, x_N) := \int_0^1 (1 - \prod_{i=1}^N (1-t^{x_i})) dt/t$. It is desired to know whether $f_N$ is convex.

Classification: Primary, classical analysis; Secondary, convex functions

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