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1−(1−x)1−xxx1-(1-x)^{1-x}x^x1−(1−x)1−xxx The curve looks like a semicircle with a radius 0.5.
Which is larger,∫011−(1−x)1−xxxdx\displaystyle\int_0^1 1-(1-x)^{1-x}x^x dx∫011−(1−x)1−xxxdx or π8\dfrac{\pi}88π?
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