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I need to calculate the following integral $$\int_0^1 e^{i \pi x}x^x(1-x)^{(1-x)} dx$$ I tried parts integration, but it became more complicated, using mathematica shows the result looks like a pure imaginary number.

Any help or hint will be Appreciated

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marked as duplicate by r9m, Clement C., Rohan, Community Dec 30 '16 at 9:42

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