Pi和e的積分

Evaluate integral $$\int_{0}^{1}{x^{-x}(1-x)^{x-1}\sin{\pi x}dx}$$ Well,I think we have $$\int_{0}^{1}{x^{-x}(1-x)^{x-1}\sin{\pi x}dx}=\frac{\pi}{e}$$   and   $$\int_{0}^{1}{x^{x}(1-x)^{1-x}\sin{\pi x

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