# How to calculate $\int_0^1e^{i \pi x}x^x(1-x)^{(1-x)}dx$=? [duplicate]

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.