First of all, we should know a conclusion: ∫ [-∞→ +∞] e (-x? )dx=√π。 For the specific calculation method, please refer to an example in the polar coordinate part of double integral in the second volume of advanced mathematics textbook of Tongji University.

e^(ix？ )dx

=e^(-i)∫ e^i*e^(ix？ )dx

=e^(-i)∫ e^(-x？ )dx

=√πe^(-i)

=√π(cos 1-isin 1)

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