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## Main Question or Discussion Point

Is it possible to do integrals like this with eulers formula

[itex] \int e^{-x^2}cos(-x^2) [/itex]

and this integral is over all space.

then we write [itex] e^{-x^2}e^{-ix^2} [/itex]

then can we square that integral and then do it in polar coordinates, and then we will eventually take the square root

of our answer. But it seems like we would need to take the real part at some point.

Is this a right path to take?

[itex] \int e^{-x^2}cos(-x^2) [/itex]

and this integral is over all space.

then we write [itex] e^{-x^2}e^{-ix^2} [/itex]

then can we square that integral and then do it in polar coordinates, and then we will eventually take the square root

of our answer. But it seems like we would need to take the real part at some point.

Is this a right path to take?