Integral over infinity of $F(x) = e^{ix}$ how to calculate integral of following function over infinity ?
$F(x) = e^{ix}$  ($i$ imaginary)
$$
\int\limits_{-\infty}^\infty e^{ix} \, dx
$$

$$\int_0^{\infty}e^{ix}dx=\left[\frac{e^{ix}}{i}\right|_0^{\infty}=\left[-ie^{ix}\right|_0^{\infty}=\left[ie^{ix}\right|^0_{\infty}=i-e^{i\infty}$$
this result not converge, are you sure the sign in the exponential is correct?
