## Borel resummation of an integral

let be the integral $$\int_{0}^{\infty}dxf(x)e^{ix}$$

from the technique of Borel resummation applied to series , would it be corect to assign the 'Borel resummation' for the integral above as

$$\int_{0}^{\infty}\int_{0}^{\infty}dtdx \frac{t^{x}f(x)e^{ix-t}}{\Gamma (x+1)}$$
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