An integrating factor of the differential equation: , where is a function of , , is , then is:

An integrating factor of the differential equation: $x \frac{dy}{dx} + y \cdot P = x \cdot e^x \cdot x^{-1/2} \log x$, where $P$ is a function of $x$, $x > 0$, is $(\sqrt{e})^{(\log x)^2}$, then $P$ is: