The integrating factor of the differential equation $\frac{dy}{dx} (x \log x) + y = 2 \log x$ is:

$\log x$

The correct answer is Option (2) → $\log x$ ##

The given differential equation is

$\frac{dy}{dx} (x \log x) + y = 2 \log x$

Rewrite the differential equation:

$\frac{dy}{dx} + \frac{y}{x \log x} = \frac{2}{x}$

The integrating factor is

$e^{\int \frac{dx}{x \log x}} = e^{\log(\log x)} = \log x$