Integrate the function $\frac{(x+1)(x+\log x)^{2}}{x}$.

(N/A) The given function can be rewritten as:
$\frac{(x+1)(x+\log x)^{2}}{x} = \left(1+\frac{1}{x}\right)(x+\log x)^{2}$.
Let $t = x + \log x$.
Then,differentiating with respect to $x$,we get $dt = (1 + \frac{1}{x}) dx$.
Substituting these into the integral,we have:
$\int (x + \log x)^{2} (1 + \frac{1}{x}) dx = \int t^{2} dt$.
Integrating $t^{2}$ with respect to $t$ gives $\frac{t^{3}}{3} + C$.
Substituting back $t = x + \log x$,the final result is $\frac{1}{3}(x + \log x)^{3} + C$,where $C$ is an arbitrary constant.