In the following exercises, verify by differentiation that $\int \ln x \, dx = x(\ln x - 1) + C$, then use appropriate changes of variables to compute the integral.
342. $\int x \ln x \, dx$ (Hint: $\int x \ln x \, dx = \frac{1}{2} \int x \ln (x^2) \, dx$)
343. $\int x^2 \ln (x^2) \, dx$
344. $\int \frac{\ln x}{x^2} dx$ (Hint: Set $u = \frac{1}{x}$.)
345. $\int \frac{\ln x}{\sqrt{x}} dx$ (Hint: Set $u = \sqrt{x}$.)
