Example 6. Find the integral $\int \frac{\ln x}{x} d x$.
Solution. Let

$$
\ln x=t
$$

then

$$
\frac{1}{x} d x=d t
$$

Therefore,

$$
\int \frac{\ln x}{x} d x=\int \ln x \frac{1}{x} d x=\int t d t=\frac{t^{2}}{2}+C=\frac{1}{2} \ln ^{2} x+C
$$