48. $\int \frac{2 d x}{x}$.

48. $\int \frac{2 d x}{x}$. 

(Note: The mathematical expression is the same in both languages, so it remains unchanged.)
Solution. Applying property 2 and formula 11, we find

$$
\int \frac{2 d x}{x}=2 \int \frac{d x}{x}=2 \ln |x|+C
$$

Verification: $\quad d(2 \ln x+C)=2 \cdot \frac{1}{x} d x=\frac{2 d x}{x}$. We obtained the integrand; therefore, the integral is found correctly.