Question

Find the indefinite integral. $$ \int \frac{5}{x} d x $$

Short answer

The integral of \( \int \frac{5}{x} dx \) is \( 5 \ln |x| + C \).

Step-by-step solution

Integration Rule Recall

The integral \(\int \frac{1}{x} dx \) is a standard integral that is equal to \( \ln |x| + C \), where C is the constant of integration. Thus, to find the integral of a function \( \int \frac{k}{x} dx \), where k is a constant, you multiply \( \ln |x| + C \) by k.

Applying the Scaling Factor

In this problem, the scaling factor (k) is 5. Hence, the integral of \( \int \frac{5}{x} dx \) equals \( 5 \cdot \ln |x| + C \).