To integrate the given expression, we'll integrate each term separately:

1. Integrate \( \frac{1}{x} \) with respect to \( x \):

\( \int \frac{1}{x} \, dx = \ln|x| + C_1 \(

2. Integrate \( \cos(x) \) with respect to \( x \):

\( \int \cos(x) \, dx = \sin(x) + C_2 \(

Now, we add the constants of integration to the results from each term:

\( \int \left(\frac{1}{x} + \cos(x)\right) \, dx = \ln|x| + \sin(x) + C \(

Combining the terms, we get the final integral:

\( \int \left(\frac{1}{x} + \cos(x)\right) dx = \ln|x| + \sin(x) + k \(