Answer
$$x + \ln \left| x \right| + C$$
Work Step by Step
$$\eqalign{
& \int {\frac{{x + 1}}{x}} dx \cr
& {\text{split the numerator}} \cr
& = \int {\left( {\frac{x}{x} + \frac{1}{x}} \right)} dx \cr
& = \int {\left( {1 + \frac{1}{x}} \right)} dx \cr
& {\text{sum rule}} \cr
& = \int {dx} + \int {\frac{1}{x}} dx \cr
& {\text{integrating}} \cr
& = x + \ln \left| x \right| + C \cr} $$
