Answer
$8 + \ln 3$
Work Step by Step
$$\eqalign{
& \int_1^3 {\left( {2x + \frac{1}{x}} \right)} dx \cr
& {\text{Integrate by using: }}\int {{x^n}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C{\text{ and }}\int {\frac{1}{x}} dx = \ln \left| x \right| + C \cr
& = \left[ {\frac{{2{x^2}}}{2} + \ln \left| x \right|} \right]_1^3 \cr
& = \left[ {{x^2} + \ln \left| x \right|} \right]_1^3 \cr
& {\text{Use The Fundamental Theorem of Calculus}},{\text{ Part 2}} \cr
& = \left[ {{{\left( 3 \right)}^2} + \ln \left| 3 \right|} \right] - \left[ {{{\left( 1 \right)}^2} + \ln \left| 1 \right|} \right] \cr
& {\text{Simplifying}} \cr
& = \left( {9 + \ln 3} \right) - \left( {1 + 0} \right) \cr
& = 8 + \ln 3 \cr} $$