Answer
$$\ln \left( {\frac{2}{3}} \right)$$
Work Step by Step
$$\eqalign{
& \int_{ - 3}^{ - 2} {\frac{{dx}}{x}} \cr
& {\text{integrate using the rule }}\int {\frac{1}{x}} dx = \ln \left| x \right| + C{\text{; then}}{\text{,}} \cr
& \int_{ - 3}^{ - 2} {\frac{{dx}}{x}} = \left( {\ln \left| x \right|} \right)_{ - 3}^{ - 2} \cr
& {\text{use the fundamental theorem of calculus }} \cr
& \int_a^b {f\left( x \right)} dx = F\left( b \right) - F\left( a \right).\,\,\left( {{\text{see page 281}}} \right) \cr
& {\text{then}}{\text{,}} \cr
& = \ln \left| { - 2} \right| - \ln \left| { - 3} \right| \cr
& {\text{simplifying}} \cr
& = \ln 2 - \ln 3 \cr
& {\text{use the quotient property for logarithms}} \cr
& = \ln \left( {\frac{2}{3}} \right) \cr} $$
