Answer
$$\ln 2$$
Work Step by Step
$$\eqalign{
& \int_1^{32} {\frac{1}{{5x}}} dx \cr
& = \frac{1}{5}\int_1^{32} {\frac{1}{x}} dx \cr
& {\text{integrate using }}\int {\frac{1}{x}} dx = \ln \left| x \right| + C \cr
& = \frac{1}{5}\left( {\ln \left| x \right|} \right)_1^{32} \cr
& {\text{use the fundamental theorem of calculus }}\int_a^b {f\left( x \right)} dx = F\left( b \right) - F\left( a \right).\,\,\,\,\left( {{\text{see page 281}}} \right) \cr
& = \frac{1}{5}\left( {\ln \left| {32} \right| - \ln \left| 1 \right|} \right) \cr
& = \frac{1}{5}\ln 32 \cr
& {\text{simplifying, we get:}} \cr
& = \ln {\left( {32} \right)^{1/5}} \cr
& = \ln 2 \cr} $$
