Answer
$$\ln 25$$
Work Step by Step
$$\eqalign{
& \int_1^5 {\int_2^4 {\frac{1}{y}} } dxdy \cr
& = \int_1^5 {\left[ {\int_2^4 {\frac{1}{y}} dx} \right]} dy \cr
& {\text{solve the inner integral}} \cr
& \int_2^4 {\frac{1}{y}} dx = \frac{1}{y}\int_2^4 {dx} \cr
& = \frac{1}{y}\left[ x \right]_2^4 \cr
& = \frac{1}{y}\left( {4 - 2} \right) \cr
& = \frac{2}{y} \cr
& {\text{then}} \cr
& \int_1^5 {\int_2^4 {\frac{1}{y}} } dxdy = \int_1^5 {\frac{2}{y}} dy \cr
& {\text{integrating}} \cr
& \left[ {2\ln \left| y \right|} \right]_1^5 \cr
& = 2\left( {\ln 5 - \ln 1} \right) \cr
& = 2\ln 5 \cr
& = \ln 25 \cr} $$
