Answer
$$\ln \left( {\frac{3}{2}} \right)$$
Work Step by Step
$$\eqalign{
& \int_{\ln 2}^{\ln 3} {\operatorname{csch} y} dy \cr
& {\text{Using the theorem 6}}{\text{.9 }}\left( {formula{\text{ 4}}} \right){\text{ }}\int {\operatorname{csch} x} dx = \ln \left| {\tanh \left( {\frac{x}{2}} \right)} \right| + C \cr
& {\text{then}}{\text{, }} \cr
& \int_{\ln 2}^{\ln 3} {\operatorname{csch} y} dy = \left( {\ln \left| {\tanh \left( {\frac{y}{2}} \right)} \right|} \right)_{\ln 2}^{\ln 3} \cr
& {\text{evaluate the limits}} \cr
& = \ln \left| {\tanh \left( {\frac{{\ln 3}}{2}} \right)} \right| - \ln \left| {\tanh \left( {\frac{{\ln 2}}{2}} \right)} \right| \cr
& {\text{simplifying}} \cr
& = \ln \left( {\frac{1}{2}} \right) - \ln \left( {\frac{1}{3}} \right) \cr
& {\text{using logarithmic properties}} \cr
& = \ln \left( {\frac{{1/2}}{{1/3}}} \right) \cr
& = \ln \left( {\frac{3}{2}} \right) \cr} $$
