Answer
$\dfrac{\ln 3\ln^25}{2}$
Work Step by Step
$\int_{1}^{3}\int_{1}^{5}\dfrac{\ln y}{xy}\, dy\, dx=\int_{1}^{3}\dfrac{1}{x}\, dx\int_{1}^{5}\dfrac{\ln y}{y}\, dy=\biggl[\ln x\biggr]_{1}^{3}\biggl[\dfrac{\ln^2y}{2}\biggr]_{1}^{5}=\dfrac{\ln3\ln^25}{2}$
