Evaluate the following integral:

${\displaystyle \underset{1}{\overset{3}{}}}{\displaystyle \underset{0}{\overset{2}{}}}(x^3{y}^2+x^2{e}^y+\frac{x}{y})dxdy$

$A.\frac{ln729+8e(e^2+1)+104}{3}$

$B.\frac{ln729+8e(e^2-1)+104}{3}$

$C.\frac{ln216+8e(e^2-1)+104}{3}$

$D.\frac{ln216+8e(e^2+1)+104}{3}$

$E.\frac{ln18+8e(e^2-1)+104}{3}$