Calculate the Iterated Integral $\int _ { 0 } ^ { \ln 2 } \left( \int _ { 1 } ^ { 2 } x y + y e ^ { x y } d x \right)$

Calculate the iterated integral $\int _ { 0 } ^ { \ln 2 } \left( \int _ { 1 } ^ { 2 } x y + y e ^ { x y } d x \right)$ dy.

A) $\frac { 3 } { 2 }$ ln - $e ^ { 2 } \ln 2$ - $\frac { 3 } { 2 }$
B) $\frac { 3 } { 2 }$ ln 2 - $\frac { 1 } { 2 }$ $\mathrm{ex}^{2}$ - $\frac { 5 } { 2 }$
C) $\frac { 3 } { 4 }$ (ln 2) + $\frac { 1 } { 2 }$
D) $\frac { 3 } { 4 }$ $( \ln 2 ) ^ { 2 }$ + $\frac { 1 } { 2 }$
E) none of these

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