Compute $\iint_D \frac{dx dy}{\sqrt{1+x+2y}}$  on $D=[0,1]\times [0,1]$

Compute $\iint_D \frac{dx dy}{\sqrt{1+x+2y}}$ on $D=[0,1]\times [0,1]$ by setting $T(u,v)=(u,\frac{v}{2})$ and evaluating an integral over $D^*$, where $T(D^*)=D.$


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