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Evaluate the following iterated integral:

$$I=\int_1^2 \int_0^1 \frac{y}{\sqrt{x+y^2}}dydx$$

A

$\cfrac{2}{3}\sqrt{2}$

B

$\pi$

C

$40\sqrt{5}-\cfrac{17}{3}\sqrt{17}+1$

D

$2\sqrt{3}-\cfrac{8}{3}\sqrt{2}+\cfrac{2}{3}$

E

$11\sqrt{2}-\cfrac{5}{2}\sqrt{5}-\cfrac{1}{2}$

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