Evaluate the integral ${\displaystyle \underset{0}{\overset{4}{}}}{\displaystyle \underset{0}{\overset{3}{}}}{\displaystyle \underset{2y}{\overset{6}{}}}\frac{5cos(x^2)}{2\sqrt[\phantom{2}]{z}}dxdydz$ by changing the order of integration in an appropriate way.

${\displaystyle \underset{0}{\overset{4}{}}}{\displaystyle \underset{0}{\overset{3}{}}}{\displaystyle \underset{2y}{\overset{6}{}}}\frac{5cos(x^2)}{2\sqrt[\phantom{2}]{z}}dxdydz=$

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$($Type an exact answer.$)$