By using the substitution $u=\sqrt[\phantom{2}]{2x1}$ or otherwise, compute

${\displaystyle \underset{0}{\overset{4}{}}}{e}^{\sqrt[\phantom{2}]{2x1}}dx$

A $2e^3$

B $3e^2$

C$.2-2e^2$

D$.2ln3$

E $3ln2$