Problem $2(4$ pts$)$ Evaluate the line integral

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}\frac{2}{1+2x}ds$

where $C$ is parametrized by

$r(t)=(t,\frac{2\sqrt[\phantom{2}]{2}}{3}{t}^{\frac{3}{2}}),0t2.$