Arc length y=4x^3/2 between x=1/3 and x=5

Find dy/dx. $$ \frac{\differentialD y}{\differentialD x}=4\times\frac{3}{2}x^{\frac{1}{2}}=6\sqrt{x} $$ Now, find the arc length using integration. $$ S=\int_{\frac{1}{3}}^5\sqrt{1+\left(6\sqrt{x}\right)^2}\differentialD x $$ $$ S=44.23 $$