The integral ${\displaystyle \underset{a}{\overset{}{}}}f(x)dx$ is improper because the interval $[a,)$ is infinite. If $f$ has an infinite dis as a sum of improper integrals of Type $2$ and Type $1$ as follows.

${\displaystyle \underset{a}{\overset{}{}}}f(x)dx={\displaystyle \underset{a}{\overset{c}{}}}f(x)dx{\displaystyle \underset{c}{\overset{}{}}}f(x)dx,c>a$

Evaluate the following integral if it is convergent. $($If the quantity diverges, enter DIVERGES.$)$

${\displaystyle \underset{0}{\overset{}{}}}\frac{8}{\sqrt[\phantom{2}]{x}(1x)}dx$