The integral ${\displaystyle \underset{a}{\overset{}{}}}f(x)dxis$ improper because the interval $[a,)is$ infinite. $Iff$ has $an$ infinite discontinuity $ata,$ then the integral $is$ improper for a second reason. $In$ this case $we$

evaluate the integral $by$ expressing $itas$ a sum $of$ improper integrals $of$ Type $2$ and Type $1as$ 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 $ifitis$ convergent. $(If$ the quantity diverges, enter DIVERGES.$)$

${\displaystyle \underset{0}{\overset{}{}}}\frac{9}{\sqrt[\phantom{2}]{x}(1+x)}dx$