$(4$ points$)$ Determine, with proof, the infimum and supremum of the following set

$A$:$=\{qinQ$:EEa,ninN,$q=\frac{5a}{an}\}.$

$(4$ points$)$ Compute the following integrals.

$($a$)(2$ points$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}arctan(\sqrt[\phantom{2}]{x})dx.$

$($b$)(2$ points$){\displaystyle \underset{-\frac{}{3}}{\overset{\frac{}{3}}{}}}sec(x)dx.$