Compute the following integrals by using the proper integral method and$/$or proper notation:

$($a$){\displaystyle \underset{3}{\overset{}{}}}\frac{1}{9+x^2}dx$

$($This integral is improper. Explain why and use proper limit notation to compute.$)$

$($b$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{2x+9}{(x+3)(x-5)}dx.$