Q$2(2$ points$)$

$($a$)$ Use a trigonometric substitution to calculate the indefinite integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{(x^{2}25{)}^{\frac{3}{2}}}dx.$ Show your work.

$($b$)$ Calculate the improper integral ${\displaystyle \underset{-}{\overset{}{}}}\frac{1}{(x^{2}25{)}^{\frac{1}{4}}}dx,$ or show that it diverges. Show your work.