Problem $20.$ Use integration by trigonometric substitution to evaluate the integrals.

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

$($e$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{xdx}{\sqrt[\phantom{2}]{1+x^4}}$

$($b$){\displaystyle \underset{-2}{\overset{2}{}}}\frac{dx}{4+x^2}$

$($f$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{\sqrt[\phantom{2}]{1-(lnx{)}^2}}{xlnx}dx$

$($c$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\sqrt[\phantom{2}]{25-t^2}dt$

$($g$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{\sqrt[\phantom{2}]{x-2}}{\sqrt[\phantom{2}]{x-1}}$

$($d$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{\sqrt[\phantom{2}]{4x^2-49}},x>\frac{7}{2}$

$($h$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^2}{4+x^2}dx$