Derive the integration formula:

$21.$ Integration

$a>0$ Formula ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{du}{\sqrt[\phantom{2}]{a^2-u^2}}=$Acsin$(\frac{u}{a})+C-a>0$

constant

$22.$ Integration ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{du}{a^2+u^2}=\frac{1}{a^2}$Arctan$(\frac{u}{a})+C$

$a>0$ Formula $a$ is a constant

$23.$ Integration Formula ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{-du}{a^2+u^2}=\frac{1}{a}$Arccot$(\frac{u}{a})+C$

$a>0a$ is a constant

$24.$ Integration $a>0$ Formula ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{du}{u\sqrt[\phantom{2}]{u^2-a^2}}=\frac{1}{a}$Arcsec$(\frac{u}{a})+Ca$ is constant