Question:

Let $I = \int \frac{dx}{\sqrt{a^2 - x^2}}$<br>Put $x = a \sin \theta \Rightarrow dx = a \cos \theta d\theta$<br>$\therefore I = \int \frac{a \cos \theta d\theta}{a \cos \theta} = \int d\theta = \theta + C = \sin^{-1} (\frac{x}{a}) + C$