\(\displaystyle \int \frac{dx}{\sqrt(36-x^{2})}. \ Let \ x \ = \ 6sin(\theta), \ then \ dx \ = \ 6cos(\theta)d\theta.\)
\(\displaystyle Ergo, \ 6\int \frac{cos(\theta)d\theta}{\sqrt(36-36sin^{2}(\theta))}\)
\(\displaystyle = \ \int\frac{cos(\theta)d\theta}{\sqrt cos^{2}(\theta)} \ = \ \int d\theta \ = \ \theta+C\)
\(\displaystyle Now, \ x \ = \ 6sin(\theta), \ sin(\theta) \ = \ \frac{x}{6}, \ hence \ \theta \ = \ arcsin(x/6)\)
\(\displaystyle Therefore, \ \int \frac{dx}{\sqrt(36-x^{2})} \ = \ arcsin(x/6)+C.\)
