Contoh 01

$$\begin{array}{rl}& \int \frac{1}{\sqrt{9-4x^2}}dx\\ \\ & \int \frac{1}{\sqrt{3^2-(2x{)}^2}}dx\end{array}$$

$$\begin{array}{rl}2x& =3\sin \theta \to \sin \theta =\frac{2x}{3}\\ \\ 2x& =3\sin \theta \text{(diturunkan)}\\ \\ 2dx& =3\cos \theta d\theta \\ \\ dx& =\frac{3}{2}\cos \theta d\theta \end{array}$$

$$\begin{array}{rl}& \int \frac{1}{\sqrt{9-4x^2}}dx\\ \\ & \int \frac{1}{\sqrt{3^2-(2x{)}^2}}dx\\ \\ & \int \frac{1}{\sqrt{3^2-(3\sin \theta {)}^2}}.\frac{3}{2}\cos \theta d\theta \\ \\ & \frac{3}{2}\int \frac{1}{\sqrt{9-9{\sin }^2\theta }}.\cos \theta d\theta \\ \\ & \frac{3}{2}\int \frac{1}{\sqrt{9(1-{\sin }^2\theta )}}.\cos \theta d\theta \\ \\ & \frac{3}{2}\int \frac{1}{3\sqrt{{\cos }^2\theta }}.\cos \theta d\theta \\ \\ & \frac{1}{2}\int \frac{1}{\cos \theta }.\cos \theta d\theta \\ \\ & \frac{1}{2}\int d\theta \\ \\ & \frac{1}{2}\theta +C\\ \\ & \frac{1}{2}\arcsin \left(\frac{2x}{3}\right)+c\end{array}$$