Sample Equations

1. x' + y² = z_i²

2. $-2 \, \ln \vert x-2\vert + 3 \, \ln \vert x-3\vert + C$

3. $y = k \, e^{x^2/2} - 1\;\;$

4. $$\frac{dr}{dt} = \frac{1}{\pi}$$

5. $[-1/\sqrt{3},0] \cup [1/\sqrt{3},+\infty[$

6. $$\frac{\cos x}{2 \sqrt{\sin x}}$$

7. $$A = \int_0^1 \frac{\ln(x+1) \, \sqrt{x^2 + 2x + 2}}{x + 1} \, dx$$

8. $$\frac{1}{2} \int_0^{\pi/3} \sin^2 3\theta \; d\theta = \frac{\pi}{12}$$