Test
test
$$ \int_{0}^{\pi}\frac{x^{4}\left(1-x\right)^{4}}{1+x^{2}}dx =\frac{22}{7}-\pi$$
\begin{aligned}
\dot{x} & = \sigma(y-x) \\
\dot{y} & = \rho x - y - xz \\
\dot{z} & = -\beta z + xy
\end{aligned}
$$\left [ - \frac{\hbar^2}{2 m} \frac{\partial^2}{\partial x^2} + V \right ] \Psi
= i \hbar \frac{\partial}{\partial t} \Psi$$
Johan
$\int_{-\infty}^\infty e^{-x^2}\,dx=\sqrt{\pi}$
$\displaystyle \begin{array}{6,2} I\times I &= \int_{-\infty}^{\infty} e^{-x^{2}}dx \times\int_{-\infty}^{\infty} e^{-y^{2}}dy \\ &= \int_{-\infty}^{\infty}\int_{-\infty}^{\infty} e^{-(x^{2}+y^{2}}dxdy \\ &= \int_{0}^{2\pi }\int_{0}^{\infty} re^{-r^{2}}drd\phi \\ &= \int_{0}^{2\pi }\left( -\frac{1}{2}e^{-r^{2}}\big|_{0}^{\infty} \right)d\phi \\ &= \int_{0}^{2\pi } \frac{1}{2}( 1 - 0)d\phi \\ &= 2\pi\times \frac{1}{2} = \pi, \end{array}$