integration in latex code example

Example 1: how to do limits in latex

$\lim_{x \to +\infty} f(x)$

Example 2: latex integral

$ \int_{a}^{b} x^2 \,dx $

Example 3: integral latex

integral 
\[ \int_{a}^{b} x^2 \,dx \]

Example 4: integral latex

$\int_0^{2a}{\cos(x)dx}$