Mathematic formulas

This is a sample formula:

$\displaystyle c = \pm\sqrt{a^2 + b^2}$

$\displaystyle \int_0^1 f(x)dx = F(x)\vert _0^1$

And this is an inline formula: $\int_0^1 f(x)dx = F(x)\vert _0^1$ and so it goes.

$\displaystyle a$	$\textstyle =$	$\displaystyle 2(b+c)$	(1)
	$\textstyle =$	$\displaystyle 2b + 2c$	(2)