Latex preview fragment - latex error + blank square

I'm new into latex, org and latex in org so it may sounds like a total newbie question... I want to preview latex in emacs with org-preview-latex-fragment, I have followed instructions from here and trying to preview this code :

#+BEGIN_SRC late :tangle /tmp/example.tex
\documentclass{article}

\begin{document}
$e^{i\pi} = -1$

$\int_0^\infty e^{-x^2} dx = \frac{\sqrt{\pi}}{2}$

\end{document}

#+END_SRC


but it fails with a blank square. I have checked the log in /tmp and latex has an error but I don't know why :

File: ts1cmr.fd 2014/09/29 v2.5h Standard LaTeX font definitions
LaTeX Font Info:    ... okay on input line 33.

! LaTeX Error: Can be used only in preamble.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
...

l.34 \begin{document}

?
! Emergency stop.
...

l.34 \begin{document}

Type  I <command> <return>  to replace it with another command,
or  <return>  to continue without it.

Here is how much of TeX's memory you used:
3089 strings out of 493055
35108 string characters out of 6140611
80703 words of memory out of 5000000
6607 multiletter control sequences out of 15000+600000
4509 words of font info for 16 fonts, out of 8000000 for 9000
1141 hyphenation exceptions out of 8191
27i,1n,26p,236b,50s stack positions out of                     5000i,500n,10000p,200000b,80000s
No pages of output.


I have tried to compile out of emacs and get the same message, but as it's interactive when I type it works. So why do I get this error and how to make it works within emacs ?

ps: if you need the full log please tell me, it's just that it is huge and doesn't work on my google chrome.

Remove the stuff like \documentclass, \begin{document} and \end{document}. This does not belong into an org-document.