[AUCTeX] auctex output in shell buffer

[Benno]

Dear AUCTeX experts.

How can I redirect the AUCTeX output to a shell buffer (M-x shell) of emacs?
(= use a shell buffer instead of the AUCTeX output buffer). This way one
could seamlessly combine (LaTeX) shell commands and AUCTeX commands, and got
also the history of all outputs at ones disposal. (I know this feature from
other TeX shells).
In fact, when using emacs without the auctex package but only with its basic
(La)Tex-mode, an interactive tex-shell is always there, allowing arbitrary
shell input and "endless" history (the shell). I'm looking for this under
auctex.

Thank you for hints!

  Benno