Can a human survive inside a titan? In Attack on Titan, it is said that titans do not have any digestive organs and the only way they get stuff out of their stomach is by puking it out.

Now, if a human is swallowed whole by the titan, will the human survive inside the titan? Yet no one is said to have survived this way.
As far as I know, there was no case where a human was swallowed whole by a titan. Most of the time the titan would give a fatal bite on the human before swallowing him/her. As such, even if the inside of a titan was just an empty bag, the eaten human would die from blood loss.

Now, assuming that somehow the human was swallowed wholly by a titan, and the human is in perfect condition, with the standard gear of the scouting legion, then he might be able to survive if someone were to kill the titan immediately after he was swallowed. If it took too long, then he won't survive. The reasons are as follow:


The titan would keep eating other humans, thus human bodies would come raining down on the already eaten human, potentially injuring them. If injured then his chance of surviving would get even lower due to the panic the injury caused him and the injury potentially hindering him from avoiding the next batch of dead bodies which could injure him even further. I doubt anyone who knows that he was inside the stomach of a titan and is injured would be able to stay calm.
The inside of a titan's stomach is not an empty bag. It has a liquid there. I'm not sure whether it has an acidic properties or not, but if it is then the eaten human would have his body melt due to the acid. If it is not, then being in the liquid itself would hinder his movement, which would disable him from avoiding dead bodies raining down on him as the titan eat more humans.
It was shown that after eating humans, titan would vomit them back since they lack digestive organs. The vomit was a crystal with the dead bodies inside. Assuming that somehow he was able to avoid getting injured while inside, he won't survived being crystallized since it means that he won't be able to breathe.