Does the prayer become invalid if one recites the Qur'an by mistake during the last Tashahhud?

The prayer is not invalidated by reciting the Quran during the Tashahhud, whether done intentionally or unintentionally. If done intentionally, the act is not permissible. If done unintentionally, the prostration of forgetfulness (sujud as-sahw) is prescribed for it. Thus, if any permissible utterance in prayer is made by the worshipper out of its proper place, the prayer is not invalidated, and the prostration of forgetfulness is prescribed for it.