Does the prayer become invalid if the worshipper, out of ignorance, recites only the first Tashahhud and not the second? And is it obligatory to repeat it?

If you do not send blessings upon the Prophet, peace and blessings be upon him, in the final sitting, your prayer is valid according to most scholars. It is obligatory in the sound opinion of the Shafi'i and Ishaq schools, and not obligatory according to Malik, Al-Thawri, the Ashab al-Ra'y (people of opinion), and most scholars.