Sahih al-Bukhari Book 32, Hadith 11
With the start of the last ten days of Ramadan, the Prophet (ﷺ) used to tighten his waist belt (i.e. work
hard) and used to pray all the night, and used to keep his family awake for the prayers.
The Prophet (ﷺ) came out to inform us about the Night of Qadr but two Muslims were quarreling with each other. So, the Prophet (ﷺ) said, "I came out to inform you about the Night of Qadr but such-and-such persons were quarreling, so the news about it had been taken away; yet that might be for your own good, so search for it on the 29th, 27th and 25th (of Ramadan).
Allah's Messenger (ﷺ) used to practice I`tikaf in the last ten days of the month of Ramadan.