Sunan Abi Dawud Book 2, Hadith 379
There is no harm in uttering supplication in prayer, in its beginning, in its middle, and in the end, in obligatory prayer or other.
When he stood up, he said the takbir (Allah is most great) and said. . . .
One day we were praying behind the Messenger of Allah (ﷺ). When the Messenger of Allah (ﷺ) raised his head after bowing, he said: Allah listened to him who praised Him. A man behind the Messenger of Allah(ﷺ) said: O Allah, Our Lord, and to Thee be praise, much praise, good and blessed. When the Messenger of Allah (ﷺ) finished his prayer, he asked: Which of you if the one who spoke (the words) just now. The man said: I (uttered) these words, Prophet of Allah. The Messenger of Allah(ﷺ) said: I saw more than thirty angels racing against one another to be the one to write them first.