Where in the Old Testament books is the birth of Jesus prohesied?

Yup Isaiah is correct,

Regarding Jesus’ birth—Isaiah 7:14: “Therefore the Lord himself will give you a sign: The virgin will be with child and will give birth to a son, and will call him Immanuel.” Isaiah 9:6: “For to us a child is born, to us a son is given, and the government will be on his shoulders. And he will be called Wonderful Counselor, Mighty God, Everlasting Father, Prince of Peace.”

Isaiah 9:5-7 (NIV) Every warrior's boot used in battle and every garment rolled in blood will be destined for burning, will be fuel for the fire. 6 For to us a child is born, to us a son is given, and the government will be on his shoulders. And he will be called Wonderful Counselor, Mighty God, Everlasting Father, Prince of Peace. 7 Of the increase of his government and peace there will be no end. He will reign on David's throne and over his kingdom, establishing and upholding it with justice and righteousness from that time on and forever. The zeal of the LORD Almighty will accomplish this.

Jeremiah 23:5-6 (NIV) "The days are coming," declares the LORD, "when I will raise up to David a righteous Branch, a King who will reign wisely and do what is just and right in the land. 6 In his days Judah will be saved and Israel will live in safety. This is the name by which he will be called: The LORD Our Righteousness.

Psalms 2:6 (NIV) "I have installed my King on Zion, my holy hill."

aniel 9:24-26 (NIV) "Seventy 'sevens' are decreed for your people and your holy city to finish transgression, to put an end to sin, to atone for wickedness, to bring in everlasting righteousness, to seal up vision and prophecy and to anoint the most holy. 25 "Know and understand this: From the issuing of the decree to restore and rebuild Jerusalem until the Anointed One, the ruler, comes, there will be seven 'sevens,' and sixty-two 'sevens.' It will be rebuilt with streets and a trench, but in times of trouble. 26 After the sixty-two 'sevens,' the Anointed One will be cut off and will have nothing. The people of the ruler who will come will destroy the city and the sanctuary. The end will come like a flood: War will continue until the end, and desolations have been decreed.