Where exactly are copyrights and patents mentioned in the United States Constitution?
Patents and copyrights are mentioned in the United States Constitution in Article I, Section 8, Clause 8. The Framers of the Constitution felt that it was very important to protect intellectual property of this sort because they believed that inventors had to be able to profit from their work. If inventors were able to do so, they would have the incentive to continue to come up with new inventions and, thereby, improve the US economy.
In order to make that happen, the Framers inserted a clause into the Constitution that protected copyrights and patents. The clause says that Congress has the power to
... promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors exclusive Right to their respective Writings and Discoveries.
The words "copyright" and "patent" are not used, but the idea is there.