# Integral of Power/Historical Note

The conventional proof of Integral of Power of course holds for all real $n \ne -1$, not just where $n$ is a strictly positive rational.
Bonaventura Francesco Cavalieri had previously made progress with this problem, proving it for integral $1 \le n \le 9$ but the algebra for the proof of each power was more difficult than the previous one, and he found $10$ too much hard work. The clear beauty of Fermat's approach was that it works for all $n$, rational as well as integral.