The problem is from the MIT Integration Bee 2023 Semifinal 2 Question 1.
The goal is to evaluate the integral: $\int (\sqrt{x+1}-\sqrt{x})^\pi dx$, and the provided answer is $\frac{1}{2}(\frac{(\sqrt{x+1}-\sqrt{x}))^{\pi+2}}{\pi+2}-\frac{(\sqrt{x+1}-\sqrt{x})^{\pi-2}}{\pi-2})$
I tried integration by part and trigonometric substitution, but I'm still not sure how to deal with this. I wonder what approach can be used to solve this problem. Please help.