$ \int^{\frac{\pi}{2}}_{0} \cos^nx \ dx = \frac{n-1}{n} \int^{\frac{\pi}{2}}_{0} \cos^{n-2}x \ dx$ for $n \in \{ \mathbb{N} > 2 \}$ proof
Prove $\int\cos^n x \ dx = \frac{1}n \cos^{n-1}x \sin x + \frac{n-1}{n}\int\cos^{n-2} x \ dx$