Determine the value of the integral I=∫0π/2cosn(x)cos(nx) dxI = \int_0^{\pi/2} \cos^n(x) \cos(nx) \, dxI=∫0π/2cosn(x)cos(nx)dx for n>−1n > -1n>−1.
π2n+1\frac{\pi}{2^{n+1}}2n+1π
π2n\frac{\pi}{2^n}2nπ
πn+1\frac{\pi}{n+1}n+1π
12n\frac{1}{2^n}2n1