# Hunter become the huntee

Calculus Level 4

$\large \displaystyle \int_{0}^{\frac{\pi}{2}}\cos ^{n}\left ( \varphi \right )\, d\varphi$

If the value of the integral above can be expressed as $$\displaystyle \frac{2^{2\cdot 864}\left ( 864! \right )^{2}}{\left ( 2\cdot 864+1 \right )!}$$ for constant $$n$$, find the value of $$n$$.

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