# Simple ?

Calculus Level 4

Given that ${ I }(n)=\int _{ 0 }^{ \frac { \pi }{ 4 } }{ \cos ^{ n }{ x } \, dx },$ if $$I(5) = \cfrac { a\sqrt { b } }{ c }$$, what is $$a + b + c?$$

Details and Assumptions:

• You can use $$\int { \cos { ax } } \, dx =\cfrac { 1 }{ a } \sin { ax }$$.
• $$a, b, c$$ are positive integers, $$\gcd(a,c)=1,$$ and $$b$$ is a square free integer.
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