Summation of Integrals Mashup!!

Calculus Level 4

\(Let\quad { I }_{ n }=\quad\displaystyle \int _{ 0 }^{ \pi /2 }{ { x }^{ n }\cos { x } dx,\quad where\quad n\quad is\quad a\quad non-negative\quad integer. } \\ Then:\quad \quad \displaystyle\sum _{ n=2 }^{ \infty }{ \left( \frac { { I }_{ n } }{ n! } +\frac { { I }_{ n-2 } }{ (n-2)! } \right) } equals?? \)
Also Try: \( \href{https://brilliant.org/community-problem/integrals-of-the-years/?group=mJXtqmVrO6YT&ref_id=444794}{here}\)

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