Who's up to the challenge? 5

Calculus Level 5

\[ \displaystyle\int _{ 0 }^{ 1 }{ { x }^{ 4 } { e }^{ x }\sin { x } } \, dx=\frac { Ae }{ B } (\sin { C } +D\cos { E } )-F\]

where \(A,B,C,D,E,F\) are positive integers, and \(A, B\) are coprime.

Find the minimum value of \(A+B+C+D+E+F\).


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