Who's up to the challenge? 4

Calculus Level 4

\[ \large \displaystyle\int _{ 0 }^{ 1 }{ \frac { x\sin { x } \cos { x } }{ { e }^{ x } } } \, dx \]

Can be represented in the form

\[-\dfrac { -Ae+\sin { B } +C\cos { D } }{ Fe } \]

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

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


this is a part of Who's up to the challenge?

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