# 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 $$A+B+C+D+E+F$$.

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

×