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If an antiderivative of $\large x^4 e^x$ is in the form $e^x\left(Ax^4 - Bx^3 + Cx^2 - Dx + E\right)$, where $A,B,C,D$ and $E$ are positive integers, find $A+B+C+D+E$.

Notation: $e \approx 2.71828$ is the Euler's number.

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