\[\int_{1}^{e} x^2 \ln{x} \, dx=\dfrac{A+C e^D}{B}\]

The above equation is true for positive integers \(A,B,C\) and \(D\), where \(\gcd(A,C,B)=1\). Find \(A+B+C+D\).

**Clarification**: \(\gcd(\cdot) \) denotes the greatest common divisor function.

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