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Calculus Level 4

\(I={ \int _{ 0 }^{ \infty }{ \frac { { x }^{ 2 }\cdot dx }{ { 2 }^{ x } } } }\)

If \(I\) can be expressed in the form \(\frac { A }{ { \left( \ln { A } \right) }^{ B } }\), find \(A+B\).


This problem is original.
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