Infant Monster

Calculus Level 3

\[\large \displaystyle \sum _{ n=2 }^{ \infty }{ \left( \frac { 1 }{ \left( \displaystyle\prod _{ x=1 }^{ n }{ \left| \sqrt { 2 \int _{ 0 }^{ x }{ t \, dt }} \right| } \right) } \right) } +2 = \ ? \]

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