Infant Monster

Calculus Level 4

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