π\piece of cake

Calculus Level 2

1dxx2=πab \large \displaystyle\int _{ 1 }^{ \infty }{ \dfrac { dx }{ \lfloor x \rfloor ^{ 2 } } } =\dfrac { { \pi }^{ a } }{ b }

The equation above holds true for positive integers aa and bb. Find a+ba+b.

Notation: \lfloor \cdot \rfloor denotes the floor function.

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