$$\pi$$ece of cake

Calculus Level 2

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

The equation above holds true for positive integers $$a$$ and $$b$$. Find $$a+b$$.

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

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