# Greatest Integer Function Integral

Calculus Level 5

$\large 8\int_{1}^{ \infty} \frac {\left\lfloor x \right\rfloor} {x^{5}}\, dx$

If the value of the above integral is equal to $$\dfrac { \pi^{a} } {b}$$, find the value of $$a+b$$.

Note:$$\left\lfloor x \right\rfloor$$ is the greatest integer function.

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