Greatest Integer Function Integral

Calculus Level 4

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

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.

Inspiration.

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