An integral with the floor function

Calculus Level 4

1xx3dx=3a+πb12+π2c241\large \int_1^\infty\frac{\lfloor x\rfloor}{x^3}\, dx = \frac{3}{a}+\frac{\pi b}{12}+\frac{\pi^2 c}{24}-1

The equation above holds true for where a,ba,b and cc are integers aa, bb and cc. Compute the value of ca+bc^{a+b}.

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

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