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∫1∞⌊x⌋x3 dx=3a+πb12+π2c24−1\large \int_1^\infty\frac{\lfloor x\rfloor}{x^3}\, dx = \frac{3}{a}+\frac{\pi b}{12}+\frac{\pi^2 c}{24}-1∫1∞x3⌊x⌋dx=a3+12πb+24π2c−1
The equation above holds true for where a,ba,ba,b and ccc are integers aaa, bbb and ccc. Compute the value of ca+bc^{a+b}ca+b.
Notation: ⌊⋅⌋ \lfloor \cdot \rfloor ⌊⋅⌋ denotes the floor function.
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