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Integralshard
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A population density function is defined as ρ(x)=1x3+8\rho(x) = \frac{1}{x^3 + 8}ρ(x)=x3+81​ for x≥0x \ge 0x≥0. If the total population is given by ∫0∞ρ(x)dx\int_0^{\infty} \rho(x) dx∫0∞​ρ(x)dx, determine the value of this convergent improper integral.