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Integralshard
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A physical system has a density function ρ(x)=1x2+2x+2\rho(x) = \frac{1}{x^2+2x+2}ρ(x)=x2+2x+21​ along a wire of infinite length x∈[0,∞)x \in [0, \infty)x∈[0,∞). Determine the total mass M=∫0∞ρ(x)dxM = \int_0^{\infty} \rho(x) dxM=∫0∞​ρ(x)dx.