Let $p(x)=2+4x+3x^{2}+5x^{3}+3x^{4}+4x^{5}+2x^{6}$. For $k$ with $0<k<5$, define $$I_{k}=\int_{0}^{\infty} \frac{x^{k}}{p(x)} d x$$ For which $k$ is $I_{k}$ smallest?

Let's think step by step and output the final answer within \boxed{}.
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