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

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