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  1. MHB Craftsman

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    Let $ \displaystyle p(x)=2x^6+4x^5+3x^4+5x^3+3x^2+4x+2.$ Let $ \displaystyle \displaystyle I_{k}=\int^{\infty}_{0}\frac{x^k}{p(x)}dx$

    where $ \displaystyle 0<k<5.$ Then value of $ \displaystyle k$ for which $ \displaystyle \displaystyle I_{k}$ is smallest.

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