proving inequation of integral in condition for a polynomial – math.stackexchange.com

proving inequation of integral in condition for a polynomial – math.stackexchange.com

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I need to prove this: $$\int_{2}^{4}\frac{\mathrm{d} x}{p(x)}\leq \frac{2}{7}$$ when the polynomial $p(x)$ is: $$p(x)=x^{3}+(x-1)^{2}-2$$ How shell I begin?

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