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Question Number 161529 by qaz last updated on 19/Dec/21

$$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim n}({\left({\int }_1^{+\mathrm{\infty }}\frac{{\mathrm{x}}^{\mathrm{n}}-{\mathrm{x}}^2+1}{{\mathrm{x}}^2({\mathrm{x}}^{\mathrm{n}}+1)}\mathrm{dx}\right)}^{\mathrm{n}}-\frac{1}{2})=?$$

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