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\[\large {\begin{eqnarray} \displaystyle I_n &=& \int_0^1 \sqrt{ \frac 1 x + n^2 x^{2n} } \ \mathrm dx \\ \\ \left . \right . \\ \displaystyle \lim _{ n\rightarrow \infty }{ { I }_{ n } } &=& \ ? \end{eqnarray}} \]

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