Rudimental Doctrine with concern to Transformation

Calculus Level 5

\[ {\displaystyle {\lim_{n\to \infty} \int_{n}^{2n} \frac{n^{3}x}{x^{5}+1} \ dx} =k}, \ \ \ \ \ \ \frac 1 k = \ ? \]

Give your answer to two decimal places.

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