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Well, I mean, imagine that you have a function: $f(x)=\lim\limits_{x\to n}{\dfrac{nx}{x^n}}$ Would it be possible to write an integral of that? Something like this: $\int{\biggl(\lim_{x\to n}\dfrac{nx}{x^n}\biggl)}dx$

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    we will calculate the integral of a constant.2012-04-27

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yes, you can do it but if $\lim\limits_{n\to +\infty}f_{n}(x)=f(x)\in L^1$

$\int \lim_{n\to +\infty}f_{n}(x)dx=\int f(x)dx$

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Of course you can do it,

$\displaystyle\int{\biggl(\lim\limits_{x\to n}\dfrac{nx}{x^n}\biggl)}dx= \displaystyle\int L.dx = Lx +c $

$L= n^{2-n}$

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    @Garmen1778 yes L(limit) is $n^{2-n}$2012-04-28