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I found a way to evaluate $\displaystyle \int_0^\infty \frac{dx}{x^s (x+1)}$ using the assumption that $s\in\mathbb{R}$ and $0.

Apparently it should be easily extended to all $s\in\mathbb{C}$ with $0.

I posted my solution here: http://thetactician.net/Math/Analysis/Integral1.pdf

I'm pretty sure there's a more concise method for evaluating it...and I'd also like to make the extension to $\mathbb{C}$ more rigorous.

Any ideas?

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    Knowledge on some special functions (especially Gamma function and Beta function) allows us to evaluate the integral in few lines. You can confirm at [here](http://math.stackexchange.com/questions/110457/closed-form-of-integral/110478#110478). However, I'm not sure you will agree that this is elementary.2012-02-29
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    @user1952500 You're not supposed to use \displaystyle in titles (or anything else that causes excessive scaling). See [here](https://math.meta.stackexchange.com/q/18982/232456). I'm not sure why some of your recent edits were approved. Also, keep in mind that editing an old question bumps the question. So you really shouldn't edit an old question just to make minor formatting changes that you might personally prefer.2017-07-02
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    Thanks for the advice and explanations @user232456.2017-07-02

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