$$\displaystyle \begin{align*} & \int_{0}^{+\infty }{\frac{\text{d}x}{1+{{x}^{n}}}} \\ & \int_{-\infty }^{+\infty }{\frac{{{x}^{2m}}}{1+{{x}^{2n}}}\text{d}x} \\ & \int_{0}^{+\infty }{\frac{{{x}^{s-1}}}{1+x}\text{d}x} \\ \end{align*}$$
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2What about them? Do you have a question? – JavaMan Jan 04 '13 at 04:44
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8There must be something wrong with MSE at the moment. Your question mark doesn't appear on my screen. – Michael Albanese Jan 04 '13 at 04:44
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1What class are these questions from? Those are rather non-trivial for introductory Calculus. – user7530 Jan 04 '13 at 04:48
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You can use the following technique to evaluate them – Mhenni Benghorbal Jan 04 '13 at 04:49
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Do you want to compute them or determine under what conditions they converge? – mrf Jan 04 '13 at 20:58
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All of them can be solved using the beta function technique. See (I), (II), (III). Notice that, the second integral can be written as,
$$ \int_{-\infty }^{+\infty }{\frac{{{x}^{2m}}}{1+{{x}^{2n}}}\text{d}x}=2\int_{0 }^{+\infty }{\frac{{{x}^{2m}}}{1+{{x}^{2n}}}\text{d}x}. $$
Mhenni Benghorbal
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I don't feel like that down votes in previous question you've got. Sometimes, some of us forget that we are here just to share our thoughts for solving a problem and help someone to understand a problem but not to war. +1 – Mikasa Jan 04 '13 at 06:58
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@BabakSorouh: As you see, I just suggested an idea for solving the problem, but I do not know why they made all of this argument!! Thanks for comment. – Mhenni Benghorbal Jan 04 '13 at 07:03
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1@BabakSorouh: Thank you. I really appreciate it. This website serves a good purpose for humanity. – Mhenni Benghorbal Jan 04 '13 at 07:11
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8@Babak Did you actually ma(k)e some + for other (Mhenni's) answers (Mhenni) made because (you) don't feel like that down votes in previous question (Mhenni's) got? Everybody is entitled to one's own opinions about upvotes and downvotes on the site, of course, but if you did vote on some answers by compensation, you might wish to reconsider and to stop doing it: this is misleading other users about your opinion of the posts you upvote, and definitely not the way the system is supposed to work. – Did Jan 04 '13 at 14:56
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I accidentally down voted this because I'm on an iPhone, if you make any edit to the question I will undo it (I was attempting to view up/down casts and accidentally hit down). – guy Jan 06 '13 at 03:21
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