# A few improper integral

\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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What about them? Do you have a question? –  JavaMan Jan 4 '13 at 4:44
There must be something wrong with MSE at the moment. Your question mark doesn't appear on my screen. –  Michael Albanese Jan 4 '13 at 4:44
What class are these questions from? Those are rather non-trivial for introductory Calculus. –  user7530 Jan 4 '13 at 4:48
You can use the following technique to evaluate them –  Mhenni Benghorbal Jan 4 '13 at 4:49
Do you want to compute them or determine under what conditions they converge? –  mrf Jan 4 '13 at 20:58

$$\int_{-\infty }^{+\infty }{\frac{{{x}^{2m}}}{1+{{x}^{2n}}}\text{d}x}=2\int_{0 }^{+\infty }{\frac{{{x}^{2m}}}{1+{{x}^{2n}}}\text{d}x}.$$