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I would like to know the value of the following improper integral: $$\int \limits_{-\infty}^{\infty}\frac{2x}{1+x^2}dx$$

as the function $f(x)=\displaystyle\frac{2x}{1+x^2}$ satisfies $f(-x)=-f(x)$ can I immediately conclude that the integral is equal to zero?

Thank you in advance for any suggestion.

  • 0
    This looks as if it might be an attempt to calculate the [mean of a Cauchy distribution](http://en.wikipedia.org/wiki/Cauchy_distribution#Mean). If so, then it cannot be calculated2011-03-08

3 Answers 3