Hi,

My question is more related to calculus here but it has a probability component so I decided to stick to the main thread

I have a pdf defined as $\frac{k}{1+y^2}, y \in R$;

I found $k = \frac{1}{\arctan(y)}$

Then I need to show that the random variable Y has a Cauchy distribution; for this I tried to find E[X], and here I get stuck:

$E[X] = \int_{-\infty}^{+\infty} yf(y)dy = \int_{-\infty}^{+\infty} \frac{y}{arctan(y)(1+y^2)}dy = ???$

- without that $y$ in the numerator I can do some nice substitutions but in this form...

I would really appreciate your help guys, in evaluating this integral,

Thank you