Find the Fourier Transform of $2x/(1+x^2)$ I tried doing this the same way you would find the Fourier transform for $1/(1+x^2)$ but I guess I'm having some trouble dealing with the 2x on top and I could really use some help here.

Hint: Taking the derivative with respect to $k$ of $$F(k)=\int_{-\infty}^{\infty}\frac{1}{1+x^2}e^{ikx}dx$$
yields
$$F'(k)=i\int_{-\infty}^{\infty}\frac{x}{1+x^2}e^{ikx}dx$$
Thus, the Fourier Transform of $\frac{2x}{1+x^2}$ is $-2i$ times the derivative with respect to $k$ of the Fourier Transform of $\frac{1}{1+x^2}$.
$$\mathscr{F}\left(\frac{2x}{1+x^2}\right)(k)=-2i \mathscr{F}\left(\frac{1}{1+x^2}\right)(k)$$
