Please help me integrate the following: $\int \frac{y^2 - x^2}{(x^2 + y^2)^2}dy$ I'm self-studying a Cramster solution and I came across this integral and I don't know what they've done with it. Help would be appreciated. 
$$\int \frac{y^2 - x^2}{(x^2 + y^2)^2} ~dy.$$

In an integral $dy$, $x$ is a constant. Rewirite this as:
$$\int\frac{y^2-x^2}{\left(x^2+y^2\right)^2}dy=\int\frac{y^2+x^2-2x^2}{\left(x^2+y^2\right)^2}dy=\int\frac{dy}{x^2+y^2}-2x^2\int\frac{dy}{\left(x^2+y^2\right)^2}$$
Can you continue from here?
