Find the $\int \frac{(1-y^2)}{(1+y^2)}dy$ $\int \frac{(1-y^2)}{(1+y^2)}dy$ first I tried to divide then I got 1-$\frac{2y^2}{1+y^2}$ and i still can't integrate it. 

Hint: 
$$ \int \frac{1-y^2}{1+y^2}dy = \int \frac{1}{1+y^2}dy-\int \frac{y^2}{1+y^2}dy$$
Note (using long division or otherwise): $$\int \frac{y^2}{1+y^2}dy = \int dy -\int \frac{1}{1+y^2}dy$$
Therefore:$$  \int \frac{1-y^2}{1+y^2}dy = 2\int\frac{1}{1+y^2}dy -\int dy$$
The solution should be straight forward from here.
