\frac{1}{(x^2+1)^2}=\frac{x^2+1-x^2}{(x^2+1)^2}=\frac{1}{x^2+1} -\frac{x^2}{(x^2+1)^2}=\frac{1}{(x^2+1)} - x*\frac{x}{(x^2+1)^2}