indefinite integral I

Calculus Level 3

$\large \int \frac{1}{(x^2+1)^2}dx$

Evaluate the indefinite integral above.

Notation: $C$ denotes the arbitrary constant of integration.

Use

$\cos^2 x = \dfrac {1+\cos2x}{2}$
$\sin(\arctan x) = \dfrac{x}{\sqrt{x^2+1}}$
$\cos(\arctan x) = \dfrac{1}{\sqrt{x^2+1}}$