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

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