indefinite integral I

Calculus Level 3

1(x2+1)2dx\large \int \frac{1}{(x^2+1)^2}dx

Evaluate the indefinite integral above.

Notation: CC denotes the arbitrary constant of integration.

Use

  • cos2x=1+cos2x2\cos^2 x = \dfrac {1+\cos2x}{2}
  • sin(arctanx)=xx2+1\sin(\arctan x) = \dfrac{x}{\sqrt{x^2+1}}
  • cos(arctanx)=1x2+1\cos(\arctan x) = \dfrac{1}{\sqrt{x^2+1}}
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