How do you find the integral of $dx/(1+x^2)$ ?

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Answer 1 · 2015-10-11T17:18:56

$tan^-1 x +C$

Let $x = tan theta$ , so that $dx=sec^2 theta d theta$

$int (1dx)/(1+x^2)$ = $int (sec^2 theta d theta)/ sec^2 theta$

$int d theta = theta +C$

= $tan^-1 x +C$

How do you find the integral of dx/(1+x^2)dx/(1+x^2)?