Question #21195

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Answer 1 · 2016-06-28T22:23:45

$= arctan x + C$

this is a pretty common and therefore standard integral

use the sub: $x = tan varphi$
so: $dx = sec^2 varphi \ d varphi$

the integral becomes

$int (1)/(1 + tan^2 varphi) \ sec^2 varphi \ d varphi = int (1)/(1 + tan^2 varphi) \ sec^2 varphi \ d varphi$

$= int \ d varphi$

$= varphi + C$

$= arctan x + C$