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#