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-ArcCot[a*x]^2/(2*a)

Integrate[ArcCot[a*x]/(1 + a^2*x^2), x] ==
-ArcCot[a*x]^2/(2*a) 

          ArcCot[a x]
Integrate[-----------, x] == 
                2  2
           1 + a  x

            2
-ArcCot[a x]
-------------
     2 a
Time to compute: < 0.01 second
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