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ArcTan[(b*x)/a]/(a*b)

Integrate[1/(a^2 + b^2*x^2), x] ==
ArcTan[(b*x)/a]/(a*b) 

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

       b x
ArcTan[---]
        a
-----------
    a b
Time to compute: < 0.01 second
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