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ArcTan[x/Sqrt[a]]/Sqrt[a]

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

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

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