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

Integrate[1/(a^2 - b^2*x^2), x] ==
ArcTanh[(b*x)/a]/(a*b) 

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

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