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ArcCosh[a*x]^2/(2*a)

Integrate[ArcCos[a*x]/Sqrt[1 - a^2*x^2], x] ==
ArcCosh[a*x]^2/(2*a) 

            ArcCos[a x]
Integrate[---------------, x] == 
                    2  2
          Sqrt[1 - a  x ]

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