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-2*x - (2*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/a + x*ArcCos[a*x]^2


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



                     2
Integrate[ArcCos[a x] , x] == 

                   2  2
       2 Sqrt[1 - a  x ] ArcCos[a x]                2
-2 x - ----------------------------- + x ArcCos[a x]
                     a

Time to compute: 0.03 second

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