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x*ArcTanh[a*x] + Log[1 - a^2*x^2]/(2*a)


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



Integrate[ArcTanh[a x], x] == 

                          2  2
                 Log[1 - a  x ]
x ArcTanh[a x] + --------------
                      2 a

Time to compute: < 0.01 second

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