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

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

Integrate[ArcCoth[a x], x] == 

                          2  2
                 Log[1 - a  x ]
x ArcCoth[a x] + --------------
                      2 a
Time to compute: < 0.01 second
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