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x*ArcSec[x] - (Sqrt[-1 + x^2]*Log[2*(x + Sqrt[-1 + x^2])])/(Sqrt[1 - x^(-2)]*x)

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

Integrate[ArcSec[x], x] == 

                         2                        2
              Sqrt[-1 + x ] Log[2 (x + Sqrt[-1 + x ])]
x ArcSec[x] - ----------------------------------------
                                    -2
                          Sqrt[1 - x  ] x
Time to compute: 0.09 second
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