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


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



Integrate[ArcCsc[x], x] == 

                         2                        2
              Sqrt[-1 + x ] Log[2 (x + Sqrt[-1 + x ])]
x ArcCsc[x] + ----------------------------------------
                                    -2
                          Sqrt[1 - x  ] x

Time to compute: 0.08 second

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