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


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



                    -2
Integrate[Sqrt[1 + x  ], x] == 

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

Time to compute: 0.04 second

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