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


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



                  a
Integrate[ArcSinh[-], x] == 
                  x

          a
x ArcSinh[-] + 
          x
 
           2    2                   2    2
   a Sqrt[a  + x ] Log[2 (x + Sqrt[a  + x ])]
   ------------------------------------------
                           2
                          a
                 Sqrt[1 + --] x
                           2
                          x

Time to compute: 0.13 second

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