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(Sqrt[a + b/x^2]*x*(Sqrt[b + a*x^2] + Sqrt[b]*Log[b^(3/2)*x] - Sqrt[b]*Log[2*(b + Sqrt[b]*Sqrt[b + a*x^2])]))/Sqrt[b + a*x^2]


Integrate[Sqrt[a + b/x^2], x] ==
(Sqrt[a + b/x^2]*x*(Sqrt[b + a*x^2] + Sqrt[b]*Log[b^(3/2)*x] - Sqrt[b]*Log[2*(b + Sqrt[b]*Sqrt[b + a*x^2])]))/ Sqrt[b + a*x^2]



                   b
Integrate[Sqrt[a + --], x] == 
                    2
                   x

          b                  2
(Sqrt[a + --] x (Sqrt[b + a x ] + 
           2
          x
 
                   3/2
      Sqrt[b] Log[b    x] - 
 
                                             2
      Sqrt[b] Log[2 (b + Sqrt[b] Sqrt[b + a x ])])) / 
 
              2
  Sqrt[b + a x ]

Time to compute: 0.11 second

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