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


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



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

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

Time to compute: 0.07 second

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