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(4*Sqrt[b]*ArcTanh[Sqrt[b + a*x]/Sqrt[b]] + 2*Sqrt[b + a*x]*(-2 + Log[x]))/a


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



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

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

Time to compute: 0.08 second

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