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

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

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

                                  2
b Sqrt[x]                b       b  Log[b + a Sqrt[x]]
--------- + x Log[a + -------] - ---------------------
    a                 Sqrt[x]              2
                                          a
Time to compute: 0.03 second
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