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

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

                 1
Integrate[----------------, x] == 
                        2
          Sqrt[2 a x + x ]

(2 Sqrt[x] Sqrt[2 a + x] 
 
    Log[2 (Sqrt[x] + Sqrt[2 a + x])]) / 
 
  Sqrt[x (2 a + x)]
Time to compute: 0.04 second
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