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

                      1
Integrate[-------------------------, x] == 
          Sqrt[(a + b x) (c + d x)]

(Sqrt[a + b x] Sqrt[c + d x] 
 
    Log[b c + a d + 2 b d x + 
 
      2 Sqrt[b] Sqrt[d] Sqrt[a + b x] Sqrt[c + d x]])\
 
   / (Sqrt[b] Sqrt[d] Sqrt[(a + b x) (c + d x)])
Time to compute: 0.10 second
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