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

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

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

       2    2
Sqrt[-a  + x ]
--------------
  a (a + x)
Time to compute: 0.03 second
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