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


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



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

              2    2
        Sqrt[a  - b ] x
ArcTanh[---------------]
                2    2
        b Sqrt[a  - x ]
------------------------
            2    2
    b Sqrt[a  - b ]

Time to compute: 0.06 second

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