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a*Sqrt[1 - x^2/a^2] + x*ArcSin[x/a]

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

                 x
Integrate[ArcSin[-], x] == 
                 a

            2
           x              x
a Sqrt[1 - --] + x ArcSin[-]
            2             a
           a
Time to compute: 0.04 second
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