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x*ArcSin[x^a] - (a*x^(1 + a)*Hypergeometric2F1[1/2, (1 + a)/(2*a), (3 + a^(-1))/2, x^(2*a)])/(1 + a)

Integrate[ArcSin[x^a], x] ==
x*ArcSin[x^a] - (a*x^(1 + a)*Hypergeometric2F1[1/2, (1 + a)/(2*a), (3 + a^(-1))/2, x^(2*a)])/(1 + a) 

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

          a
x ArcSin[x ] - 
 
                                            1
                                        3 + -
      1 + a                   1  1 + a      a   2 a
   a x      Hypergeometric2F1[-, -----, -----, x   ]
                              2   2 a     2
   -------------------------------------------------
                         1 + a
Time to compute: 0.08 second
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