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


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



                  E
Integrate[ArcSin[x ], x] == 

          E
x ArcSin[x ] - 
 
                                            1
                                        3 + -
      1 + E                   1  1 + E      E   2 E
   E x      Hypergeometric2F1[-, -----, -----, x   ]
                              2   2 E     2
   -------------------------------------------------
                         1 + E

Time to compute: 0.07 second

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