integrals.wolfram.com   Use one of Mathematica's 2500+ functions FREE online

Wolfram Mathematica Online Integrator
The world's only full-power integration solver
∫
An image showing the results of your requested integral.

Integrate[ArcSin[a*x]^n, x] ==
((I/2)*ArcSin[a*x]^n* (-((I*ArcSin[a*x])^n*Gamma[1 + n, (-I)*ArcSin[a*x]]) + ((-I)*ArcSin[a*x])^n* Gamma[1 + n, I*ArcSin[a*x]]))/ (a*(ArcSin[a*x]^2)^n) 

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

 I            n                   n
(- ArcSin[a x]  (-((I ArcSin[a x])  
 2
 
         Gamma[1 + n, -I ArcSin[a x]]) + 
 
                      n
      (-I ArcSin[a x])  Gamma[1 + n, I ArcSin[a x]]))\
 
                    2 n
   / (a (ArcSin[a x] ) )
Time to compute: 0.13 second
Spread the word: