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-(x^m*((I*a*x)^m*Gamma[1 + m, (-I)*a*x] + ((-I)*a*x)^m*Gamma[1 + m, I*a*x]))/(2*a*(a^2*x^2)^m)

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

           m
Integrate[x  Sin[a x], x] == 

   m         m
-(x  ((I a x)  Gamma[1 + m, -I a x] + 
 
               m
       (-I a x)  Gamma[1 + m, I a x])) / 
 
         2  2 m
  (2 a (a  x ) )
Time to compute: 0.05 second
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