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

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

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

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