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-((x*(-6 + a^2*x^2)*Cos[a*x])/a^3) + (3*(-2 + a^2*x^2)*Sin[a*x])/a^4

Integrate[x^3*Sin[a*x], x] ==
-((x*(-6 + a^2*x^2)*Cos[a*x])/a^3) + (3*(-2 + a^2*x^2)*Sin[a*x])/a^4 

           3
Integrate[x  Sin[a x], x] == 

           2  2                       2  2
  x (-6 + a  x ) Cos[a x]    3 (-2 + a  x ) Sin[a x]
-(-----------------------) + -----------------------
             3                          4
            a                          a
Time to compute: 0.06 second
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