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(-3*x*Cos[a*x])/(4*a) + (x*Cos[3*a*x])/(12*a) + (3*Sin[a*x])/(4*a^2) - Sin[3*a*x]/(36*a^2)

Integrate[x*Sin[a*x]^3, x] ==
(-3*x*Cos[a*x])/(4*a) + (x*Cos[3*a*x])/(12*a) + (3*Sin[a*x])/(4*a^2) - Sin[3*a*x]/(36*a^2) 

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

-3 x Cos[a x]   x Cos[3 a x]   3 Sin[a x]   Sin[3 a x]
------------- + ------------ + ---------- - ----------
     4 a            12 a             2            2
                                  4 a         36 a
Time to compute: 0.01 second
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