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


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



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

3 Cos[a x]   Cos[3 a x]   3 x Sin[a x]   x Sin[3 a x]
---------- + ---------- + ------------ + ------------
      2            2          4 a            12 a
   4 a         36 a

Time to compute: 0.01 second

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