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(4*b^3*x^3 + 6*b*x*Cos[2*(a + b*x)] + (-3 + 6*b^2*x^2)*Sin[2*(a + b*x)])/(24*b^3)

Integrate[x^2*Cos[a + b*x]^2, x] ==
(4*b^3*x^3 + 6*b*x*Cos[2*(a + b*x)] + (-3 + 6*b^2*x^2)*Sin[2*(a + b*x)])/(24*b^3) 

           2             2
Integrate[x  Cos[a + b x] , x] == 

    3  3
(4 b  x  + 6 b x Cos[2 (a + b x)] + 
 
             2  2                           3
    (-3 + 6 b  x ) Sin[2 (a + b x)]) / (24 b )
Time to compute: 0.20 second
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