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x^2/4 + Cos[2*a*x]/(8*a^2) + (x*Sin[2*a*x])/(4*a)


Integrate[x*Cos[a*x]^2, x] ==
x^2/4 + Cos[2*a*x]/(8*a^2) + (x*Sin[2*a*x])/(4*a)



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

 2
x    Cos[2 a x]   x Sin[2 a x]
-- + ---------- + ------------
4          2          4 a
        8 a

Time to compute: < 0.01 second

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