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

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

                    2
Integrate[x Sin[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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