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

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

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

-(a x Cos[a x]) + Sin[a x]
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             2
            a
Time to compute: < 0.01 second
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