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(-(a*x) + (1 + a^2*x^2)*ArcTan[a*x])/(2*a^2)

Integrate[x*ArcTan[a*x], x] ==
(-(a*x) + (1 + a^2*x^2)*ArcTan[a*x])/(2*a^2) 

Integrate[x ArcTan[a x], x] == 

               2  2
-(a x) + (1 + a  x ) ArcTan[a x]
--------------------------------
                 2
              2 a
Time to compute: < 0.01 second
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