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


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



Integrate[x ArcCot[x], x] == 

     2
x   x  ArcCot[x]   ArcTan[x]
- + ------------ - ---------
2        2             2

Time to compute: < 0.01 second

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