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x*ArcCot[x/a] + (a*Log[a^2 + x^2])/2


Integrate[ArcCot[x/a], x] ==
x*ArcCot[x/a] + (a*Log[a^2 + x^2])/2



                 x
Integrate[ArcCot[-], x] == 
                 a

                     2    2
         x    a Log[a  + x ]
x ArcCot[-] + --------------
         a          2

Time to compute: < 0.01 second

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