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

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

               2    2
Integrate[Log[a  + x ], x] == 

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