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x*Log[Log[a*x]] - LogIntegral[a*x]/a

Integrate[Log[Log[a*x]], x] ==
x*Log[Log[a*x]] - LogIntegral[a*x]/a 

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

                  LogIntegral[a x]
x Log[Log[a x]] - ----------------
                         a
Time to compute: < 0.01 second
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