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If range of f (x)= ((ln x) (ln x ^(2))+l...

If range of `f (x)= ((ln x) (ln x ^(2))+ln x ^(3)+3)/(ln ^(2) x+ln x ^(2)+2)` can be expressed as `[ (a)/(b),(c )/(d)]` where a,b,c and d are prime numbers (not nacessarily distinct) then find the value of `((a+b+c+d))/(2).`

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