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let-f-x-x-x-2-dt-lnt-with-x-gt-0-and-x-1-1-prove-that-x-gt-1-x-x-2-xdt-tlnt-f-x-x-x-2-x-2-dt-tlnt-after-find-lim-x-1-f-x-2-calculate-f-x-

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Question Number 32043 by abdo imad last updated on 18/Mar/18
let f(x)= ∫_x ^x^2 (dt/(lnt)) with x>0 and x≠1 1) prove that ∀ x>1 ∫_x ^x^2 ((xdt)/(tlnt)) ≤f(x)≤ ∫_x ^x^2 ((x^2 dt)/(tlnt)) after find lim_(x→1) f(x) 2) calculate f^′ (x) .
letf(x)=∫xx2dtlntwithx>0andx≠11)provethat∀x>1∫xx2xdttlnt⩽f(x)⩽∫xx2x2dttlntafterfindlimx→1f(x)2)calculatef′(x).

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