" 36."int(e)^(e^(2)){(1)/(log x)-(1)/((l...

" 36."int_(e)^(e^(2)){(1)/(log x)-(1)/((log x)^(2))}dx

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Evaluate :int_(e)^(e^(2)){(1)/(log x)-(1)/((log x)^(2))}dx

int_(e )^(e^(2))log x dx =

int_(2)^(e) ((1)/(ln x) - (1)/((ln x)^(2)))dx=

int_(1)^(e)(dx)/(x(1+log x))

int_(1)^(e^(2))(dx)/(x(1+log x)^(2))=

int_(2)^(e)((1)/(ln x)-(1)/(ln^(2)x))dx

"int_(1)^(e)(1+log x)/(x)dx=

int_(1)^(e )(1)/(6x(log x)^(2)+7x log x + 2x)dx=

int_(e)^(e^(2))(log xdx)/((1+log x)^(2))=(e)/(6)(2e-3)

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