How do you evaluate the integral #int lnx/xdx# from 0 to 1 if it converges?

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Answer 1 · 2016-08-15T11:36:31

Does not converge

#int_0^1 lnx/xdx#

#=int_0^1 d/dx (1/2 ln^2x)dx#

#= 1/2 lim_(t to 0) [ ln^2x ]_t^1#

#= - 1/2 lim_(t to 0) ln^2t#

and limit of product is product of limits

#= - 1/2 lim_(t to 0) lnt * lim_(t to 0) lnt#

Given #lim_(t to 0) lnt = -oo#, does not converge