# Have i made a correct presumption

1. Apr 17, 2009

### Dell

i am asked about convergance/divergance of the integral (from 0 to 1)

$$\int$$dx/ln(x)

i say that
t=lnx
x=et
dt=dx/x

$$\int$$(et/t)dt ( from -infinity to 0 )

now there is no way i have found to actuallt solve this integral,
but i do know that in number series' there is a rule that if {lim(n->inf)An not= o} then the series diverges for sure,

so i split my integral up so i get
$$\int$$(et/t)dt ( from -infinity to -1 ) + $$\int$$(et/t)dt ( from -1 to 0 )

now there is no problem at -1, so i checked the lims at 0 and -inf

lim et/t = -infinity
t->0

lim et/t = 0
t->-inf

so from here i concur that even though the integral MIGHT converge at -inf, it CANNOT converge at 0, therefore the integral diverges.

is this correct?? the end answer is correct 100% but i am asking about my method.

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