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PhoenixFire
Group Title
\[\int_{e^1}^{e} {\frac{1}{t(1+\left  ln(t) \right )} dt}\]
Can anyone guide me on starting this integral? I've tried numerous times but keep getting a division by zero.
No need to answer the full question, just a hint on starting would be helpful.
 one year ago
 one year ago
PhoenixFire Group Title
\[\int_{e^1}^{e} {\frac{1}{t(1+\left  ln(t) \right )} dt}\] Can anyone guide me on starting this integral? I've tried numerous times but keep getting a division by zero. No need to answer the full question, just a hint on starting would be helpful.
 one year ago
 one year ago

This Question is Closed

divu.mkr Group TitleBest ResponseYou've already chosen the best response.0
tell me what have you done untill now?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.0
substitute 1+ln t = x hace u donee this ?
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.0
**have done
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.0
and if u have done that, have you changed the limits ?
 one year ago

PhoenixFire Group TitleBest ResponseYou've already chosen the best response.0
I have tried x=1+ln(t), the limits become 2 and 0. when you integrate 1/x you get lnx.. but you can't put in the limit of 0 into that. this is what I kept getting stuck on.
 one year ago

divu.mkr Group TitleBest ResponseYou've already chosen the best response.0
then take the limits of 0... that what we do..
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.0
\(\lim \limits_{y \rightarrow 0} \int \limits_y^2dx/x\)
 one year ago

PhoenixFire Group TitleBest ResponseYou've already chosen the best response.0
Okay, I have never been taught such things. I'll give that a go.
 one year ago

PhoenixFire Group TitleBest ResponseYou've already chosen the best response.0
For \(ln(t)\gt 0\) \[\lim \limits_{y \rightarrow 0} \int \limits_y^2dx/x\]\[=ln(2)\lim \limits_{y \rightarrow 0}ln(y)\] For \(ln(t)\lt 0\) \[\lim \limits_{y \rightarrow 0} \int \limits_y^2dx/x\]\[=\lim \limits_{y \rightarrow 0}ln(y)ln(2)\] The limit of \(ln(y)\) as \(y\rightarrow 0\) is \(\infty\). So how does this work? I have two solutions both at infinity... or have I messed up somewhere?
 one year ago

PhoenixFire Group TitleBest ResponseYou've already chosen the best response.0
@hartnn
 one year ago
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